Stochastic Linear Quadratic Optimal Control Problems
International Nuclear Information System (INIS)
Chen, S.; Yong, J.
2001-01-01
This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well
Optimal Control for Stochastic Delay Evolution Equations
Energy Technology Data Exchange (ETDEWEB)
Meng, Qingxin, E-mail: mqx@hutc.zj.cn [Huzhou University, Department of Mathematical Sciences (China); Shen, Yang, E-mail: skyshen87@gmail.com [York University, Department of Mathematics and Statistics (Canada)
2016-08-15
In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we apply stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.
Optimal Control Inventory Stochastic With Production Deteriorating
Affandi, Pardi
2018-01-01
In this paper, we are using optimal control approach to determine the optimal rate in production. Most of the inventory production models deal with a single item. First build the mathematical models inventory stochastic, in this model we also assume that the items are in the same store. The mathematical model of the problem inventory can be deterministic and stochastic models. In this research will be discussed how to model the stochastic as well as how to solve the inventory model using optimal control techniques. The main tool in the study problems for the necessary optimality conditions in the form of the Pontryagin maximum principle involves the Hamilton function. So we can have the optimal production rate in a production inventory system where items are subject deterioration.
Optimal Control and Optimization of Stochastic Supply Chain Systems
Song, Dong-Ping
2013-01-01
Optimal Control and Optimization of Stochastic Supply Chain Systems examines its subject in the context of the presence of a variety of uncertainties. Numerous examples with intuitive illustrations and tables are provided, to demonstrate the structural characteristics of the optimal control policies in various stochastic supply chains and to show how to make use of these characteristics to construct easy-to-operate sub-optimal policies. In Part I, a general introduction to stochastic supply chain systems is provided. Analytical models for various stochastic supply chain systems are formulated and analysed in Part II. In Part III the structural knowledge of the optimal control policies obtained in Part II is utilized to construct easy-to-operate sub-optimal control policies for various stochastic supply chain systems accordingly. Finally, Part IV discusses the optimisation of threshold-type control policies and their robustness. A key feature of the book is its tying together of ...
Optimal control of stochastic difference Volterra equations an introduction
Shaikhet, Leonid
2015-01-01
This book showcases a subclass of hereditary systems, that is, systems with behaviour depending not only on their current state but also on their past history; it is an introduction to the mathematical theory of optimal control for stochastic difference Volterra equations of neutral type. As such, it will be of much interest to researchers interested in modelling processes in physics, mechanics, automatic regulation, economics and finance, biology, sociology and medicine for all of which such equations are very popular tools. The text deals with problems of optimal control such as meeting given performance criteria, and stabilization, extending them to neutral stochastic difference Volterra equations. In particular, it contrasts the difference analogues of solutions to optimal control and optimal estimation problems for stochastic integral Volterra equations with optimal solutions for corresponding problems in stochastic difference Volterra equations. Optimal Control of Stochastic Difference Volterra Equation...
Optimal management strategies in variable environments: Stochastic optimal control methods
Williams, B.K.
1985-01-01
Dynamic optimization was used to investigate the optimal defoliation of salt desert shrubs in north-western Utah. Management was formulated in the context of optimal stochastic control theory, with objective functions composed of discounted or time-averaged biomass yields. Climatic variability and community patterns of salt desert shrublands make the application of stochastic optimal control both feasible and necessary. A primary production model was used to simulate shrub responses and harvest yields under a variety of climatic regimes and defoliation patterns. The simulation results then were used in an optimization model to determine optimal defoliation strategies. The latter model encodes an algorithm for finite state, finite action, infinite discrete time horizon Markov decision processes. Three questions were addressed: (i) What effect do changes in weather patterns have on optimal management strategies? (ii) What effect does the discounting of future returns have? (iii) How do the optimal strategies perform relative to certain fixed defoliation strategies? An analysis was performed for the three shrub species, winterfat (Ceratoides lanata), shadscale (Atriplex confertifolia) and big sagebrush (Artemisia tridentata). In general, the results indicate substantial differences among species in optimal control strategies, which are associated with differences in physiological and morphological characteristics. Optimal policies for big sagebrush varied less with variation in climate, reserve levels and discount rates than did either shadscale or winterfat. This was attributed primarily to the overwintering of photosynthetically active tissue and to metabolic activity early in the growing season. Optimal defoliation of shadscale and winterfat generally was more responsive to differences in plant vigor and climate, reflecting the sensitivity of these species to utilization and replenishment of carbohydrate reserves. Similarities could be seen in the influence of both
Semilinear Kolmogorov Equations and Applications to Stochastic Optimal Control
International Nuclear Information System (INIS)
Masiero, Federica
2005-01-01
Semilinear parabolic differential equations are solved in a mild sense in an infinite-dimensional Hilbert space. Applications to stochastic optimal control problems are studied by solving the associated Hamilton-Jacobi-Bellman equation. These results are applied to some controlled stochastic partial differential equations
Optimal Stochastic Modeling and Control of Flexible Structures
1988-09-01
1.37] and McLane [1.18] considered multivariable systems and derived their optimal control characteristics. Kleinman, Gorman and Zaborsky considered...Leondes [1.72,1.73] studied various aspects of multivariable linear stochastic, discrete-time systems that are partly deterministic, and partly stochastic...June 1966. 1.8. A.V. Balaknishnan, Applied Functional Analaysis , 2nd ed., New York, N.Y.: Springer-Verlag, 1981 1.9. Peter S. Maybeck, Stochastic
Centralized Stochastic Optimal Control of Complex Systems
Energy Technology Data Exchange (ETDEWEB)
Malikopoulos, Andreas [ORNL
2015-01-01
In this paper we address the problem of online optimization of the supervisory power management control in parallel hybrid electric vehicles (HEVs). We model HEV operation as a controlled Markov chain using the long-run expected average cost per unit time criterion, and we show that the control policy yielding the Pareto optimal solution minimizes the average cost criterion online. The effectiveness of the proposed solution is validated through simulation and compared to the solution derived with dynamic programming using the average cost criterion.
Stochastic optimal control of single neuron spike trains
DEFF Research Database (Denmark)
Iolov, Alexandre; Ditlevsen, Susanne; Longtin, Andrë
2014-01-01
stimulation of a neuron to achieve a target spike train under the physiological constraint to not damage tissue. Approach. We pose a stochastic optimal control problem to precisely specify the spike times in a leaky integrate-and-fire (LIF) model of a neuron with noise assumed to be of intrinsic or synaptic...... origin. In particular, we allow for the noise to be of arbitrary intensity. The optimal control problem is solved using dynamic programming when the controller has access to the voltage (closed-loop control), and using a maximum principle for the transition density when the controller only has access...... to the spike times (open-loop control). Main results. We have developed a stochastic optimal control algorithm to obtain precise spike times. It is applicable in both the supra-threshold and sub-threshold regimes, under open-loop and closed-loop conditions and with an arbitrary noise intensity; the accuracy...
A Connection between Singular Stochastic Control and Optimal Stopping
International Nuclear Information System (INIS)
Espen Benth, Fred; Reikvam, Kristin
2003-01-01
We show that the value function of a singular stochastic control problem is equal to the integral of the value function of an associated optimal stopping problem. The connection is proved for a general class of diffusions using the method of viscosity solutions
Stochastic optimal control in a danger zone
Lefebvre, Mario
2011-04-01
Let X(t) be a one-dimensional controlled Wiener process, and let τ(x) be the first time X(t) takes on the value A, given that X(0) = x. The problem of finding the control that minimises the expected value of a cost function with quadratic control costs on the way and an instantaneous reward (or penalty) given for survival in the continuation region is solved explicitly in the case when A is a random variable.
Energy Technology Data Exchange (ETDEWEB)
Paul, Wolfgang; Koeppe, Jeanette [Institut fuer Physik, Martin Luther Universitaet, 06099 Halle (Germany); Grecksch, Wilfried [Institut fuer Mathematik, Martin Luther Universitaet, 06099 Halle (Germany)
2016-07-01
The standard approach to solve a non-relativistic quantum problem is through analytical or numerical solution of the Schroedinger equation. We show a way to go around it. This way is based on the derivation of the Schroedinger equation from conservative diffusion processes and the establishment of (several) stochastic variational principles leading to the Schroedinger equation under the assumption of a kinematics described by Nelson's diffusion processes. Mathematically, the variational principle can be considered as a stochastic optimal control problem linked to the forward-backward stochastic differential equations of Nelson's stochastic mechanics. The Hamilton-Jacobi-Bellmann equation of this control problem is the Schroedinger equation. We present the mathematical background and how to turn it into a numerical scheme for analyzing a quantum system without using the Schroedinger equation and exemplify the approach for a simple 1d problem.
Stochastic Optimal Control for Online Seller under Reputational Mechanisms
Directory of Open Access Journals (Sweden)
Milan Bradonjić
2015-12-01
Full Text Available In this work we propose and analyze a model which addresses the pulsing behavior of sellers in an online auction (store. This pulsing behavior is observed when sellers switch between advertising and processing states. We assert that a seller switches her state in order to maximize her profit, and further that this switch can be identified through the seller’s reputation. We show that for each seller there is an optimal reputation, i.e., the reputation at which the seller should switch her state in order to maximize her total profit. We design a stochastic behavioral model for an online seller, which incorporates the dynamics of resource allocation and reputation. The design of the model is optimized by using a stochastic advertising model from [1] and used effectively in the Stochastic Optimal Control of Advertising [2]. This model of reputation is combined with the effect of online reputation on sales price empirically verified in [3]. We derive the Hamilton-Jacobi-Bellman (HJB differential equation, whose solution relates optimal wealth level to a seller’s reputation. We formulate both a full model, as well as a reduced model with fewer parameters, both of which have the same qualitative description of the optimal seller behavior. Coincidentally, the reduced model has a closed form analytical solution that we construct.
A combined stochastic programming and optimal control approach to personal finance and pensions
DEFF Research Database (Denmark)
Konicz, Agnieszka Karolina; Pisinger, David; Rasmussen, Kourosh Marjani
2015-01-01
The paper presents a model that combines a dynamic programming (stochastic optimal control) approach and a multi-stage stochastic linear programming approach (SLP), integrated into one SLP formulation. Stochastic optimal control produces an optimal policy that is easy to understand and implement....
A stochastic optimal feedforward and feedback control methodology for superagility
Halyo, Nesim; Direskeneli, Haldun; Taylor, Deborah B.
1992-01-01
A new control design methodology is developed: Stochastic Optimal Feedforward and Feedback Technology (SOFFT). Traditional design techniques optimize a single cost function (which expresses the design objectives) to obtain both the feedforward and feedback control laws. This approach places conflicting demands on the control law such as fast tracking versus noise atttenuation/disturbance rejection. In the SOFFT approach, two cost functions are defined. The feedforward control law is designed to optimize one cost function, the feedback optimizes the other. By separating the design objectives and decoupling the feedforward and feedback design processes, both objectives can be achieved fully. A new measure of command tracking performance, Z-plots, is also developed. By analyzing these plots at off-nominal conditions, the sensitivity or robustness of the system in tracking commands can be predicted. Z-plots provide an important tool for designing robust control systems. The Variable-Gain SOFFT methodology was used to design a flight control system for the F/A-18 aircraft. It is shown that SOFFT can be used to expand the operating regime and provide greater performance (flying/handling qualities) throughout the extended flight regime. This work was performed under the NASA SBIR program. ICS plans to market the software developed as a new module in its commercial CACSD software package: ACET.
Sequential stochastic optimization
Cairoli, Renzo
1996-01-01
Sequential Stochastic Optimization provides mathematicians and applied researchers with a well-developed framework in which stochastic optimization problems can be formulated and solved. Offering much material that is either new or has never before appeared in book form, it lucidly presents a unified theory of optimal stopping and optimal sequential control of stochastic processes. This book has been carefully organized so that little prior knowledge of the subject is assumed; its only prerequisites are a standard graduate course in probability theory and some familiarity with discrete-paramet
Directory of Open Access Journals (Sweden)
Rashad O. Mastaliev
2016-12-01
Full Text Available The optimal control problem of nonlinear stochastic systems which mathematical model is given by Ito stochastic differential equation with delay argument is considered. Assuming that the concerned region is open for the control by the first and the second variation (classical sense of the quality functional we obtain the necessary optimality condition of the first and the second order. In the particular case we receive the stochastic analog of the Legendre—Clebsch condition and some constructively verified conclusions from the second order necessary condition. We investigate the Legendre–Clebsch conditions for the degeneration case and obtain the necessary conditions of optimality for a special control, in the classical sense.
Optimal adaptive control for a class of stochastic systems
Bagchi, Arunabha; Chen, Han-Fu
1995-01-01
We study linear-quadratic adaptive tracking problems for a special class of stochastic systems expressed in the state-space form. This is a long-standing problem in the control of aircraft flying through atmospheric turbulence. Using an ELS-based algorithm and introducing dither in the control law
Optimization of stochastic discrete systems and control on complex networks computational networks
Lozovanu, Dmitrii
2014-01-01
This book presents the latest findings on stochastic dynamic programming models and on solving optimal control problems in networks. It includes the authors' new findings on determining the optimal solution of discrete optimal control problems in networks and on solving game variants of Markov decision problems in the context of computational networks. First, the book studies the finite state space of Markov processes and reviews the existing methods and algorithms for determining the main characteristics in Markov chains, before proposing new approaches based on dynamic programming and combinatorial methods. Chapter two is dedicated to infinite horizon stochastic discrete optimal control models and Markov decision problems with average and expected total discounted optimization criteria, while Chapter three develops a special game-theoretical approach to Markov decision processes and stochastic discrete optimal control problems. In closing, the book's final chapter is devoted to finite horizon stochastic con...
Stochastic optimal control in infinite dimension dynamic programming and HJB equations
Fabbri, Giorgio; Święch, Andrzej
2017-01-01
Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite ...
Willigenburg, van L.G.; Koning, de W.L.
2013-01-01
Two different descriptions are used in the literature to formulate the optimal dynamic output feedback control problem for linear dynamical systems with white stochastic parameters and quadratic criteria, called the optimal compensation problem. One describes the matrix valued white stochastic
Dynamic stochastic optimization
Ermoliev, Yuri; Pflug, Georg
2004-01-01
Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for precise evaluations and, as a result, the lack of proper management (control) may create significant risks. In order to develop robust strategies we need approaches which explic itly deal with uncertainties, risks and changing conditions. One rather general approach is to characterize (explicitly or implicitly) uncertainties by objec tive or subjective probabilities (measures of confidence or belief). This leads us to stochastic optimization problems which can rarely be solved by using the standard deterministic optimization and optimal control methods. In the stochastic optimization the accent is on problems with a large number of deci sion and random variables, and consequently the focus ofattention is directed to efficient solution procedures rather than to (analytical) closed-form solu tions. Objective an...
Scalable algorithms for optimal control of stochastic PDEs
Ghattas, Omar
2016-01-07
We present methods for the optimal control of systems governed by partial differential equations with infinite-dimensional uncertain parameters. We consider an objective function that involves the mean and variance of the control objective, leading to a risk-averse optimal control formulation. To make the optimal control problem computationally tractable, we employ a local quadratic approximation of the objective with respect to the uncertain parameter. This enables computation of the mean and variance of the control objective analytically. The resulting risk-averse optimization problem is formulated as a PDE-constrained optimization problem with constraints given by the forward and adjoint PDEs for the first and second-order derivatives of the quantity of interest with respect to the uncertain parameter, and with an objective that involves the trace of a covariance-preconditioned Hessian (of the objective with respect to the uncertain parameters) operator. A randomized trace estimator is used to make tractable the trace computation. Adjoint-based techniques are used to derive an expression for the infinite-dimensional gradient of the risk-averse objective function via the Lagrangian, leading to a quasi-Newton method for solution of the optimal control problem. A specific problem of optimal control of a linear elliptic PDE that describes flow of a fluid in a porous medium with uncertain permeability field is considered. We present numerical results to study the consequences of the local quadratic approximation and the efficiency of the method.
Scalable algorithms for optimal control of stochastic PDEs
Ghattas, Omar; Alexanderian, Alen; Petra, Noemi; Stadler, Georg
2016-01-01
We present methods for the optimal control of systems governed by partial differential equations with infinite-dimensional uncertain parameters. We consider an objective function that involves the mean and variance of the control objective, leading to a risk-averse optimal control formulation. To make the optimal control problem computationally tractable, we employ a local quadratic approximation of the objective with respect to the uncertain parameter. This enables computation of the mean and variance of the control objective analytically. The resulting risk-averse optimization problem is formulated as a PDE-constrained optimization problem with constraints given by the forward and adjoint PDEs for the first and second-order derivatives of the quantity of interest with respect to the uncertain parameter, and with an objective that involves the trace of a covariance-preconditioned Hessian (of the objective with respect to the uncertain parameters) operator. A randomized trace estimator is used to make tractable the trace computation. Adjoint-based techniques are used to derive an expression for the infinite-dimensional gradient of the risk-averse objective function via the Lagrangian, leading to a quasi-Newton method for solution of the optimal control problem. A specific problem of optimal control of a linear elliptic PDE that describes flow of a fluid in a porous medium with uncertain permeability field is considered. We present numerical results to study the consequences of the local quadratic approximation and the efficiency of the method.
Multistage stochastic optimization
Pflug, Georg Ch
2014-01-01
Multistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, among other areas. They describe decision situations under uncertainty and with a longer planning horizon. This book contains a comprehensive treatment of today’s state of the art in multistage stochastic optimization. It covers the mathematical backgrounds of approximation theory as well as numerous practical algorithms and examples for the generation and handling of scenario trees. A special emphasis is put on estimation and bounding of the modeling error using novel distance concepts, on time consistency and the role of model ambiguity in the decision process. An extensive treatment of examples from electricity production, asset liability management and inventory control concludes the book
Directory of Open Access Journals (Sweden)
Jingtao Shi
2013-01-01
Full Text Available This paper is concerned with the relationship between maximum principle and dynamic programming for stochastic recursive optimal control problems. Under certain differentiability conditions, relations among the adjoint processes, the generalized Hamiltonian function, and the value function are given. A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result.
Optimal Stochastic Control Problem for General Linear Dynamical Systems in Neuroscience
Directory of Open Access Journals (Sweden)
Yan Chen
2017-01-01
Full Text Available This paper considers a d-dimensional stochastic optimization problem in neuroscience. Suppose the arm’s movement trajectory is modeled by high-order linear stochastic differential dynamic system in d-dimensional space, the optimal trajectory, velocity, and variance are explicitly obtained by using stochastic control method, which allows us to analytically establish exact relationships between various quantities. Moreover, the optimal trajectory is almost a straight line for a reaching movement; the optimal velocity bell-shaped and the optimal variance are consistent with the experimental Fitts law; that is, the longer the time of a reaching movement, the higher the accuracy of arriving at the target position, and the results can be directly applied to designing a reaching movement performed by a robotic arm in a more general environment.
Institute of Scientific and Technical Information of China (English)
Li Shu; Zhuo Jiashou; Ren Qingwen
2000-01-01
In this paper, an optimal criterion is presented for adaptive Kalman filter in a control sys tem with unknown variances of stochastic vibration by constructing a function of noise variances and minimizing the function. We solve the model and measure variances by using DFP optimal method to guarantee the results of Kalman filter to be optimized. Finally, the control of vibration can be implemented by LQG method.
Stochastic models, estimation, and control
Maybeck, Peter S
1982-01-01
This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws.
Adaptive optimal stochastic state feedback control of resistive wall modes in tokamaks
International Nuclear Information System (INIS)
Sun, Z.; Sen, A.K.; Longman, R.W.
2006-01-01
An adaptive optimal stochastic state feedback control is developed to stabilize the resistive wall mode (RWM) instability in tokamaks. The extended least-square method with exponential forgetting factor and covariance resetting is used to identify (experimentally determine) the time-varying stochastic system model. A Kalman filter is used to estimate the system states. The estimated system states are passed on to an optimal state feedback controller to construct control inputs. The Kalman filter and the optimal state feedback controller are periodically redesigned online based on the identified system model. This adaptive controller can stabilize the time-dependent RWM in a slowly evolving tokamak discharge. This is accomplished within a time delay of roughly four times the inverse of the growth rate for the time-invariant model used
Optimal Liquidation under Stochastic Liquidity
Becherer, Dirk; Bilarev, Todor; Frentrup, Peter
2016-01-01
We solve explicitly a two-dimensional singular control problem of finite fuel type for infinite time horizon. The problem stems from the optimal liquidation of an asset position in a financial market with multiplicative and transient price impact. Liquidity is stochastic in that the volume effect process, which determines the inter-temporal resilience of the market in spirit of Predoiu, Shaikhet and Shreve (2011), is taken to be stochastic, being driven by own random noise. The optimal contro...
Directory of Open Access Journals (Sweden)
Sie Long Kek
2015-01-01
Full Text Available A computational approach is proposed for solving the discrete time nonlinear stochastic optimal control problem. Our aim is to obtain the optimal output solution of the original optimal control problem through solving the simplified model-based optimal control problem iteratively. In our approach, the adjusted parameters are introduced into the model used such that the differences between the real system and the model used can be computed. Particularly, system optimization and parameter estimation are integrated interactively. On the other hand, the output is measured from the real plant and is fed back into the parameter estimation problem to establish a matching scheme. During the calculation procedure, the iterative solution is updated in order to approximate the true optimal solution of the original optimal control problem despite model-reality differences. For illustration, a wastewater treatment problem is studied and the results show the efficiency of the approach proposed.
Stochastic Optimal Control of Parallel Hybrid Electric Vehicles
Directory of Open Access Journals (Sweden)
Feiyan Qin
2017-02-01
Full Text Available Energy management strategies (EMSs in hybrid electric vehicles (HEVs are highly related to the fuel economy and emission performances. However, EMS constitutes a challenging problem due to the complex structure of a HEV and the unknown or partially known driving cycles. To meet this problem, this paper adopts a stochastic dynamic programming (SDP method for the EMS of a specially designed vehicle, a pre-transmission single-shaft torque-coupling parallel HEV. In this parallel HEV, the auto clutch output is connected to the transmission input through an electric motor, which benefits an efficient motor assist operation. In this EMS, demanded torque of driver is modeled as a one-state Markov process to represent the uncertainty of future driving situations. The obtained EMS has been evaluated with ADVISOR2002 over two standard government drive cycles and a self-defined one, and compared with a dynamic programming (DP one and a rule-based one. Simulation results have shown the real-time performance of the proposed approach, and potential vehicle performance improvement relative to the rule-based one.
Stochastic optimization methods
Marti, Kurt
2005-01-01
Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.
Stochastic processes, optimization, and control theory a volume in honor of Suresh Sethi
Yan, Houmin
2006-01-01
This edited volume contains 16 research articles. It presents recent and pressing issues in stochastic processes, control theory, differential games, optimization, and their applications in finance, manufacturing, queueing networks, and climate control. One of the salient features is that the book is highly multi-disciplinary. The book is dedicated to Professor Suresh Sethi on the occasion of his 60th birthday, in view of his distinguished career.
Directory of Open Access Journals (Sweden)
Peimin Chen
2017-01-01
Full Text Available In this paper, we consider the optimization problem of dividends for the terminal bankruptcy model, in which some money would be returned to shareholders at the state of terminal bankruptcy, while accounting for the tax rate and transaction cost for dividend payout. Maximization of both expected total discounted dividends before bankruptcy and expected discounted returned money at the state of terminal bankruptcy becomes a mixed classical-impulse stochastic control problem. In order to solve this problem, we reduce it to quasi-variational inequalities with a nonzero boundary condition. We explicitly construct and verify solutions of these inequalities and present the value function together with the optimal policy.
Pan, Indranil; Das, Saptarshi; Gupta, Amitava
2011-01-01
An optimal PID and an optimal fuzzy PID have been tuned by minimizing the Integral of Time multiplied Absolute Error (ITAE) and squared controller output for a networked control system (NCS). The tuning is attempted for a higher order and a time delay system using two stochastic algorithms viz. the Genetic Algorithm (GA) and two variants of Particle Swarm Optimization (PSO) and the closed loop performances are compared. The paper shows that random variation in network delay can be handled efficiently with fuzzy logic based PID controllers over conventional PID controllers. Copyright © 2010 ISA. Published by Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Weifeng Wang
2014-01-01
Full Text Available We study an optimal control problem governed by a semilinear parabolic equation, whose control variable is contained only in the boundary condition. An existence theorem for the optimal control is obtained.
DEFF Research Database (Denmark)
Maurico-Iglesias, Miguel; Castro, Ignacio Montero; Mollerup, Ane Loft
2015-01-01
. Such controller is aimed at keeping the system close to the optimal performance, thanks to an optimal selection of controlled variables. The definition of an optimal performance was carried out by a two-stage optimisation (stochastic and deterministic) to take into account both the overflow during the current......The design of sewer system control is a complex task given the large size of the sewer networks, the transient dynamics of the water flow and the stochastic nature of rainfall. This contribution presents a generic methodology for the design of a self-optimising controller in sewer systems...
El-Khoury, O.; Kim, C.; Shafieezadeh, A.; Hur, J. E.; Heo, G. H.
2015-06-01
This study performs a series of numerical simulations and shake-table experiments to design and assess the performance of a nonlinear clipped feedback control algorithm based on optimal polynomial control (OPC) to mitigate the response of a two-span bridge equipped with a magnetorheological (MR) damper. As an extended conventional linear quadratic regulator, OPC provides more flexibility in the control design and further enhances system performance. The challenges encountered in this case are (1) the linearization of the nonlinear behavior of various components and (2) the selection of the weighting matrices in the objective function of OPC. The first challenge is addressed by using stochastic linearization which replaces the nonlinear portion of the system behavior with an equivalent linear time-invariant model considering the stochasticity in the excitation. Furthermore, a genetic algorithm is employed to find optimal weighting matrices for the control design. The input current to the MR damper installed between adjacent spans is determined using a clipped stochastic optimal polynomial control algorithm. The performance of the controlled system is assessed through a set of shake-table experiments for far-field and near-field ground motions. The proposed method showed considerable improvements over passive cases especially for the far-field ground motion.
International Nuclear Information System (INIS)
El-Khoury, O; Shafieezadeh, A; Hur, J E; Kim, C; Heo, G H
2015-01-01
This study performs a series of numerical simulations and shake-table experiments to design and assess the performance of a nonlinear clipped feedback control algorithm based on optimal polynomial control (OPC) to mitigate the response of a two-span bridge equipped with a magnetorheological (MR) damper. As an extended conventional linear quadratic regulator, OPC provides more flexibility in the control design and further enhances system performance. The challenges encountered in this case are (1) the linearization of the nonlinear behavior of various components and (2) the selection of the weighting matrices in the objective function of OPC. The first challenge is addressed by using stochastic linearization which replaces the nonlinear portion of the system behavior with an equivalent linear time-invariant model considering the stochasticity in the excitation. Furthermore, a genetic algorithm is employed to find optimal weighting matrices for the control design. The input current to the MR damper installed between adjacent spans is determined using a clipped stochastic optimal polynomial control algorithm. The performance of the controlled system is assessed through a set of shake-table experiments for far-field and near-field ground motions. The proposed method showed considerable improvements over passive cases especially for the far-field ground motion. (paper)
A Unified Pricing of Variable Annuity Guarantees under the Optimal Stochastic Control Framework
Directory of Open Access Journals (Sweden)
Pavel V. Shevchenko
2016-07-01
Full Text Available In this paper, we review pricing of the variable annuity living and death guarantees offered to retail investors in many countries. Investors purchase these products to take advantage of market growth and protect savings. We present pricing of these products via an optimal stochastic control framework and review the existing numerical methods. We also discuss pricing under the complete/incomplete financial market models, stochastic mortality and optimal/sub-optimal policyholder behavior, and in the presence of taxes. For numerical valuation of these contracts in the case of simple risky asset process, we develop a direct integration method based on the Gauss-Hermite quadratures with a one-dimensional cubic spline for calculation of the expected contract value, and a bi-cubic spline interpolation for applying the jump conditions across the contract cashflow event times. This method is easier to implement and faster when compared to the partial differential equation methods if the transition density (or its moments of the risky asset underlying the contract is known in closed form between the event times. We present accurate numerical results for pricing of a Guaranteed Minimum Accumulation Benefit (GMAB guarantee available on the market that can serve as a numerical benchmark for practitioners and researchers developing pricing of variable annuity guarantees to assess the accuracy of their numerical implementation.
Chernyak, Vladimir Y.; Chertkov, Michael; Bierkens, Joris; Kappen, Hilbert J.
2014-01-01
In stochastic optimal control (SOC) one minimizes the average cost-to-go, that consists of the cost-of-control (amount of efforts), cost-of-space (where one wants the system to be) and the target cost (where one wants the system to arrive), for a system participating in forced and controlled Langevin dynamics. We extend the SOC problem by introducing an additional cost-of-dynamics, characterized by a vector potential. We propose derivation of the generalized gauge-invariant Hamilton-Jacobi-Bellman equation as a variation over density and current, suggest hydrodynamic interpretation and discuss examples, e.g., ergodic control of a particle-within-a-circle, illustrating non-equilibrium space-time complexity.
Feedback optimal control of dynamic stochastic two-machine flowshop with a finite buffer
Directory of Open Access Journals (Sweden)
Thang Diep
2010-06-01
Full Text Available This paper examines the optimization of production involving a tandem two-machine system producing a single part type, with each machine being subject to random breakdowns and repairs. An analytical model is formulated with a view to solving an optimal stochastic production problem of the system with machines having up-downtime non-exponential distributions. The model developed is obtained by using a dynamic programming approach and a semi-Markov process. The control problem aims to find the production rates needed by the machines to meet the demand rate, through a minimization of the inventory/shortage cost. Using the Bellman principle, the optimality conditions obtained satisfy the Hamilton-Jacobi-Bellman equation, which depends on time and system states, and ultimately, leads to a feedback control. Consequently, the new model enables us to improve the coefficient of variation (CVup/down to be less than one while it is equal to one in Markov model. Heuristics methods are used to involve the problem because of the difficulty of the analytical model using several states, and to show what control law should be used in each system state (i.e., including Kanban, feedback and CONWIP control. Numerical methods are used to solve the optimality conditions and to show how a machine should produce.
Adaptively Constrained Stochastic Model Predictive Control for the Optimal Dispatch of Microgrid
Directory of Open Access Journals (Sweden)
Xiaogang Guo
2018-01-01
Full Text Available In this paper, an adaptively constrained stochastic model predictive control (MPC is proposed to achieve less-conservative coordination between energy storage units and uncertain renewable energy sources (RESs in a microgrid (MG. Besides the economic objective of MG operation, the limits of state-of-charge (SOC and discharging/charging power of the energy storage unit are formulated as chance constraints when accommodating uncertainties of RESs, considering mild violations of these constraints are allowed during long-term operation, and a closed-loop online update strategy is performed to adaptively tighten or relax constraints according to the actual deviation probability of violation level from the desired one as well as the current change rate of deviation probability. Numerical studies show that the proposed adaptively constrained stochastic MPC for MG optimal operation is much less conservative compared with the scenario optimization based robust MPC, and also presents a better convergence performance to the desired constraint violation level than other online update strategies.
Stochastic optimization: beyond mathematical programming
CERN. Geneva
2015-01-01
Stochastic optimization, among which bio-inspired algorithms, is gaining momentum in areas where more classical optimization algorithms fail to deliver satisfactory results, or simply cannot be directly applied. This presentation will introduce baseline stochastic optimization algorithms, and illustrate their efficiency in different domains, from continuous non-convex problems to combinatorial optimization problem, to problems for which a non-parametric formulation can help exploring unforeseen possible solution spaces.
Optimal control strategy for an impulsive stochastic competition system with time delays and jumps
Liu, Lidan; Meng, Xinzhu; Zhang, Tonghua
2017-07-01
Driven by both white and jump noises, a stochastic delayed model with two competitive species in a polluted environment is proposed and investigated. By using the comparison theorem of stochastic differential equations and limit superior theory, sufficient conditions for persistence in mean and extinction of two species are established. In addition, we obtain that the system is asymptotically stable in distribution by using ergodic method. Furthermore, the optimal harvesting effort and the maximum of expectation of sustainable yield (ESY) are derived from Hessian matrix method and optimal harvesting theory of differential equations. Finally, some numerical simulations are provided to illustrate the theoretical results.
International Nuclear Information System (INIS)
Guatteri, Giuseppina; Tessitore, Gianmario
2008-01-01
We study the Riccati equation arising in a class of quadratic optimal control problems with infinite dimensional stochastic differential state equation and infinite horizon cost functional. We allow the coefficients, both in the state equation and in the cost, to be random.In such a context backward stochastic Riccati equations are backward stochastic differential equations in the whole positive real axis that involve quadratic non-linearities and take values in a non-Hilbertian space. We prove existence of a minimal non-negative solution and, under additional assumptions, its uniqueness. We show that such a solution allows to perform the synthesis of the optimal control and investigate its attractivity properties. Finally the case where the coefficients are stationary is addressed and an example concerning a controlled wave equation in random media is proposed
Stochastic and global optimization
National Research Council Canada - National Science Library
Dzemyda, Gintautas; Šaltenis, Vydūnas; Zhilinskas, A; Mockus, Jonas
2002-01-01
... and Effectiveness of Controlled Random Search E. M. T. Hendrix, P. M. Ortigosa and I. García 129 9. Discrete Backtracking Adaptive Search for Global Optimization B. P. Kristinsdottir, Z. B. Zabinsky and...
Mauricio-Iglesias, Miguel; Montero-Castro, Ignacio; Mollerup, Ane L; Sin, Gürkan
2015-05-15
The design of sewer system control is a complex task given the large size of the sewer networks, the transient dynamics of the water flow and the stochastic nature of rainfall. This contribution presents a generic methodology for the design of a self-optimising controller in sewer systems. Such controller is aimed at keeping the system close to the optimal performance, thanks to an optimal selection of controlled variables. The definition of an optimal performance was carried out by a two-stage optimisation (stochastic and deterministic) to take into account both the overflow during the current rain event as well as the expected overflow given the probability of a future rain event. The methodology is successfully applied to design an optimising control strategy for a subcatchment area in Copenhagen. The results are promising and expected to contribute to the advance of the operation and control problem of sewer systems. Copyright © 2015 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Sutrisno; Widowati; Solikhin
2016-01-01
In this paper, we propose a mathematical model in stochastic dynamic optimization form to determine the optimal strategy for an integrated single product inventory control problem and supplier selection problem where the demand and purchasing cost parameters are random. For each time period, by using the proposed model, we decide the optimal supplier and calculate the optimal product volume purchased from the optimal supplier so that the inventory level will be located at some point as close as possible to the reference point with minimal cost. We use stochastic dynamic programming to solve this problem and give several numerical experiments to evaluate the model. From the results, for each time period, the proposed model was generated the optimal supplier and the inventory level was tracked the reference point well. (paper)
Finite approximations in discrete-time stochastic control quantized models and asymptotic optimality
Saldi, Naci; Yüksel, Serdar
2018-01-01
In a unified form, this monograph presents fundamental results on the approximation of centralized and decentralized stochastic control problems, with uncountable state, measurement, and action spaces. It demonstrates how quantization provides a system-independent and constructive method for the reduction of a system with Borel spaces to one with finite state, measurement, and action spaces. In addition to this constructive view, the book considers both the information transmission approach for discretization of actions, and the computational approach for discretization of states and actions. Part I of the text discusses Markov decision processes and their finite-state or finite-action approximations, while Part II builds from there to finite approximations in decentralized stochastic control problems. This volume is perfect for researchers and graduate students interested in stochastic controls. With the tools presented, readers will be able to establish the convergence of approximation models to original mo...
DEFF Research Database (Denmark)
Feng, Ju; Ying, Zu-Guang; Zhu, Wei-Qiu
2012-01-01
A minimax stochastic optimal semi-active control strategy for stochastically excited quasi-integrable Hamiltonian systems with parametric uncertainty by using magneto-rheological (MR) dampers is proposed. Firstly, the control problem is formulated as an n-degree-of-freedom (DOF) controlled, uncer...
Stochastic optimal control of non-stationary response of a single-degree-of-freedom vehicle model
Narayanan, S.; Raju, G. V.
1990-09-01
An active suspension system to control the non-stationary response of a single-degree-of-freedom (sdf) vehicle model with variable velocity traverse over a rough road is investigated. The suspension is optimized with respect to ride comfort and road holding, using stochastic optimal control theory. The ground excitation is modelled as a spatial homogeneous random process, being the output of a linear shaping filter to white noise. The effect of the rolling contact of the tyre is considered by an additional filter in cascade. The non-stationary response with active suspension is compared with that of a passive system.
Stochastic optimization methods
Marti, Kurt
2008-01-01
Optimization problems arising in practice involve random model parameters. This book features many illustrations, several examples, and applications to concrete problems from engineering and operations research.
Optimal Advertising with Stochastic Demand
George E. Monahan
1983-01-01
A stochastic, sequential model is developed to determine optimal advertising expenditures as a function of product maturity and past advertising. Random demand for the product depends upon an aggregate measure of current and past advertising called "goodwill," and the position of the product in its life cycle measured by sales-to-date. Conditions on the parameters of the model are established that insure that it is optimal to advertise less as the product matures. Additional characteristics o...
Helbing, Dirk; Schönhof, Martin; Kern, Daniel
2002-06-01
The coordinated and efficient distribution of limited resources by individual decisions is a fundamental, unsolved problem. When individuals compete for road capacities, time, space, money, goods, etc, they normally make decisions based on aggregate rather than complete information, such as TV news or stock market indices. In related experiments, we have observed a volatile decision dynamics and far-from-optimal payoff distributions. We have also identified methods of information presentation that can considerably improve the overall performance of the system. In order to determine optimal strategies of decision guidance by means of user-specific recommendations, a stochastic behavioural description is developed. These strategies manage to increase the adaptibility to changing conditions and to reduce the deviation from the time-dependent user equilibrium, thereby enhancing the average and individual payoffs. Hence, our guidance strategies can increase the performance of all users by reducing overreaction and stabilizing the decision dynamics. These results are highly significant for predicting decision behaviour, for reaching optimal behavioural distributions by decision support systems and for information service providers. One of the promising fields of application is traffic optimization.
International Nuclear Information System (INIS)
Wu, Yuhu; Kumar, Madan; Shen, Tielong
2016-01-01
Highlights: • An in-cylinder pressure based measuring method for the RGF is derived. • A stochastic logical dynamical model is proposed to represent the transient behavior of the RGF. • The receding horizon controller is designed to reduce the variance of the RGF. • The effectiveness of the proposed model and control approach is validated by the experimental evidence. - Abstract: In four stroke internal combustion engines, residual gas from the previous cycle is an important factor influencing the combustion quality of the current cycle, and the residual gas fraction (RGF) is a popular index to monitor the influence of residual gas. This paper investigates the cycle-to-cycle transient behavior of the RGF in the view of systems theory and proposes a multi-valued logic-based control strategy for attenuation of RGF fluctuation. First, an in-cylinder pressure sensor-based method for measuring the RGF is provided by following the physics of the in-cylinder transient state of four-stroke internal combustion engines. Then, the stochastic property of the RGF is examined based on statistical data obtained by conducting experiments on a full-scale gasoline engine test bench. Based on the observation of the examination, a stochastic logical transient model is proposed to represent the cycle-to-cycle transient behavior of the RGF, and with the model an optimal feedback control law, which targets on rejection of the RGF fluctuation, is derived in the framework of stochastic logical system theory. Finally, experimental results are demonstrated to show the effectiveness of the proposed model and the control strategy.
Fuzzy Stochastic Optimal Guaranteed Cost Control of Bio-Economic Singular Markovian Jump Systems.
Li, Li; Zhang, Qingling; Zhu, Baoyan
2015-11-01
This paper establishes a bio-economic singular Markovian jump model by considering the price of the commodity as a Markov chain. The controller is designed for this system such that its biomass achieves the specified range with the least cost in a finite-time. Firstly, this system is described by Takagi-Sugeno fuzzy model. Secondly, a new design method of fuzzy state-feedback controllers is presented to ensure not only the regularity, nonimpulse, and stochastic singular finite-time boundedness of this kind of systems, but also an upper bound achieved for the cost function in the form of strict linear matrix inequalities. Finally, two examples including a practical example of eel seedling breeding are given to illustrate the merit and usability of the approach proposed in this paper.
Portfolio Optimization with Stochastic Dividends and Stochastic Volatility
Varga, Katherine Yvonne
2015-01-01
We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…
Economic policy optimization based on both one stochastic model and the parametric control theory
Ashimov, Abdykappar; Borovskiy, Yuriy; Onalbekov, Mukhit
2016-06-01
A nonlinear dynamic stochastic general equilibrium model with financial frictions is developed to describe two interacting national economies in the environment of the rest of the world. Parameters of nonlinear model are estimated based on its log-linearization by the Bayesian approach. The nonlinear model is verified by retroprognosis, estimation of stability indicators of mappings specified by the model, and estimation the degree of coincidence for results of internal and external shocks' effects on macroeconomic indicators on the basis of the estimated nonlinear model and its log-linearization. On the base of the nonlinear model, the parametric control problems of economic growth and volatility of macroeconomic indicators of Kazakhstan are formulated and solved for two exchange rate regimes (free floating and managed floating exchange rates)
Liu, Xiaomei; Li, Shengtao; Zhang, Kanjian
2017-08-01
In this paper, we solve an optimal control problem for a class of time-invariant switched stochastic systems with multi-switching times, where the objective is to minimise a cost functional with different costs defined on the states. In particular, we focus on problems in which a pre-specified sequence of active subsystems is given and the switching times are the only control variables. Based on the calculus of variation, we derive the gradient of the cost functional with respect to the switching times on an especially simple form, which can be directly used in gradient descent algorithms to locate the optimal switching instants. Finally, a numerical example is given, highlighting the validity of the proposed methodology.
Directory of Open Access Journals (Sweden)
Yuying Wang
2017-11-01
Full Text Available This paper presents an energy management strategy for plug-in hybrid electric vehicles (PHEVs that not only tries to minimize the energy consumption, but also considers the battery health. First, a battery model that can be applied to energy management optimization is given. In this model, battery health damage can be estimated in the different states of charge (SOC and temperature of the battery pack. Then, because of the inevitability that limiting the battery health degradation will increase energy consumption, a Pareto energy management optimization problem is formed. This multi-objective optimal control problem is solved numerically by using stochastic dynamic programming (SDP and particle swarm optimization (PSO for satisfying the vehicle power demand and considering the tradeoff between energy consumption and battery health at the same time. The optimization solution is obtained offline by utilizing real historical traffic data and formed as mappings on the system operating states so as to implement online in the actual driving conditions. Finally, the simulation results carried out on the GT-SUITE-based PHEV test platform are illustrated to demonstrate that the proposed multi-objective optimal control strategy would effectively yield benefits.
Stochastic Feedforward Control Technique
Halyo, Nesim
1990-01-01
Class of commanded trajectories modeled as stochastic process. Advanced Transport Operating Systems (ATOPS) research and development program conducted by NASA Langley Research Center aimed at developing capabilities for increases in capacities of airports, safe and accurate flight in adverse weather conditions including shear, winds, avoidance of wake vortexes, and reduced consumption of fuel. Advances in techniques for design of modern controls and increased capabilities of digital flight computers coupled with accurate guidance information from Microwave Landing System (MLS). Stochastic feedforward control technique developed within context of ATOPS program.
Stochastic dynamics and control
Sun, Jian-Qiao; Zaslavsky, George
2006-01-01
This book is a result of many years of author's research and teaching on random vibration and control. It was used as lecture notes for a graduate course. It provides a systematic review of theory of probability, stochastic processes, and stochastic calculus. The feedback control is also reviewed in the book. Random vibration analyses of SDOF, MDOF and continuous structural systems are presented in a pedagogical order. The application of the random vibration theory to reliability and fatigue analysis is also discussed. Recent research results on fatigue analysis of non-Gaussian stress proc
Stochastic Control - External Models
DEFF Research Database (Denmark)
Poulsen, Niels Kjølstad
2005-01-01
This note is devoted to control of stochastic systems described in discrete time. We are concerned with external descriptions or transfer function model, where we have a dynamic model for the input output relation only (i.e.. no direct internal information). The methods are based on LTI systems...
Dynamic optimization deterministic and stochastic models
Hinderer, Karl; Stieglitz, Michael
2016-01-01
This book explores discrete-time dynamic optimization and provides a detailed introduction to both deterministic and stochastic models. Covering problems with finite and infinite horizon, as well as Markov renewal programs, Bayesian control models and partially observable processes, the book focuses on the precise modelling of applications in a variety of areas, including operations research, computer science, mathematics, statistics, engineering, economics and finance. Dynamic Optimization is a carefully presented textbook which starts with discrete-time deterministic dynamic optimization problems, providing readers with the tools for sequential decision-making, before proceeding to the more complicated stochastic models. The authors present complete and simple proofs and illustrate the main results with numerous examples and exercises (without solutions). With relevant material covered in four appendices, this book is completely self-contained.
Sensory optimization by stochastic tuning.
Jurica, Peter; Gepshtein, Sergei; Tyukin, Ivan; van Leeuwen, Cees
2013-10-01
Individually, visual neurons are each selective for several aspects of stimulation, such as stimulus location, frequency content, and speed. Collectively, the neurons implement the visual system's preferential sensitivity to some stimuli over others, manifested in behavioral sensitivity functions. We ask how the individual neurons are coordinated to optimize visual sensitivity. We model synaptic plasticity in a generic neural circuit and find that stochastic changes in strengths of synaptic connections entail fluctuations in parameters of neural receptive fields. The fluctuations correlate with uncertainty of sensory measurement in individual neurons: The higher the uncertainty the larger the amplitude of fluctuation. We show that this simple relationship is sufficient for the stochastic fluctuations to steer sensitivities of neurons toward a characteristic distribution, from which follows a sensitivity function observed in human psychophysics and which is predicted by a theory of optimal allocation of receptive fields. The optimal allocation arises in our simulations without supervision or feedback about system performance and independently of coupling between neurons, making the system highly adaptive and sensitive to prevailing stimulation. PsycINFO Database Record (c) 2013 APA, all rights reserved.
Optimizing Multi-Product Multi-Constraint Inventory Control Systems with Stochastic Replenishments
Allah Taleizadeh, Ata; Aryanezhad, Mir-Bahador; Niaki, Seyed Taghi Akhavan
Multi-periodic inventory control problems are mainly studied employing two assumptions. The first is the continuous review, where depending on the inventory level orders can happen at any time and the other is the periodic review, where orders can only happen at the beginning of each period. In this study, we relax these assumptions and assume that the periodic replenishments are stochastic in nature. Furthermore, we assume that the periods between two replenishments are independent and identically random variables. For the problem at hand, the decision variables are of integer-type and there are two kinds of space and service level constraints for each product. We develop a model of the problem in which a combination of back-order and lost-sales are considered for the shortages. Then, we show that the model is of an integer-nonlinear-programming type and in order to solve it, a search algorithm can be utilized. We employ a simulated annealing approach and provide a numerical example to demonstrate the applicability of the proposed methodology.
Topology optimization under stochastic stiffness
Asadpoure, Alireza
Topology optimization is a systematic computational tool for optimizing the layout of materials within a domain for engineering design problems. It allows variation of structural boundaries and connectivities. This freedom in the design space often enables discovery of new, high performance designs. However, solutions obtained by performing the optimization in a deterministic setting may be impractical or suboptimal when considering real-world engineering conditions with inherent variabilities including (for example) variabilities in fabrication processes and operating conditions. The aim of this work is to provide a computational methodology for topology optimization in the presence of uncertainties associated with structural stiffness, such as uncertain material properties and/or structural geometry. Existing methods for topology optimization under deterministic conditions are first reviewed. Modifications are then proposed to improve the numerical performance of the so-called Heaviside Projection Method (HPM) in continuum domains. Next, two approaches, perturbation and Polynomial Chaos Expansion (PCE), are proposed to account for uncertainties in the optimization procedure. These approaches are intrusive, allowing tight and efficient coupling of the uncertainty quantification with the optimization sensitivity analysis. The work herein develops a robust topology optimization framework aimed at reducing the sensitivity of optimized solutions to uncertainties. The perturbation-based approach combines deterministic topology optimization with a perturbation method for the quantification of uncertainties. The use of perturbation transforms the problem of topology optimization under uncertainty to an augmented deterministic topology optimization problem. The PCE approach combines the spectral stochastic approach for the representation and propagation of uncertainties with an existing deterministic topology optimization technique. The resulting compact representations
Stochastic Optimization of Wind Turbine Power Factor Using Stochastic Model of Wind Power
DEFF Research Database (Denmark)
Chen, Peiyuan; Siano, Pierluigi; Bak-Jensen, Birgitte
2010-01-01
This paper proposes a stochastic optimization algorithm that aims to minimize the expectation of the system power losses by controlling wind turbine (WT) power factors. This objective of the optimization is subject to the probability constraints of bus voltage and line current requirements....... The optimization algorithm utilizes the stochastic models of wind power generation (WPG) and load demand to take into account their stochastic variation. The stochastic model of WPG is developed on the basis of a limited autoregressive integrated moving average (LARIMA) model by introducing a crosscorrelation...... structure to the LARIMA model. The proposed stochastic optimization is carried out on a 69-bus distribution system. Simulation results confirm that, under various combinations of WPG and load demand, the system power losses are considerably reduced with the optimal setting of WT power factor as compared...
Stochastic Optimal Control of a Heave Point Wave Energy Converter Based on a Modified LQG Approach
DEFF Research Database (Denmark)
Sun, Tao; Nielsen, Søren R. K.
2018-01-01
and actuator force are approximately considered by counteracting the absorbed power in the objective quadratic functional. Based on rational approximations to the radiation force and the wave load, the integrated dynamic system can be reformulated as a linear stochastic differential equation which is driven...
Delayed Stochastic Linear-Quadratic Control Problem and Related Applications
Directory of Open Access Journals (Sweden)
Li Chen
2012-01-01
stochastic differential equations (FBSDEs with Itô’s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the optimal feedback regulator for the time delay system via a new type of Riccati equations and also apply to a population optimal control problem.
Stochastic control with rough paths
International Nuclear Information System (INIS)
Diehl, Joscha; Friz, Peter K.; Gassiat, Paul
2017-01-01
We study a class of controlled differential equations driven by rough paths (or rough path realizations of Brownian motion) in the sense of Lyons. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory for controlled diffusion processes and typically involve anticipating stochastic analysis. We make the link to old work of Davis and Burstein (Stoch Stoch Rep 40:203–256, 1992) and then prove a continuous-time generalization of Roger’s duality formula [SIAM J Control Optim 46:1116–1132, 2007]. The generic case of controlled volatility is seen to give trivial duality bounds, and explains the focus in Burstein–Davis’ (and this) work on controlled drift. Our study of controlled rough differential equations also relates to work of Mazliak and Nourdin (Stoch Dyn 08:23, 2008).
Stochastic control with rough paths
Energy Technology Data Exchange (ETDEWEB)
Diehl, Joscha [University of California San Diego (United States); Friz, Peter K., E-mail: friz@math.tu-berlin.de [TU & WIAS Berlin (Germany); Gassiat, Paul [CEREMADE, Université Paris-Dauphine, PSL Research University (France)
2017-04-15
We study a class of controlled differential equations driven by rough paths (or rough path realizations of Brownian motion) in the sense of Lyons. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory for controlled diffusion processes and typically involve anticipating stochastic analysis. We make the link to old work of Davis and Burstein (Stoch Stoch Rep 40:203–256, 1992) and then prove a continuous-time generalization of Roger’s duality formula [SIAM J Control Optim 46:1116–1132, 2007]. The generic case of controlled volatility is seen to give trivial duality bounds, and explains the focus in Burstein–Davis’ (and this) work on controlled drift. Our study of controlled rough differential equations also relates to work of Mazliak and Nourdin (Stoch Dyn 08:23, 2008).
Approximative solutions of stochastic optimization problem
Czech Academy of Sciences Publication Activity Database
Lachout, Petr
2010-01-01
Roč. 46, č. 3 (2010), s. 513-523 ISSN 0023-5954 R&D Projects: GA ČR GA201/08/0539 Institutional research plan: CEZ:AV0Z10750506 Keywords : Stochastic optimization problem * sensitivity * approximative solution Subject RIV: BA - General Mathematics Impact factor: 0.461, year: 2010 http://library.utia.cas.cz/separaty/2010/SI/lachout-approximative solutions of stochastic optimization problem.pdf
Constrained Optimal Stochastic Control of Non-Linear Wave Energy Point Absorbers
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Chen, Jian-Bing; Kramer, Morten
2014-01-01
to extract energy. Constrains are enforced on the control force to prevent large structural stresses in the floater at specific hot spots with the risk of inducing fatigue damage, or because the demanded control force cannot be supplied by the actuator system due to saturation. Further, constraints...... are enforced on the motion of the floater to prevent it from hitting the bottom of the sea or to make unacceptable jumps out of the water. The applied control law, which is of the feedback type with feedback from the displacement, velocity, and acceleration of the floater, contains two unprovided gain...
Stochastic global optimization as a filtering problem
International Nuclear Information System (INIS)
Stinis, Panos
2012-01-01
We present a reformulation of stochastic global optimization as a filtering problem. The motivation behind this reformulation comes from the fact that for many optimization problems we cannot evaluate exactly the objective function to be optimized. Similarly, we may not be able to evaluate exactly the functions involved in iterative optimization algorithms. For example, we may only have access to noisy measurements of the functions or statistical estimates provided through Monte Carlo sampling. This makes iterative optimization algorithms behave like stochastic maps. Naive global optimization amounts to evolving a collection of realizations of this stochastic map and picking the realization with the best properties. This motivates the use of filtering techniques to allow focusing on realizations that are more promising than others. In particular, we present a filtering reformulation of global optimization in terms of a special case of sequential importance sampling methods called particle filters. The increasing popularity of particle filters is based on the simplicity of their implementation and their flexibility. We utilize the flexibility of particle filters to construct a stochastic global optimization algorithm which can converge to the optimal solution appreciably faster than naive global optimization. Several examples of parametric exponential density estimation are provided to demonstrate the efficiency of the approach.
STOCHASTIC GRADIENT METHODS FOR UNCONSTRAINED OPTIMIZATION
Directory of Open Access Journals (Sweden)
Nataša Krejić
2014-12-01
Full Text Available This papers presents an overview of gradient based methods for minimization of noisy functions. It is assumed that the objective functions is either given with error terms of stochastic nature or given as the mathematical expectation. Such problems arise in the context of simulation based optimization. The focus of this presentation is on the gradient based Stochastic Approximation and Sample Average Approximation methods. The concept of stochastic gradient approximation of the true gradient can be successfully extended to deterministic problems. Methods of this kind are presented for the data fitting and machine learning problems.
On benchmarking Stochastic Global Optimization Algorithms
Hendrix, E.M.T.; Lancinskas, A.
2015-01-01
A multitude of heuristic stochastic optimization algorithms have been described in literature to obtain good solutions of the box-constrained global optimization problem often with a limit on the number of used function evaluations. In the larger question of which algorithms behave well on which
Ep for efficient stochastic control with obstacles
Mensink, T.; Verbeek, J.; Kappen, H.J.
2010-01-01
Abstract. We address the problem of continuous stochastic optimal control in the presence of hard obstacles. Due to the non-smooth character of the obstacles, the traditional approach using dynamic programming in combination with function approximation tends to fail. We consider a recently
Sparse Learning with Stochastic Composite Optimization.
Zhang, Weizhong; Zhang, Lijun; Jin, Zhongming; Jin, Rong; Cai, Deng; Li, Xuelong; Liang, Ronghua; He, Xiaofei
2017-06-01
In this paper, we study Stochastic Composite Optimization (SCO) for sparse learning that aims to learn a sparse solution from a composite function. Most of the recent SCO algorithms have already reached the optimal expected convergence rate O(1/λT), but they often fail to deliver sparse solutions at the end either due to the limited sparsity regularization during stochastic optimization (SO) or due to the limitation in online-to-batch conversion. Even when the objective function is strongly convex, their high probability bounds can only attain O(√{log(1/δ)/T}) with δ is the failure probability, which is much worse than the expected convergence rate. To address these limitations, we propose a simple yet effective two-phase Stochastic Composite Optimization scheme by adding a novel powerful sparse online-to-batch conversion to the general Stochastic Optimization algorithms. We further develop three concrete algorithms, OptimalSL, LastSL and AverageSL, directly under our scheme to prove the effectiveness of the proposed scheme. Both the theoretical analysis and the experiment results show that our methods can really outperform the existing methods at the ability of sparse learning and at the meantime we can improve the high probability bound to approximately O(log(log(T)/δ)/λT).
Advances in stochastic and deterministic global optimization
Zhigljavsky, Anatoly; Žilinskas, Julius
2016-01-01
Current research results in stochastic and deterministic global optimization including single and multiple objectives are explored and presented in this book by leading specialists from various fields. Contributions include applications to multidimensional data visualization, regression, survey calibration, inventory management, timetabling, chemical engineering, energy systems, and competitive facility location. Graduate students, researchers, and scientists in computer science, numerical analysis, optimization, and applied mathematics will be fascinated by the theoretical, computational, and application-oriented aspects of stochastic and deterministic global optimization explored in this book. This volume is dedicated to the 70th birthday of Antanas Žilinskas who is a leading world expert in global optimization. Professor Žilinskas's research has concentrated on studying models for the objective function, the development and implementation of efficient algorithms for global optimization with single and mu...
Hsia, Wei-Shen
1986-01-01
In the Control Systems Division of the Systems Dynamics Laboratory of the NASA/MSFC, a Ground Facility (GF), in which the dynamics and control system concepts being considered for Large Space Structures (LSS) applications can be verified, was designed and built. One of the important aspects of the GF is to design an analytical model which will be as close to experimental data as possible so that a feasible control law can be generated. Using Hyland's Maximum Entropy/Optimal Projection Approach, a procedure was developed in which the maximum entropy principle is used for stochastic modeling and the optimal projection technique is used for a reduced-order dynamic compensator design for a high-order plant.
Linear System Control Using Stochastic Learning Automata
Ziyad, Nigel; Cox, E. Lucien; Chouikha, Mohamed F.
1998-01-01
This paper explains the use of a Stochastic Learning Automata (SLA) to control switching between three systems to produce the desired output response. The SLA learns the optimal choice of the damping ratio for each system to achieve a desired result. We show that the SLA can learn these states for the control of an unknown system with the proper choice of the error criteria. The results of using a single automaton are compared to using multiple automata.
Manning, Robert M.
1990-01-01
A static and dynamic rain-attenuation model is presented which describes the statistics of attenuation on an arbitrarily specified satellite link for any location for which there are long-term rainfall statistics. The model may be used in the design of the optimal stochastic control algorithms to mitigate the effects of attenuation and maintain link reliability. A rain-statistics data base is compiled, which makes it possible to apply the model to any location in the continental U.S. with a resolution of 0-5 degrees in latitude and longitude. The model predictions are compared with experimental observations, showing good agreement.
Fuzzy Stochastic Optimization Theory, Models and Applications
Wang, Shuming
2012-01-01
Covering in detail both theoretical and practical perspectives, this book is a self-contained and systematic depiction of current fuzzy stochastic optimization that deploys the fuzzy random variable as a core mathematical tool to model the integrated fuzzy random uncertainty. It proceeds in an orderly fashion from the requisite theoretical aspects of the fuzzy random variable to fuzzy stochastic optimization models and their real-life case studies. The volume reflects the fact that randomness and fuzziness (or vagueness) are two major sources of uncertainty in the real world, with significant implications in a number of settings. In industrial engineering, management and economics, the chances are high that decision makers will be confronted with information that is simultaneously probabilistically uncertain and fuzzily imprecise, and optimization in the form of a decision must be made in an environment that is doubly uncertain, characterized by a co-occurrence of randomness and fuzziness. This book begins...
Some Topics in Stochastic Control
2010-10-14
assimilation problems. (a) Papers published in peer-reviewed journals (N/A for none) 1. R. Atar and A. Budhiraja. A stochastic differential game for...the inhomogeneous infinity-Laplace equation. Ann. Prob., 38 (2010), no. 2, 498--531. 2. R. Atar and A. Budhiraja. On near optimal trajectories for a...G. Aronsson. A mathematical model in sand mechanics: presentation and analysis. SIAM J. Appl. Math., 22 (1972), 437-458 [3] R. Atar and A. Budhiraja
Stochastic Finite Elements in Reliability-Based Structural Optimization
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Engelund, S.
1995-01-01
Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to optimi......Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...... to optimization variables can be performed. A computer implementation is described and an illustrative example is given....
Stochastic control theory dynamic programming principle
Nisio, Makiko
2015-01-01
This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems. First we consider completely observable control problems with finite horizons. Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the Hamilton–Jacobi–Bellman (HJB) equation, and we characterize the value function via the nonlinear semigroup, besides the viscosity solution theory. When we control not only the dynamics of a system but also the terminal time of its evolution, control-stopping problems arise. This problem is treated in the same frameworks, via the nonlinear semigroup. Its results are applicable to the American option price problem. Zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games are studied via a nonlinear semigroup related to DPP (the min-ma...
Model predictive control classical, robust and stochastic
Kouvaritakis, Basil
2016-01-01
For the first time, a textbook that brings together classical predictive control with treatment of up-to-date robust and stochastic techniques. Model Predictive Control describes the development of tractable algorithms for uncertain, stochastic, constrained systems. The starting point is classical predictive control and the appropriate formulation of performance objectives and constraints to provide guarantees of closed-loop stability and performance. Moving on to robust predictive control, the text explains how similar guarantees may be obtained for cases in which the model describing the system dynamics is subject to additive disturbances and parametric uncertainties. Open- and closed-loop optimization are considered and the state of the art in computationally tractable methods based on uncertainty tubes presented for systems with additive model uncertainty. Finally, the tube framework is also applied to model predictive control problems involving hard or probabilistic constraints for the cases of multiplic...
Decoding suprathreshold stochastic resonance with optimal weights
International Nuclear Information System (INIS)
Xu, Liyan; Vladusich, Tony; Duan, Fabing; Gunn, Lachlan J.; Abbott, Derek; McDonnell, Mark D.
2015-01-01
We investigate an array of stochastic quantizers for converting an analog input signal into a discrete output in the context of suprathreshold stochastic resonance. A new optimal weighted decoding is considered for different threshold level distributions. We show that for particular noise levels and choices of the threshold levels optimally weighting the quantizer responses provides a reduced mean square error in comparison with the original unweighted array. However, there are also many parameter regions where the original array provides near optimal performance, and when this occurs, it offers a much simpler approach than optimally weighting each quantizer's response. - Highlights: • A weighted summing array of independently noisy binary comparators is investigated. • We present an optimal linearly weighted decoding scheme for combining the comparator responses. • We solve for the optimal weights by applying least squares regression to simulated data. • We find that the MSE distortion of weighting before summation is superior to unweighted summation of comparator responses. • For some parameter regions, the decrease in MSE distortion due to weighting is negligible
Stochastic network optimization with application to communication and queueing systems
Neely, Michael
2010-01-01
This text presents a modern theory of analysis, control, and optimization for dynamic networks. Mathematical techniques of Lyapunov drift and Lyapunov optimization are developed and shown to enable constrained optimization of time averages in general stochastic systems. The focus is on communication and queueing systems, including wireless networks with time-varying channels, mobility, and randomly arriving traffic. A simple drift-plus-penalty framework is used to optimize time averages such as throughput, throughput-utility, power, and distortion. Explicit performance-delay tradeoffs are prov
Stochastic optimization of loading pattern for PWR
International Nuclear Information System (INIS)
Smuc, T.; Pevec, D.
1994-01-01
The application of stochastic optimization methods in solving in-core fuel management problems is restrained by the need for a large number of proposed solutions loading patterns, if a high quality final solution is wanted. Proposed loading patterns have to be evaluated by core neutronics simulator, which can impose unrealistic computer time requirements. A new loading pattern optimization code Monte Carlo Loading Pattern Search has been developed by coupling the simulated annealing optimization algorithm with a fast one-and-a-half dimensional core depletion simulator. The structure of the optimization method provides more efficient performance and allows the user to empty precious experience in the search process, thus reducing the search space size. Hereinafter, we discuss the characteristics of the method and illustrate them on the results obtained by solving the PWR reload problem. (authors). 7 refs., 1 tab., 1 fig
Stochastic Finite Elements in Reliability-Based Structural Optimization
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Engelund, S.
Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to optimi......Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...
Li, Shuangyan; Li, Xialian; Zhang, Dezhi; Zhou, Lingyun
2017-01-01
This study develops an optimization model to integrate facility location and inventory control for a three-level distribution network consisting of a supplier, multiple distribution centers (DCs), and multiple retailers. The integrated model addressed in this study simultaneously determines three types of decisions: (1) facility location (optimal number, location, and size of DCs); (2) allocation (assignment of suppliers to located DCs and retailers to located DCs, and corresponding optimal transport mode choices); and (3) inventory control decisions on order quantities, reorder points, and amount of safety stock at each retailer and opened DC. A mixed-integer programming model is presented, which considers the carbon emission taxes, multiple transport modes, stochastic demand, and replenishment lead time. The goal is to minimize the total cost, which covers the fixed costs of logistics facilities, inventory, transportation, and CO2 emission tax charges. The aforementioned optimal model was solved using commercial software LINGO 11. A numerical example is provided to illustrate the applications of the proposed model. The findings show that carbon emission taxes can significantly affect the supply chain structure, inventory level, and carbon emission reduction levels. The delay rate directly affects the replenishment decision of a retailer.
Directory of Open Access Journals (Sweden)
Shuangyan Li
Full Text Available This study develops an optimization model to integrate facility location and inventory control for a three-level distribution network consisting of a supplier, multiple distribution centers (DCs, and multiple retailers. The integrated model addressed in this study simultaneously determines three types of decisions: (1 facility location (optimal number, location, and size of DCs; (2 allocation (assignment of suppliers to located DCs and retailers to located DCs, and corresponding optimal transport mode choices; and (3 inventory control decisions on order quantities, reorder points, and amount of safety stock at each retailer and opened DC. A mixed-integer programming model is presented, which considers the carbon emission taxes, multiple transport modes, stochastic demand, and replenishment lead time. The goal is to minimize the total cost, which covers the fixed costs of logistics facilities, inventory, transportation, and CO2 emission tax charges. The aforementioned optimal model was solved using commercial software LINGO 11. A numerical example is provided to illustrate the applications of the proposed model. The findings show that carbon emission taxes can significantly affect the supply chain structure, inventory level, and carbon emission reduction levels. The delay rate directly affects the replenishment decision of a retailer.
Stochastic maintenance optimization at Candu power plants
International Nuclear Information System (INIS)
Doyle, E.K.; Duchesne, T.; Lee, C.G.; Cho, D.I.
2004-01-01
The use of various innovative maintenance optimization techniques at Bruce has lead to cost effective preventive maintenance applications for complex systems as previously reported at ICONE 6 in New Orleans (1996). Further refinement of the station maintenance strategy was evaluated via the applicability of statistical analysis of historical failure data. The viability of stochastic methods in Candu maintenance was illustrated at ICONE 10 in Washington DC (2002). The next phase consists of investigating the validity of using subjective elicitation techniques to obtain component lifetime distributions. This technique provides access to the elusive failure statistics, the lack of which is often referred to in the literature as the principal impediment preventing the use of stochastic methods in large industry. At the same time the technique allows very valuable information to be captured from the fast retiring 'baby boom generation'. Initial indications have been quite positive. The current reality of global competition necessitates the pursuit of all financial optimizers. The next construction phase in the power generation industry will soon begin on a worldwide basis. With the relatively high initial capital cost of new nuclear generation all possible avenues of financial optimization must be evaluated and implemented. (authors)
Han, Jing-Cheng; Huang, Guo-He; Zhang, Hua; Li, Zhong
2013-09-01
Soil erosion is one of the most serious environmental and public health problems, and such land degradation can be effectively mitigated through performing land use transitions across a watershed. Optimal land use management can thus provide a way to reduce soil erosion while achieving the maximum net benefit. However, optimized land use allocation schemes are not always successful since uncertainties pertaining to soil erosion control are not well presented. This study applied an interval-parameter fuzzy two-stage stochastic programming approach to generate optimal land use planning strategies for soil erosion control based on an inexact optimization framework, in which various uncertainties were reflected. The modeling approach can incorporate predefined soil erosion control policies, and address inherent system uncertainties expressed as discrete intervals, fuzzy sets, and probability distributions. The developed model was demonstrated through a case study in the Xiangxi River watershed, China's Three Gorges Reservoir region. Land use transformations were employed as decision variables, and based on these, the land use change dynamics were yielded for a 15-year planning horizon. Finally, the maximum net economic benefit with an interval value of [1.197, 6.311] × 109 was obtained as well as corresponding land use allocations in the three planning periods. Also, the resulting soil erosion amount was found to be decreased and controlled at a tolerable level over the watershed. Thus, results confirm that the developed model is a useful tool for implementing land use management as not only does it allow local decision makers to optimize land use allocation, but can also help to answer how to accomplish land use changes.
Han, Jing-Cheng; Huang, Guo-He; Zhang, Hua; Li, Zhong
2013-09-01
Soil erosion is one of the most serious environmental and public health problems, and such land degradation can be effectively mitigated through performing land use transitions across a watershed. Optimal land use management can thus provide a way to reduce soil erosion while achieving the maximum net benefit. However, optimized land use allocation schemes are not always successful since uncertainties pertaining to soil erosion control are not well presented. This study applied an interval-parameter fuzzy two-stage stochastic programming approach to generate optimal land use planning strategies for soil erosion control based on an inexact optimization framework, in which various uncertainties were reflected. The modeling approach can incorporate predefined soil erosion control policies, and address inherent system uncertainties expressed as discrete intervals, fuzzy sets, and probability distributions. The developed model was demonstrated through a case study in the Xiangxi River watershed, China's Three Gorges Reservoir region. Land use transformations were employed as decision variables, and based on these, the land use change dynamics were yielded for a 15-year planning horizon. Finally, the maximum net economic benefit with an interval value of [1.197, 6.311] × 10(9) $ was obtained as well as corresponding land use allocations in the three planning periods. Also, the resulting soil erosion amount was found to be decreased and controlled at a tolerable level over the watershed. Thus, results confirm that the developed model is a useful tool for implementing land use management as not only does it allow local decision makers to optimize land use allocation, but can also help to answer how to accomplish land use changes.
Stochastic Recursive Algorithms for Optimization Simultaneous Perturbation Methods
Bhatnagar, S; Prashanth, L A
2013-01-01
Stochastic Recursive Algorithms for Optimization presents algorithms for constrained and unconstrained optimization and for reinforcement learning. Efficient perturbation approaches form a thread unifying all the algorithms considered. Simultaneous perturbation stochastic approximation and smooth fractional estimators for gradient- and Hessian-based methods are presented. These algorithms: • are easily implemented; • do not require an explicit system model; and • work with real or simulated data. Chapters on their application in service systems, vehicular traffic control and communications networks illustrate this point. The book is self-contained with necessary mathematical results placed in an appendix. The text provides easy-to-use, off-the-shelf algorithms that are given detailed mathematical treatment so the material presented will be of significant interest to practitioners, academic researchers and graduate students alike. The breadth of applications makes the book appropriate for reader from sim...
Optimization and Optimal Control
Chinchuluun, Altannar; Enkhbat, Rentsen; Tseveendorj, Ider
2010-01-01
During the last four decades there has been a remarkable development in optimization and optimal control. Due to its wide variety of applications, many scientists and researchers have paid attention to fields of optimization and optimal control. A huge number of new theoretical, algorithmic, and computational results have been observed in the last few years. This book gives the latest advances, and due to the rapid development of these fields, there are no other recent publications on the same topics. Key features: Provides a collection of selected contributions giving a state-of-the-art accou
Directory of Open Access Journals (Sweden)
Jie Yu
2015-01-01
Full Text Available Virtual power plant (VPP is an aggregation of multiple distributed generations, energy storage, and controllable loads. Affected by natural conditions, the uncontrollable distributed generations within VPP, such as wind and photovoltaic generations, are extremely random and relative. Considering the randomness and its correlation of uncontrollable distributed generations, this paper constructs the chance constraints stochastic optimal dispatch of VPP including stochastic variables and its random correlation. The probability distributions of independent wind and photovoltaic generations are described by empirical distribution functions, and their joint probability density model is established by Frank-copula function. And then, sample average approximation (SAA is applied to convert the chance constrained stochastic optimization model into a deterministic optimization model. Simulation cases are calculated based on the AIMMS. Simulation results of this paper mathematic model are compared with the results of deterministic optimization model without stochastic variables and stochastic optimization considering stochastic variables but not random correlation. Furthermore, this paper analyzes how SAA sampling frequency and the confidence level influence the results of stochastic optimization. The numerical example results show the effectiveness of the stochastic optimal dispatch of VPP considering the randomness and its correlations of distributed generations.
Vesapogu, Joshi Manohar; Peddakotla, Sujatha; Kuppa, Seetha Rama Anjaneyulu
2013-01-01
With the advancements in semiconductor technology, high power medium voltage (MV) Drives are extensively used in numerous industrial applications. Challenging technical requirements of MV Drives is to control multilevel inverter (MLI) with less Total harmonic distortion (%THD) which satisfies IEEE standard 519-1992 harmonic guidelines and less switching losses. Among all modulation control strategies for MLI, Selective harmonic elimination (SHE) technique is one of the traditionally preferred modulation control technique at fundamental switching frequency with better harmonic profile. On the other hand, the equations which are formed by SHE technique are highly non-linear in nature, may exist multiple, single or even no solution at particular modulation index (MI). However, in some MV Drive applications, it is required to operate over a range of MI. Providing analytical solutions for SHE equations during the whole range of MI from 0 to 1, has been a challenging task for researchers. In this paper, an attempt is made to solve SHE equations by using deterministic and stochastic optimization methods and comparative harmonic analysis has been carried out. An effective algorithm which minimizes %THD with less computational effort among all optimization algorithms has been presented. To validate the effectiveness of proposed MPSO technique, an experiment is carried out on a low power proto type of three phase CHB 11- level Inverter using FPGA based Xilinx's Spartan -3A DSP Controller. The experimental results proved that MPSO technique has successfully solved SHE equations over all range of MI from 0 to 1, the %THD obtained over major range of MI also satisfies IEEE 519-1992 harmonic guidelines too.
A Stochastic Multiobjective Optimization Framework for Wireless Sensor Networks
Directory of Open Access Journals (Sweden)
Shibo He
2010-01-01
Full Text Available In wireless sensor networks (WSNs, there generally exist many different objective functions to be optimized. In this paper, we propose a stochastic multiobjective optimization approach to solve such kind of problem. We first formulate a general multiobjective optimization problem. We then decompose the optimization formulation through Lagrange dual decomposition and adopt the stochastic quasigradient algorithm to solve the primal-dual problem in a distributed way. We show theoretically that our algorithm converges to the optimal solution of the primal problem by using the knowledge of stochastic programming. Furthermore, the formulation provides a general stochastic multiobjective optimization framework for WSNs. We illustrate how the general framework works by considering an example of the optimal rate allocation problem in multipath WSNs with time-varying channel. Extensive simulation results are given to demonstrate the effectiveness of our algorithm.
Stochastic control and the second law of thermodynamics
Brockett, R. W.; Willems, J. C.
1979-01-01
The second law of thermodynamics is studied from the point of view of stochastic control theory. We find that the feedback control laws which are of interest are those which depend only on average values, and not on sample path behavior. We are lead to a criterion which, when satisfied, permits one to assign a temperature to a stochastic system in such a way as to have Carnot cycles be the optimal trajectories of optimal control problems. Entropy is also defined and we are able to prove an equipartition of energy theorem using this definition of temperature. Our formulation allows one to treat irreversibility in a quite natural and completely precise way.
Aschepkov, Leonid T; Kim, Taekyun; Agarwal, Ravi P
2016-01-01
This book is based on lectures from a one-year course at the Far Eastern Federal University (Vladivostok, Russia) as well as on workshops on optimal control offered to students at various mathematical departments at the university level. The main themes of the theory of linear and nonlinear systems are considered, including the basic problem of establishing the necessary and sufficient conditions of optimal processes. In the first part of the course, the theory of linear control systems is constructed on the basis of the separation theorem and the concept of a reachability set. The authors prove the closure of a reachability set in the class of piecewise continuous controls, and the problems of controllability, observability, identification, performance and terminal control are also considered. The second part of the course is devoted to nonlinear control systems. Using the method of variations and the Lagrange multipliers rule of nonlinear problems, the authors prove the Pontryagin maximum principle for prob...
Stochastic optimization-based study of dimerization kinetics
Indian Academy of Sciences (India)
To this end, we study dimerization kinetics of protein as a model system. We follow the dimerization kinetics using a stochastic simulation algorithm and ... optimization; dimerization kinetics; sensitivity analysis; stochastic simulation ... tion in large molecules and clusters, or the design ..... An unbiased strategy of allocating.
Multivariable controller for discrete stochastic amplitude-constrained systems
Directory of Open Access Journals (Sweden)
Hannu T. Toivonen
1983-04-01
Full Text Available A sub-optimal multivariable controller for discrete stochastic amplitude-constrained systems is presented. In the approach the regulator structure is restricted to the class of linear saturated feedback laws. The stationary covariances of the controlled system are evaluated by approximating the stationary probability distribution of the state by a gaussian distribution. An algorithm for minimizing a quadratic loss function is given, and examples are presented to illustrate the performance of the sub-optimal controller.
Optimal configuration of microstructure in ferroelectric materials by stochastic optimization
Jayachandran, K. P.; Guedes, J. M.; Rodrigues, H. C.
2010-07-01
An optimization procedure determining the ideal configuration at the microstructural level of ferroelectric (FE) materials is applied to maximize piezoelectricity. Piezoelectricity in ceramic FEs differs significantly from that of single crystals because of the presence of crystallites (grains) possessing crystallographic axes aligned imperfectly. The piezoelectric properties of a polycrystalline (ceramic) FE is inextricably related to the grain orientation distribution (texture). The set of combination of variables, known as solution space, which dictates the texture of a ceramic is unlimited and hence the choice of the optimal solution which maximizes the piezoelectricity is complicated. Thus, a stochastic global optimization combined with homogenization is employed for the identification of the optimal granular configuration of the FE ceramic microstructure with optimum piezoelectric properties. The macroscopic equilibrium piezoelectric properties of polycrystalline FE is calculated using mathematical homogenization at each iteration step. The configuration of grains characterized by its orientations at each iteration is generated using a randomly selected set of orientation distribution parameters. The optimization procedure applied to the single crystalline phase compares well with the experimental data. Apparent enhancement of piezoelectric coefficient d33 is observed in an optimally oriented BaTiO3 single crystal. Based on the good agreement of results with the published data in single crystals, we proceed to apply the methodology in polycrystals. A configuration of crystallites, simultaneously constraining the orientation distribution of the c-axis (polar axis) while incorporating ab-plane randomness, which would multiply the overall piezoelectricity in ceramic BaTiO3 is also identified. The orientation distribution of the c-axes is found to be a narrow Gaussian distribution centered around 45°. The piezoelectric coefficient in such a ceramic is found to
PARAMETER IDENTIFICATION AND STOCHASTIC CONTROL ...
African Journals Online (AJOL)
parameta identification examples treated in PART I. OPTIMAL PREDICTION. As aJ.ady discussed in PART I, a discrete linear system cm be modeled by the polynomial. A(z-1)y., = z°""B(z-1)ut + C(z-1)wt (15) where Yt is the output seq~. u the control. ""'l'mcc. IOl:l ~a 2m>-lDC8ll white process noise with variance q. dis the ...
Stochastic Modeling and Optimization in a Microgrid: A Survey
Directory of Open Access Journals (Sweden)
Hao Liang
2014-03-01
Full Text Available The future smart grid is expected to be an interconnected network of small-scale and self-contained microgrids, in addition to a large-scale electric power backbone. By utilizing microsources, such as renewable energy sources and combined heat and power plants, microgrids can supply electrical and heat loads in local areas in an economic and environment friendly way. To better adopt the intermittent and weather-dependent renewable power generation, energy storage devices, such as batteries, heat buffers and plug-in electric vehicles (PEVs with vehicle-to-grid systems can be integrated in microgrids. However, significant technical challenges arise in the planning, operation and control of microgrids, due to the randomness in renewable power generation, the buffering effect of energy storage devices and the high mobility of PEVs. The two-way communication functionalities of the future smart grid provide an opportunity to address these challenges, by offering the communication links for microgrid status information collection. However, how to utilize stochastic modeling and optimization tools for efficient, reliable and economic planning, operation and control of microgrids remains an open issue. In this paper, we investigate the key features of microgrids and provide a comprehensive literature survey on the stochastic modeling and optimization tools for a microgrid. Future research directions are also identified.
Stochastic control of traffic patterns
DEFF Research Database (Denmark)
Gaididei, Yuri B.; Gorria, Carlos; Berkemer, Rainer
2013-01-01
A stochastic modulation of the safety distance can reduce traffic jams. It is found that the effect of random modulation on congestive flow formation depends on the spatial correlation of the noise. Jam creation is suppressed for highly correlated noise. The results demonstrate the advantage of h...
Symposium on Optimal Control Theory
1987-01-01
Control theory can be roughly classified as deterministic or stochastic. Each of these can further be subdivided into game theory and optimal control theory. The central problem of control theory is the so called constrained maximization (which- with slight modifications--is equivalent to minimization). One can then say, heuristically, that the major problem of control theory is to find the maximum of some performance criterion (or criteria), given a set of constraints. The starting point is, of course, a mathematical representation of the performance criterion (or criteria)- sometimes called the objective functional--along with the constraints. When the objective functional is single valued (Le. , when there is only one objective to be maximized), then one is dealing with optimal control theory. When more than one objective is involved, and the objectives are generally incompatible, then one is dealing with game theory. The first paper deals with stochastic optimal control, using the dynamic programming ...
Optimal Computing Budget Allocation for Particle Swarm Optimization in Stochastic Optimization.
Zhang, Si; Xu, Jie; Lee, Loo Hay; Chew, Ek Peng; Wong, Wai Peng; Chen, Chun-Hung
2017-04-01
Particle Swarm Optimization (PSO) is a popular metaheuristic for deterministic optimization. Originated in the interpretations of the movement of individuals in a bird flock or fish school, PSO introduces the concept of personal best and global best to simulate the pattern of searching for food by flocking and successfully translate the natural phenomena to the optimization of complex functions. Many real-life applications of PSO cope with stochastic problems. To solve a stochastic problem using PSO, a straightforward approach is to equally allocate computational effort among all particles and obtain the same number of samples of fitness values. This is not an efficient use of computational budget and leaves considerable room for improvement. This paper proposes a seamless integration of the concept of optimal computing budget allocation (OCBA) into PSO to improve the computational efficiency of PSO for stochastic optimization problems. We derive an asymptotically optimal allocation rule to intelligently determine the number of samples for all particles such that the PSO algorithm can efficiently select the personal best and global best when there is stochastic estimation noise in fitness values. We also propose an easy-to-implement sequential procedure. Numerical tests show that our new approach can obtain much better results using the same amount of computational effort.
Stochastic Robust Mathematical Programming Model for Power System Optimization
Energy Technology Data Exchange (ETDEWEB)
Liu, Cong; Changhyeok, Lee; Haoyong, Chen; Mehrotra, Sanjay
2016-01-01
This paper presents a stochastic robust framework for two-stage power system optimization problems with uncertainty. The model optimizes the probabilistic expectation of different worst-case scenarios with ifferent uncertainty sets. A case study of unit commitment shows the effectiveness of the proposed model and algorithms.
Optimal protocols and optimal transport in stochastic thermodynamics.
Aurell, Erik; Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo
2011-06-24
Thermodynamics of small systems has become an important field of statistical physics. Such systems are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, and of which there are applications in cosmology, fluid mechanics, logistics, and many other fields. We show, in particular, that minimizing expected heat released or work done during a nonequilibrium transition in finite time is solved by the Burgers equation and mass transport by the Burgers velocity field. Our contribution hence considerably extends the range of solvable optimization problems in small system thermodynamics.
Stochastic control of inertial sea wave energy converter.
Raffero, Mattia; Martini, Michele; Passione, Biagio; Mattiazzo, Giuliana; Giorcelli, Ermanno; Bracco, Giovanni
2015-01-01
The ISWEC (inertial sea wave energy converter) is presented, its control problems are stated, and an optimal control strategy is introduced. As the aim of the device is energy conversion, the mean absorbed power by ISWEC is calculated for a plane 2D irregular sea state. The response of the WEC (wave energy converter) is driven by the sea-surface elevation, which is modeled by a stationary and homogeneous zero mean Gaussian stochastic process. System equations are linearized thus simplifying the numerical model of the device. The resulting response is obtained as the output of the coupled mechanic-hydrodynamic model of the device. A stochastic suboptimal controller, derived from optimal control theory, is defined and applied to ISWEC. Results of this approach have been compared with the ones obtained with a linear spring-damper controller, highlighting the capability to obtain a higher value of mean extracted power despite higher power peaks.
Stochastic Control of Inertial Sea Wave Energy Converter
Mattiazzo, Giuliana; Giorcelli, Ermanno
2015-01-01
The ISWEC (inertial sea wave energy converter) is presented, its control problems are stated, and an optimal control strategy is introduced. As the aim of the device is energy conversion, the mean absorbed power by ISWEC is calculated for a plane 2D irregular sea state. The response of the WEC (wave energy converter) is driven by the sea-surface elevation, which is modeled by a stationary and homogeneous zero mean Gaussian stochastic process. System equations are linearized thus simplifying the numerical model of the device. The resulting response is obtained as the output of the coupled mechanic-hydrodynamic model of the device. A stochastic suboptimal controller, derived from optimal control theory, is defined and applied to ISWEC. Results of this approach have been compared with the ones obtained with a linear spring-damper controller, highlighting the capability to obtain a higher value of mean extracted power despite higher power peaks. PMID:25874267
Stochastic Control of Energy Efficient Buildings: A Semidefinite Programming Approach
Energy Technology Data Exchange (ETDEWEB)
Ma, Xiao [ORNL; Dong, Jin [ORNL; Djouadi, Seddik M [ORNL; Nutaro, James J [ORNL; Kuruganti, Teja [ORNL
2015-01-01
The key goal in energy efficient buildings is to reduce energy consumption of Heating, Ventilation, and Air- Conditioning (HVAC) systems while maintaining a comfortable temperature and humidity in the building. This paper proposes a novel stochastic control approach for achieving joint performance and power control of HVAC. We employ a constrained Stochastic Linear Quadratic Control (cSLQC) by minimizing a quadratic cost function with a disturbance assumed to be Gaussian. The problem is formulated to minimize the expected cost subject to a linear constraint and a probabilistic constraint. By using cSLQC, the problem is reduced to a semidefinite optimization problem, where the optimal control can be computed efficiently by Semidefinite programming (SDP). Simulation results are provided to demonstrate the effectiveness and power efficiency by utilizing the proposed control approach.
Stochastic Control of Inertial Sea Wave Energy Converter
Directory of Open Access Journals (Sweden)
Mattia Raffero
2015-01-01
Full Text Available The ISWEC (inertial sea wave energy converter is presented, its control problems are stated, and an optimal control strategy is introduced. As the aim of the device is energy conversion, the mean absorbed power by ISWEC is calculated for a plane 2D irregular sea state. The response of the WEC (wave energy converter is driven by the sea-surface elevation, which is modeled by a stationary and homogeneous zero mean Gaussian stochastic process. System equations are linearized thus simplifying the numerical model of the device. The resulting response is obtained as the output of the coupled mechanic-hydrodynamic model of the device. A stochastic suboptimal controller, derived from optimal control theory, is defined and applied to ISWEC. Results of this approach have been compared with the ones obtained with a linear spring-damper controller, highlighting the capability to obtain a higher value of mean extracted power despite higher power peaks.
Trip-oriented stochastic optimal energy management strategy for plug-in hybrid electric bus
International Nuclear Information System (INIS)
Du, Yongchang; Zhao, Yue; Wang, Qinpu; Zhang, Yuanbo; Xia, Huaicheng
2016-01-01
A trip-oriented stochastic optimal energy management strategy for plug-in hybrid electric bus is presented in this paper, which includes the offline stochastic dynamic programming part and the online implementation part performed by equivalent consumption minimization strategy. In the offline part, historical driving cycles of the fixed route are divided into segments according to the position of bus stops, and then a segment-based stochastic driving condition model based on Markov chain is built. With the segment-based stochastic model obtained, the control set for real-time implemented equivalent consumption minimization strategy can be achieved by solving the offline stochastic dynamic programming problem. Results of stochastic dynamic programming are converted into a 3-dimensional lookup table of parameters for online implemented equivalent consumption minimization strategy. The proposed strategy is verified by both simulation and hardware-in-loop test of real-world driving cycle on an urban bus route. Simulation results show that the proposed method outperforms both the well-tuned equivalent consumption minimization strategy and the rule-based strategy in terms of fuel economy, and even proved to be close to the optimal result obtained by dynamic programming. Furthermore, the practical application potential of the proposed control method was proved by hardware-in-loop test. - Highlights: • A stochastic problem was formed based on a stochastic segment-based driving condition model. • Offline stochastic dynamic programming was employed to solve the stochastic problem. • The instant power split decision was made by the online equivalent consumption minimization strategy. • Good performance in fuel economy of the proposed method was verified by simulation results. • Practical application potential of the proposed method was verified by the hardware-in-loop test results.
A General Theory of Markovian Time Inconsistent Stochastic Control Problems
DEFF Research Database (Denmark)
Björk, Tomas; Murgochi, Agatha
We develop a theory for stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a Bellman optimality principle. We attach these problems by viewing them within a game theoretic framework, and we look for Nash subgame perfect equilibrium points...... examples of time inconsistency in the literature are easily seen to be special cases of the present theory. We also prove that for every time inconsistent problem, there exists an associated time consistent problem such that the optimal control and the optimal value function for the consistent problem...
Generating optimized stochastic power management strategies for electric car components
Energy Technology Data Exchange (ETDEWEB)
Fruth, Matthias [TraceTronic GmbH, Dresden (Germany); Bastian, Steve [Technische Univ. Dresden (Germany)
2012-11-01
With the increasing prevalence of electric vehicles, reducing the power consumption of car components becomes a necessity. For the example of a novel traffic-light assistance system, which makes speed recommendations based on the expected length of red-light phases, power-management strategies are used to control under which conditions radio communication, positioning systems and other components are switched to low-power (e.g. sleep) or high-power (e.g. idle/busy) states. We apply dynamic power management, an optimization technique well-known from other domains, in order to compute energy-optimal power-management strategies, sometimes resulting in these strategies being stochastic. On the example of the traffic-light assistant, we present a MATLAB/Simulink-implemented framework for the generation, simulation and formal analysis of optimized power-management strategies, which is based on this technique. We study capabilities and limitations of this approach and sketch further applications in the automotive domain. (orig.)
Optimal Maintenance for Stochastically Degrading Staellite Constellations
National Research Council Canada - National Science Library
Cook, Timothy J
2005-01-01
.... Previous work has developed a methodology to compute an optimal replacement policy for a satellite constellation in which satellites were viewed as binary entities, either operational or failed...
Optimal Tax Reduction by Depreciation : A Stochastic Model
Berg, M.; De Waegenaere, A.M.B.; Wielhouwer, J.L.
1996-01-01
This paper focuses on the choice of a depreciation method, when trying to minimize the expected value of the present value of future tax payments.In a quite general model that allows for stochastic future cash- ows and a tax structure with tax brackets, we determine the optimal choice between the
Enhancement of Stochastic Resonance Using Optimization Theory
National Research Council Canada - National Science Library
Wu, Xingxing; Jiang, Zhong-Ping; Repperger, Daniel W; Guo, Yi
2006-01-01
.... The further improvement of the maximal normalized power norm of the bistable double-well dynamic system with white Gaussian noise input can be converted to an optimization problem with constraints...
Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints
International Nuclear Information System (INIS)
Pham, H.
2002-01-01
This paper deals with an extension of Merton's optimal investment problem to a multidimensional model with stochastic volatility and portfolio constraints. The classical dynamic programming approach leads to a characterization of the value function as a viscosity solution of the highly nonlinear associated Bellman equation. A logarithmic transformation expresses the value function in terms of the solution to a semilinear parabolic equation with quadratic growth on the derivative term. Using a stochastic control representation and some approximations, we prove the existence of a smooth solution to this semilinear equation. An optimal portfolio is shown to exist, and is expressed in terms of the classical solution to this semilinear equation. This reduction is useful for studying numerical schemes for both the value function and the optimal portfolio. We illustrate our results with several examples of stochastic volatility models popular in the financial literature
Stochastic Optimal Prediction with Application to Averaged Euler Equations
Energy Technology Data Exchange (ETDEWEB)
Bell, John [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Chorin, Alexandre J. [Univ. of California, Berkeley, CA (United States); Crutchfield, William [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2017-04-24
Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the Bayesian sense. In first-order OP, unresolved information is approximated by its conditional expectation with respect to the invariant measure. In higher-order OP, unresolved information is approximated by a stochastic estimator, leading to a system of random or stochastic differential equations. We explain the ideas through a simple example, and then apply them to the solution of Averaged Euler equations in two space dimensions.
Adaptively optimizing stochastic resonance in visual system
Yang, Tao
1998-08-01
Recent psychophysics experiment has showed that the noise strength could affect the perceived image quality. This work gives an adaptive process for achieving the optimal perceived image quality in a simple image perception array, which is a simple model of an image sensor. A reference image from memory is used for constructing a cost function and defining the optimal noise strength where the cost function gets its minimum point. The reference image is a binary image, which is used to define the background and the object. Finally, an adaptive algorithm is proposed for searching the optimal noise strength. Computer experimental results show that if the reference image is a thresholded version of the sub-threshold input image then the output of the sensor array gives an optimal output, in which the background and the object have the biggest contrast. If the reference image is different from a thresholded version of the sub-threshold input image then the output usually gives a sub-optimal contrast between the object and the background.
Studies in the Control of Stochastic Systems
2017-10-31
control of continuous time stochastic systems with noise that is Brownian motions or fractional Brownian motions, the control of discrete time...in both continuous and discrete time. All of the above types of problems have been studied with the support of this grant. The achievement of these...scientists and engineers. 2. Math Awareness Months (MAM) (Every April for the past twenty-three years) Agenda: workshops each year for fifth
Stochastic Optimization for Nuclear Facility Deployment Scenarios
Hays, Ross Daniel
Single-use, low-enriched uranium oxide fuel, consumed through several cycles in a light-water reactor (LWR) before being disposed, has become the dominant source of commercial-scale nuclear electric generation in the United States and throughout the world. However, it is not without its drawbacks and is not the only potential nuclear fuel cycle available. Numerous alternative fuel cycles have been proposed at various times which, through the use of different reactor and recycling technologies, offer to counteract many of the perceived shortcomings with regards to waste management, resource utilization, and proliferation resistance. However, due to the varying maturity levels of these technologies, the complicated material flow feedback interactions their use would require, and the large capital investments in the current technology, one should not deploy these advanced designs without first investigating the potential costs and benefits of so doing. As the interactions among these systems can be complicated, and the ways in which they may be deployed are many, the application of automated numerical optimization to the simulation of the fuel cycle could potentially be of great benefit to researchers and interested policy planners. To investigate the potential of these methods, a computational program has been developed that applies a parallel, multi-objective simulated annealing algorithm to a computational optimization problem defined by a library of relevant objective functions applied to the Ver ifiable Fuel Cycle Simulati on Model (VISION, developed at the Idaho National Laboratory). The VISION model, when given a specified fuel cycle deployment scenario, computes the numbers and types of, and construction, operation, and utilization schedules for, the nuclear facilities required to meet a predetermined electric power demand function. Additionally, it calculates the location and composition of the nuclear fuels within the fuel cycle, from initial mining through
Discrete stochastic processes and optimal filtering
Bertein, Jean-Claude
2012-01-01
Optimal filtering applied to stationary and non-stationary signals provides the most efficient means of dealing with problems arising from the extraction of noise signals. Moreover, it is a fundamental feature in a range of applications, such as in navigation in aerospace and aeronautics, filter processing in the telecommunications industry, etc. This book provides a comprehensive overview of this area, discussing random and Gaussian vectors, outlining the results necessary for the creation of Wiener and adaptive filters used for stationary signals, as well as examining Kalman filters which ar
Qualitative and Quantitative Integrated Modeling for Stochastic Simulation and Optimization
Directory of Open Access Journals (Sweden)
Xuefeng Yan
2013-01-01
Full Text Available The simulation and optimization of an actual physics system are usually constructed based on the stochastic models, which have both qualitative and quantitative characteristics inherently. Most modeling specifications and frameworks find it difficult to describe the qualitative model directly. In order to deal with the expert knowledge, uncertain reasoning, and other qualitative information, a qualitative and quantitative combined modeling specification was proposed based on a hierarchical model structure framework. The new modeling approach is based on a hierarchical model structure which includes the meta-meta model, the meta-model and the high-level model. A description logic system is defined for formal definition and verification of the new modeling specification. A stochastic defense simulation was developed to illustrate how to model the system and optimize the result. The result shows that the proposed method can describe the complex system more comprehensively, and the survival probability of the target is higher by introducing qualitative models into quantitative simulation.
COOMA: AN OBJECT-ORIENTED STOCHASTIC OPTIMIZATION ALGORITHM
Directory of Open Access Journals (Sweden)
Stanislav Alexandrovich Tavridovich
2017-09-01
Full Text Available Stochastic optimization methods such as genetic algorithm, particle swarm optimization algorithm, and others are successfully used to solve optimization problems. They are all based on similar ideas and need minimal adaptation when being implemented. But several factors complicate the application of stochastic search methods in practice: multimodality of the objective function, optimization with constraints, finding the best parameter configuration of the algorithm, the increasing of the searching space, etc. This paper proposes a new Cascade Object Optimization and Modification Algorithm (COOMA which develops the best ideas of known stochastic optimization methods and can be applied to a wide variety of real-world problems described in the terms of object-oriented models with practically any types of parameters, variables, and associations between objects. The objects of different classes are organized in pools and pools form the hierarchical structure according to the associations between classes. The algorithm is also executed according to the pool structure: the methods of the upper-level pools before changing their objects call the analogous methods of all their subpools. The algorithm starts with initialization step and then passes through a number of iterations during which the objects are modified until the stop criteria are satisfied. The objects are modified using movement, replication and mutation operations. Two-level version of COOMA realizes a built-in self-adaptive mechanism. The optimization statistics for a number of test problems shows that COOMA is able to solve multi-level problems (with objects of different associated classes, problems with multimodal fitness functions and systems of constraints. COOMA source code on Java is available on request.
Stochastic search in structural optimization - Genetic algorithms and simulated annealing
Hajela, Prabhat
1993-01-01
An account is given of illustrative applications of genetic algorithms and simulated annealing methods in structural optimization. The advantages of such stochastic search methods over traditional mathematical programming strategies are emphasized; it is noted that these methods offer a significantly higher probability of locating the global optimum in a multimodal design space. Both genetic-search and simulated annealing can be effectively used in problems with a mix of continuous, discrete, and integer design variables.
Stochastic control applied to the ISWEC Wave Energy System
International Nuclear Information System (INIS)
Bracco, Giovanni; Casassa, Maria; Giorcelli, Ermanno; Mattiazzo, Giuliana; Passione, Biagio; Raffero, Mattia; Vissio, Giacomo; Martini, Michele
2015-01-01
ISWEC (Inertial Sea Wave Energy Converter) is a floating marine device able to harvest sea waves energy by the interaction between the pitching motion of a floater and a spinning flywheel which can drive an electric PTO. In the ISWEC the hull dynamics is governed and controlled by the gyroscopic torque. The optimal control logic results in tuning the floater dynamics to the incoming waves in order to maximize the power transfer from the waves to the floater. In this paper the control problems of the ISWEC are stated and a control scheme based on the sub-optimal stochastic control logic is presented. The control scheme here presented has been tested using real wave records acquired at the deployment location in Pantelleria Island, which is one of the most energetic sites of the Mediterranean Sea.
Essays on variational approximation techniques for stochastic optimization problems
Deride Silva, Julio A.
This dissertation presents five essays on approximation and modeling techniques, based on variational analysis, applied to stochastic optimization problems. It is divided into two parts, where the first is devoted to equilibrium problems and maxinf optimization, and the second corresponds to two essays in statistics and uncertainty modeling. Stochastic optimization lies at the core of this research as we were interested in relevant equilibrium applications that contain an uncertain component, and the design of a solution strategy. In addition, every stochastic optimization problem relies heavily on the underlying probability distribution that models the uncertainty. We studied these distributions, in particular, their design process and theoretical properties such as their convergence. Finally, the last aspect of stochastic optimization that we covered is the scenario creation problem, in which we described a procedure based on a probabilistic model to create scenarios for the applied problem of power estimation of renewable energies. In the first part, Equilibrium problems and maxinf optimization, we considered three Walrasian equilibrium problems: from economics, we studied a stochastic general equilibrium problem in a pure exchange economy, described in Chapter 3, and a stochastic general equilibrium with financial contracts, in Chapter 4; finally from engineering, we studied an infrastructure planning problem in Chapter 5. We stated these problems as belonging to the maxinf optimization class and, in each instance, we provided an approximation scheme based on the notion of lopsided convergence and non-concave duality. This strategy is the foundation of the augmented Walrasian algorithm, whose convergence is guaranteed by lopsided convergence, that was implemented computationally, obtaining numerical results for relevant examples. The second part, Essays about statistics and uncertainty modeling, contains two essays covering a convergence problem for a sequence
Stochastic Control Synthesis of Systems with Structured Uncertainty
Padula, Sharon L. (Technical Monitor); Crespo, Luis G.
2003-01-01
This paper presents a study on the design of robust controllers by using random variables to model structured uncertainty for both SISO and MIMO feedback systems. Once the parameter uncertainty is prescribed with probability density functions, its effects are propagated through the analysis leading to stochastic metrics for the system's output. Control designs that aim for satisfactory performances while guaranteeing robust closed loop stability are attained by solving constrained non-linear optimization problems in the frequency domain. This approach permits not only to quantify the probability of having unstable and unfavorable responses for a particular control design but also to search for controls while favoring the values of the parameters with higher chance of occurrence. In this manner, robust optimality is achieved while the characteristic conservatism of conventional robust control methods is eliminated. Examples that admit closed form expressions for the probabilistic metrics of the output are used to elucidate the nature of the problem at hand and validate the proposed formulations.
Quantization of dynamical systems and stochastic control theory
International Nuclear Information System (INIS)
Guerra, F.; Morato, L.M.
1982-09-01
In the general framework of stochastic control theory we introduce a suitable form of stochastic action associated to the controlled process. Then a variational principle gives all main features of Nelson's stochastic mechanics. In particular we derive the expression of the current velocity field as the gradient of the phase action. Moreover the stochastic corrections to the Hamilton-Jacobi equation are in agreement with the quantum mechanical form of the Madelung fluid (equivalent to the Schroedinger equation). Therefore stochastic control theory can provide a very simple model simulating quantum mechanical behavior
Directory of Open Access Journals (Sweden)
M. Boychuk
2015-10-01
Full Text Available The activity of distribution companies is multifaceted. Ihey establish contacts with producers and consumers, determine the range of prices of medicines, do promotions, hold stocks of pharmaceuticals and take risks in their further selling.Their internal problems are complicated by the political crisis in the country, decreased purchasing power of national currency, and the rise in interest rates on loans. Therefore the usage of stochastic models of dynamic systems for the research into optimizing the management of pharmaceutical products distribution companies taking into account credit payments is of great current interest. A stochastic model of the optimal credit strategy of a pharmaceutical distributor in the market of pharmaceutical products has been constructed in the article considering credit payments and income limitations. From the mathematical point of view the obtained problem is the one of stochastic optimal control where the amount of monetary credit is the control and the amount of pharmaceutical product is the solution curve. The model allows to identify the optimal cash loan and the corresponding optimal quantity of pharmaceutical product that comply with the differential model of the existing quantity of pharmaceutical products in the form of Ito; the condition of the existing initial stock of pharmaceutical products; the limitation on the amount of credit and profit received from the product selling and maximize the average integral income. The research of the stochastic optimal control problem involves the construction of the left process of crediting with determination of the shift point of that control, the choice of the right crediting process and the formation of the optimal credit process. It was found that the optimal control of the credit amount and the shift point of that control are the determined values and don’t depend on the coefficient in the Wiener process and the optimal trajectory of the amount of
Local Approximation and Hierarchical Methods for Stochastic Optimization
Cheng, Bolong
In this thesis, we present local and hierarchical approximation methods for two classes of stochastic optimization problems: optimal learning and Markov decision processes. For the optimal learning problem class, we introduce a locally linear model with radial basis function for estimating the posterior mean of the unknown objective function. The method uses a compact representation of the function which avoids storing the entire history, as is typically required by nonparametric methods. We derive a knowledge gradient policy with the locally parametric model, which maximizes the expected value of information. We show the policy is asymptotically optimal in theory, and experimental works suggests that the method can reliably find the optimal solution on a range of test functions. For the Markov decision processes problem class, we are motivated by an application where we want to co-optimize a battery for multiple revenue, in particular energy arbitrage and frequency regulation. The nature of this problem requires the battery to make charging and discharging decisions at different time scales while accounting for the stochastic information such as load demand, electricity prices, and regulation signals. Computing the exact optimal policy becomes intractable due to the large state space and the number of time steps. We propose two methods to circumvent the computation bottleneck. First, we propose a nested MDP model that structure the co-optimization problem into smaller sub-problems with reduced state space. This new model allows us to understand how the battery behaves down to the two-second dynamics (that of the frequency regulation market). Second, we introduce a low-rank value function approximation for backward dynamic programming. This new method only requires computing the exact value function for a small subset of the state space and approximate the entire value function via low-rank matrix completion. We test these methods on historical price data from the
Switching neuronal state: optimal stimuli revealed using a stochastically-seeded gradient algorithm.
Chang, Joshua; Paydarfar, David
2014-12-01
Inducing a switch in neuronal state using energy optimal stimuli is relevant to a variety of problems in neuroscience. Analytical techniques from optimal control theory can identify such stimuli; however, solutions to the optimization problem using indirect variational approaches can be elusive in models that describe neuronal behavior. Here we develop and apply a direct gradient-based optimization algorithm to find stimulus waveforms that elicit a change in neuronal state while minimizing energy usage. We analyze standard models of neuronal behavior, the Hodgkin-Huxley and FitzHugh-Nagumo models, to show that the gradient-based algorithm: (1) enables automated exploration of a wide solution space, using stochastically generated initial waveforms that converge to multiple locally optimal solutions; and (2) finds optimal stimulus waveforms that achieve a physiological outcome condition, without a priori knowledge of the optimal terminal condition of all state variables. Analysis of biological systems using stochastically-seeded gradient methods can reveal salient dynamical mechanisms underlying the optimal control of system behavior. The gradient algorithm may also have practical applications in future work, for example, finding energy optimal waveforms for therapeutic neural stimulation that minimizes power usage and diminishes off-target effects and damage to neighboring tissue.
Real-Time Demand Side Management Algorithm Using Stochastic Optimization
Directory of Open Access Journals (Sweden)
Moses Amoasi Acquah
2018-05-01
Full Text Available A demand side management technique is deployed along with battery energy-storage systems (BESS to lower the electricity cost by mitigating the peak load of a building. Most of the existing methods rely on manual operation of the BESS, or even an elaborate building energy-management system resorting to a deterministic method that is susceptible to unforeseen growth in demand. In this study, we propose a real-time optimal operating strategy for BESS based on density demand forecast and stochastic optimization. This method takes into consideration uncertainties in demand when accounting for an optimal BESS schedule, making it robust compared to the deterministic case. The proposed method is verified and tested against existing algorithms. Data obtained from a real site in South Korea is used for verification and testing. The results show that the proposed method is effective, even for the cases where the forecasted demand deviates from the observed demand.
An intelligent stochastic optimization routine for nuclear fuel cycle design
International Nuclear Information System (INIS)
Parks, G.T.
1990-01-01
A simulated annealing (Metropolis algorithm) optimization routine named AMETROP, which has been developed for use on realistic nuclear fuel cycle problems, is introduced. Each stage of the algorithm is described and the means by which it overcomes or avoids the difficulties posed to conventional optimization routines by such problems are explained. Special attention is given to innovations that enhance AMETROP's performance both through artificial intelligence features, in which the routine uses the accumulation of data to influence its future actions, and through a family of simple performance aids, which allow the designer to use his heuristic knowledge to guide the routine's essentially random search. Using examples from a typical fuel cycle optimization problem, the performance of the stochastic Metropolis algorithm is compared to that of the only suitable deterministic routine in a standard software library, showing AMETROP to have many advantages
Initiating stochastic maintenance optimization at Candu Power Plants
International Nuclear Information System (INIS)
Doyle, E.K.
2003-01-01
As previously reported at ICONE 6 in New Orleans (1996), the use of various innovative maintenance optimization techniques at Bruce has lead to cost effective preventive maintenance applications for complex systems. Further cost refinement of the station maintenance strategy is being evaluated via the applicability of statistical analysis of historical failure data. Since the statistical evaluation was initiated in 1999 significant progress has been made in demonstrating the viability of stochastic methods in Candu maintenance. Some of the relevant results were presented at ICONE 10 in Washington DC (2002). Success with the graphical displays and the relatively easy to implement stochastic computer programs was sufficient to move the program along to the next significant phase. This next phase consists of investigating the validity of using subjective elicitation techniques to obtain component lifetime distributions. This technique provides access to the elusive failure statistics, the lack of which is often referred to in the literature as the principle impediment preventing the use of stochastic methods in large industry. At the same time the technique allows very valuable information to be captured from the fast retiring 'baby boom generation'. Initial indications have been quite positive. (author)
Stochastic Modelling and Optimization of Complex Infrastructure Systems
DEFF Research Database (Denmark)
Thoft-Christensen, Palle
In this paper it is shown that recent progress in stochastic modelling and optimization in combination with advanced computer systems has now made it possible to improve the design and the maintenance strategies for infrastructure systems. The paper concentrates on highway networks and single large...... bridges. united states has perhaps the largest highway networks in the world with more than 0.5 million highway bridges; see Chase, S.B. 1999. About 40% of these bridges are considered deficient and more than $50 billion is estimated needed to correct the deficiencies; see Roberts, J.E. 2001...
Optimizing ZigBee Security using Stochastic Model Checking
DEFF Research Database (Denmark)
Yuksel, Ender; Nielson, Hanne Riis; Nielson, Flemming
, we identify an important gap in the specification on key updates, and present a methodology for determining optimal key update policies and security parameters. We exploit the stochastic model checking approach using the probabilistic model checker PRISM, and assess the security needs for realistic......ZigBee is a fairly new but promising wireless sensor network standard that offers the advantages of simple and low resource communication. Nevertheless, security is of great concern to ZigBee, and enhancements are prescribed in the latest ZigBee specication: ZigBee-2007. In this technical report...
Using linear programming to analyze and optimize stochastic flow lines
DEFF Research Database (Denmark)
Helber, Stefan; Schimmelpfeng, Katja; Stolletz, Raik
2011-01-01
This paper presents a linear programming approach to analyze and optimize flow lines with limited buffer capacities and stochastic processing times. The basic idea is to solve a huge but simple linear program that models an entire simulation run of a multi-stage production process in discrete time...... programming and hence allows us to solve buffer allocation problems. We show under which conditions our method works well by comparing its results to exact values for two-machine models and approximate simulation results for longer lines....
Computing the optimal path in stochastic dynamical systems
International Nuclear Information System (INIS)
Bauver, Martha; Forgoston, Eric; Billings, Lora
2016-01-01
In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high-dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a two-dimensional system that describes a single population with internal noise. This model has an analytical solution for the optimal path. The numerical solution found using our computational method agrees well with the analytical result. The second example is a more complicated four-dimensional system where our numerical method must be used to find the optimal path. The third example, although a seemingly simple two-dimensional system, demonstrates the success of our method in finding the optimal path where other numerical methods are known to fail. In the fourth example, the optimal path lies in six-dimensional space and demonstrates the power of our method in computing paths in higher-dimensional spaces.
Stochastic synchronization of coupled neural networks with intermittent control
International Nuclear Information System (INIS)
Yang Xinsong; Cao Jinde
2009-01-01
In this Letter, we study the exponential stochastic synchronization problem for coupled neural networks with stochastic noise perturbations. Based on Lyapunov stability theory, inequality techniques, the properties of Weiner process, and adding different intermittent controllers, several sufficient conditions are obtained to ensure exponential stochastic synchronization of coupled neural networks with or without coupling delays under stochastic perturbations. These stochastic synchronization criteria are expressed in terms of several lower-dimensional linear matrix inequalities (LMIs) and can be easily verified. Moreover, the results of this Letter are applicable to both directed and undirected weighted networks. A numerical example and its simulations are offered to show the effectiveness of our new results.
Stochastic analysis and robust optimization for a deck lid inner panel stamping
International Nuclear Information System (INIS)
Hou, Bo; Wang, Wurong; Li, Shuhui; Lin, Zhongqin; Xia, Z. Cedric
2010-01-01
FE-simulation and optimization are widely used in the stamping process to improve design quality and shorten development cycle. However, the current simulation and optimization may lead to non-robust results due to not considering the variation of material and process parameters. In this study, a novel stochastic analysis and robust optimization approach is proposed to improve the stamping robustness, where the uncertainties are involved to reflect manufacturing reality. A meta-model based stochastic analysis method is developed, where FE-simulation, uniform design and response surface methodology (RSM) are used to construct meta-model, based on which Monte-Carlo simulation is performed to predict the influence of input parameters variation on the final product quality. By applying the stochastic analysis, uniform design and RSM, the mean and the standard deviation (SD) of product quality are calculated as functions of the controllable process parameters. The robust optimization model composed of mean and SD is constructed and solved, the result of which is compared with the deterministic one to show its advantages. It is demonstrated that the product quality variations are reduced significantly, and quality targets (reject rate) are achieved under the robust optimal solution. The developed approach offers rapid and reliable results for engineers to deal with potential stamping problems during the early phase of product and tooling design, saving more time and resources.
Computing Optimal Stochastic Portfolio Execution Strategies: A Parametric Approach Using Simulations
Moazeni, Somayeh; Coleman, Thomas F.; Li, Yuying
2010-09-01
Computing optimal stochastic portfolio execution strategies under appropriate risk consideration presents great computational challenge. We investigate a parametric approach for computing optimal stochastic strategies using Monte Carlo simulations. This approach allows reduction in computational complexity by computing coefficients for a parametric representation of a stochastic dynamic strategy based on static optimization. Using this technique, constraints can be similarly handled using appropriate penalty functions. We illustrate the proposed approach to minimize the expected execution cost and Conditional Value-at-Risk (CVaR).
Stochastic chaos in a Duffing oscillator and its control
International Nuclear Information System (INIS)
Wu Cunli; Lei Youming; Fang Tong
2006-01-01
Stochastic chaos discussed here means a kind of chaotic responses in a Duffing oscillator with bounded random parameters under harmonic excitations. A system with random parameters is usually called a stochastic system. The modifier 'stochastic' here implies dependent on some random parameter. As the system itself is stochastic, so is the response, even under harmonic excitations alone. In this paper stochastic chaos and its control are verified by the top Lyapunov exponent of the system. A non-feedback control strategy is adopted here by adding an adjustable noisy phase to the harmonic excitation, so that the control can be realized by adjusting the noise level. It is found that by this control strategy stochastic chaos can be tamed down to the small neighborhood of a periodic trajectory or an equilibrium state. In the analysis the stochastic Duffing oscillator is first transformed into an equivalent deterministic nonlinear system by the Gegenbauer polynomial approximation, so that the problem of controlling stochastic chaos can be reduced into the problem of controlling deterministic chaos in the equivalent system. Then the top Lyapunov exponent of the equivalent system is obtained by Wolf's method to examine the chaotic behavior of the response. Numerical simulations show that the random phase control strategy is an effective way to control stochastic chaos
Stochastic optimization of subprime residential mortgage loan funding and its risks / by B. de Waal
De Waal, Bernadine
2010-01-01
The subprime mortgage crisis (SMC) is an ongoing housing and nancial crisis that was triggered by a marked increase in mortgage delinquencies and foreclosures in the U.S. It has had major adverse consequences for banks and nancial markets around the globe since it became apparent in 2007. In our research, we examine an originator's (OR's) nonlinear stochastic optimal control problem related to choices regarding deposit inflow rates and marketable securities allocation. Here, ...
Problems of Mathematical Finance by Stochastic Control Methods
Stettner, Łukasz
The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.
Optimal control of hydroelectric facilities
Zhao, Guangzhi
This thesis considers a simple yet realistic model of pump-assisted hydroelectric facilities operating in a market with time-varying but deterministic power prices. Both deterministic and stochastic water inflows are considered. The fluid mechanical and engineering details of the facility are described by a model containing several parameters. We present a dynamic programming algorithm for optimizing either the total energy produced or the total cash generated by these plants. The algorithm allows us to give the optimal control strategy as a function of time and to see how this strategy, and the associated plant value, varies with water inflow and electricity price. We investigate various cases. For a single pumped storage facility experiencing deterministic power prices and water inflows, we investigate the varying behaviour for an oversimplified constant turbine- and pump-efficiency model with simple reservoir geometries. We then generalize this simple model to include more realistic turbine efficiencies, situations with more complicated reservoir geometry, and the introduction of dissipative switching costs between various control states. We find many results which reinforce our physical intuition about this complicated system as well as results which initially challenge, though later deepen, this intuition. One major lesson of this work is that the optimal control strategy does not differ much between two differing objectives of maximizing energy production and maximizing its cash value. We then turn our attention to the case of stochastic water inflows. We present a stochastic dynamic programming algorithm which can find an on-average optimal control in the face of this randomness. As the operator of a facility must be more cautious when inflows are random, the randomness destroys facility value. Following this insight we quantify exactly how much a perfect hydrological inflow forecast would be worth to a dam operator. In our final chapter we discuss the
A New Control Paradigm for Stochastic Differential Equations
Schmid, Matthias J. A.
This study presents a novel comprehensive approach to the control of dynamic systems under uncertainty governed by stochastic differential equations (SDEs). Large Deviations (LD) techniques are employed to arrive at a control law for a large class of nonlinear systems minimizing sample path deviations. Thereby, a paradigm shift is suggested from point-in-time to sample path statistics on function spaces. A suitable formal control framework which leverages embedded Freidlin-Wentzell theory is proposed and described in detail. This includes the precise definition of the control objective and comprises an accurate discussion of the adaptation of the Freidlin-Wentzell theorem to the particular situation. The new control design is enabled by the transformation of an ill-posed control objective into a well-conditioned sequential optimization problem. A direct numerical solution process is presented using quadratic programming, but the emphasis is on the development of a closed-form expression reflecting the asymptotic deviation probability of a particular nominal path. This is identified as the key factor in the success of the new paradigm. An approach employing the second variation and the differential curvature of the effective action is suggested for small deviation channels leading to the Jacobi field of the rate function and the subsequently introduced Jacobi field performance measure. This closed-form solution is utilized in combination with the supplied parametrization of the objective space. For the first time, this allows for an LD based control design applicable to a large class of nonlinear systems. Thus, Minimum Large Deviations (MLD) control is effectively established in a comprehensive structured framework. The construction of the new paradigm is completed by an optimality proof for the Jacobi field performance measure, an interpretive discussion, and a suggestion for efficient implementation. The potential of the new approach is exhibited by its extension
Annealing evolutionary stochastic approximation Monte Carlo for global optimization
Liang, Faming
2010-01-01
outperform simulated annealing, the genetic algorithm, annealing stochastic approximation Monte Carlo, and some other metaheuristics in function optimization. © 2010 Springer Science+Business Media, LLC.
National Research Council Canada - National Science Library
Khoo, Wai
1999-01-01
.... These problems model stochastic portfolio optimization problems (SPOPs) which assume deterministic unit weight, and normally distributed unit return with known mean and variance for each item type...
Optimal Integration of Intermittent Renewables: A System LCOE Stochastic Approach
Directory of Open Access Journals (Sweden)
Carlo Lucheroni
2018-03-01
Full Text Available We propose a system level approach to value the impact on costs of the integration of intermittent renewable generation in a power system, based on expected breakeven cost and breakeven cost risk. To do this, we carefully reconsider the definition of Levelized Cost of Electricity (LCOE when extended to non-dispatchable generation, by examining extra costs and gains originated by the costly management of random power injections. We are thus lead to define a ‘system LCOE’ as a system dependent LCOE that takes properly into account intermittent generation. In order to include breakeven cost risk we further extend this deterministic approach to a stochastic setting, by introducing a ‘stochastic system LCOE’. This extension allows us to discuss the optimal integration of intermittent renewables from a broad, system level point of view. This paper thus aims to provide power producers and policy makers with a new methodological scheme, still based on the LCOE but which updates this valuation technique to current energy system configurations characterized by a large share of non-dispatchable production. Quantifying and optimizing the impact of intermittent renewables integration on power system costs, risk and CO 2 emissions, the proposed methodology can be used as powerful tool of analysis for assessing environmental and energy policies.
Stochastic simulation and robust design optimization of integrated photonic filters
Directory of Open Access Journals (Sweden)
Weng Tsui-Wei
2016-07-01
Full Text Available Manufacturing variations are becoming an unavoidable issue in modern fabrication processes; therefore, it is crucial to be able to include stochastic uncertainties in the design phase. In this paper, integrated photonic coupled ring resonator filters are considered as an example of significant interest. The sparsity structure in photonic circuits is exploited to construct a sparse combined generalized polynomial chaos model, which is then used to analyze related statistics and perform robust design optimization. Simulation results show that the optimized circuits are more robust to fabrication process variations and achieve a reduction of 11%–35% in the mean square errors of the 3 dB bandwidth compared to unoptimized nominal designs.
A stochastic discrete optimization model for designing container terminal facilities
Zukhruf, Febri; Frazila, Russ Bona; Burhani, Jzolanda Tsavalista
2017-11-01
As uncertainty essentially affect the total transportation cost, it remains important in the container terminal that incorporates several modes and transshipments process. This paper then presents a stochastic discrete optimization model for designing the container terminal, which involves the decision of facilities improvement action. The container terminal operation model is constructed by accounting the variation of demand and facilities performance. In addition, for illustrating the conflicting issue that practically raises in the terminal operation, the model also takes into account the possible increment delay of facilities due to the increasing number of equipment, especially the container truck. Those variations expectantly reflect the uncertainty issue in the container terminal operation. A Monte Carlo simulation is invoked to propagate the variations by following the observed distribution. The problem is constructed within the framework of the combinatorial optimization problem for investigating the optimal decision of facilities improvement. A new variant of glow-worm swarm optimization (GSO) is thus proposed for solving the optimization, which is rarely explored in the transportation field. The model applicability is tested by considering the actual characteristics of the container terminal.
Using genetic algorithm to solve a new multi-period stochastic optimization model
Zhang, Xin-Li; Zhang, Ke-Cun
2009-09-01
This paper presents a new asset allocation model based on the CVaR risk measure and transaction costs. Institutional investors manage their strategic asset mix over time to achieve favorable returns subject to various uncertainties, policy and legal constraints, and other requirements. One may use a multi-period portfolio optimization model in order to determine an optimal asset mix. Recently, an alternative stochastic programming model with simulated paths was proposed by Hibiki [N. Hibiki, A hybrid simulation/tree multi-period stochastic programming model for optimal asset allocation, in: H. Takahashi, (Ed.) The Japanese Association of Financial Econometrics and Engineering, JAFFE Journal (2001) 89-119 (in Japanese); N. Hibiki A hybrid simulation/tree stochastic optimization model for dynamic asset allocation, in: B. Scherer (Ed.), Asset and Liability Management Tools: A Handbook for Best Practice, Risk Books, 2003, pp. 269-294], which was called a hybrid model. However, the transaction costs weren't considered in that paper. In this paper, we improve Hibiki's model in the following aspects: (1) The risk measure CVaR is introduced to control the wealth loss risk while maximizing the expected utility; (2) Typical market imperfections such as short sale constraints, proportional transaction costs are considered simultaneously. (3) Applying a genetic algorithm to solve the resulting model is discussed in detail. Numerical results show the suitability and feasibility of our methodology.
Process theory for supervisory control of stochastic systems with data
Markovski, J.
2012-01-01
We propose a process theory for supervisory control of stochastic nondeterministic plants with data-based observations. The Markovian process theory with data relies on the notion of Markovian partial bisimulation to capture controllability of stochastic nondeterministic systems. It presents a
On the Use of Information Quality in Stochastic Networked Control Systems
DEFF Research Database (Denmark)
Olsen, Rasmus Løvenstein; Madsen, Jacob Theilgaard; Rasmussen, Jakob Gulddahl
2017-01-01
Networked control is challenged by stochastic delays that are caused by the communication networks as well as by the approach taken to exchange information about system state and set-points. Combined with stochastic changing information, there is a probability that information at the controller....... This is first analyzed in simulation models for the example system of a wind-farm controller. As simulation analysis is subject to stochastic variability and requires large computational effort, the paper develops a Markov model of a simplified networked control system and uses numerical results from the Markov...... is not matching the true system observation, which we call mismatch probability (mmPr). The hypothesis is that the optimization of certain parameters of networked control systems targeting mmPr is equivalent to the optimization targeting control performance, while the former is practically much easier to conduct...
Topologically determined optimal stochastic resonance responses of spatially embedded networks
International Nuclear Information System (INIS)
Gosak, Marko; Marhl, Marko; Korosak, Dean
2011-01-01
We have analyzed the stochastic resonance phenomenon on spatial networks of bistable and excitable oscillators, which are connected according to their location and the amplitude of external forcing. By smoothly altering the network topology from a scale-free (SF) network with dominating long-range connections to a network where principally only adjacent oscillators are connected, we reveal that besides an optimal noise intensity, there is also a most favorable interaction topology at which the best correlation between the response of the network and the imposed weak external forcing is achieved. For various distributions of the amplitudes of external forcing, the optimal topology is always found in the intermediate regime between the highly heterogeneous SF network and the strong geometric regime. Our findings thus indicate that a suitable number of hubs and with that an optimal ratio between short- and long-range connections is necessary in order to obtain the best global response of a spatial network. Furthermore, we link the existence of the optimal interaction topology to a critical point indicating the transition from a long-range interactions-dominated network to a more lattice-like network structure.
Controlled Nonlinear Stochastic Delay Equations: Part I: Modeling and Approximations
International Nuclear Information System (INIS)
Kushner, Harold J.
2012-01-01
This two-part paper deals with “foundational” issues that have not been previously considered in the modeling and numerical optimization of nonlinear stochastic delay systems. There are new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. There are two basic and interconnected themes for these models. The first, dealt with in this part, concerns the definition of admissible control. The classical definition of an admissible control as a nonanticipative relaxed control is inadequate for these models and needs to be extended. This is needed for the convergence proofs of numerical approximations for optimal controls as well as to have a well-defined model. It is shown that the new classes of admissible controls do not enlarge the range of the value functions, is closed (together with the associated paths) under weak convergence, and is approximatable by ordinary controls. The second theme, dealt with in Part II, concerns transportation equation representations, and their role in the development of numerical algorithms with much reduced memory and computational requirements.
Momoh, James A.; Salkuti, Surender Reddy
2016-06-01
This paper proposes a stochastic optimization technique for solving the Voltage/VAr control problem including the load demand and Renewable Energy Resources (RERs) variation. The RERs often take along some inputs like stochastic behavior. One of the important challenges i. e., Voltage/VAr control is a prime source for handling power system complexity and reliability, hence it is the fundamental requirement for all the utility companies. There is a need for the robust and efficient Voltage/VAr optimization technique to meet the peak demand and reduction of system losses. The voltages beyond the limit may damage costly sub-station devices and equipments at consumer end as well. Especially, the RERs introduces more disturbances and some of the RERs are not even capable enough to meet the VAr demand. Therefore, there is a strong need for the Voltage/VAr control in RERs environment. This paper aims at the development of optimal scheme for Voltage/VAr control involving RERs. In this paper, Latin Hypercube Sampling (LHS) method is used to cover full range of variables by maximally satisfying the marginal distribution. Here, backward scenario reduction technique is used to reduce the number of scenarios effectively and maximally retain the fitting accuracy of samples. The developed optimization scheme is tested on IEEE 24 bus Reliability Test System (RTS) considering the load demand and RERs variation.
Stochastic receding horizon control: application to an octopedal robot
Shah, Shridhar K.; Tanner, Herbert G.
2013-06-01
Miniature autonomous systems are being developed under ARL's Micro Autonomous Systems and Technology (MAST). These systems can only be fitted with a small-size processor, and their motion behavior is inherently uncertain due to manufacturing and platform-ground interactions. One way to capture this uncertainty is through a stochastic model. This paper deals with stochastic motion control design and implementation for MAST- specific eight-legged miniature crawling robots, which have been kinematically modeled as systems exhibiting the behavior of a Dubin's car with stochastic noise. The control design takes the form of stochastic receding horizon control, and is implemented on a Gumstix Overo Fire COM with 720 MHz processor and 512 MB RAM, weighing 5.5 g. The experimental results show the effectiveness of this control law for miniature autonomous systems perturbed by stochastic noise.
Optimal Rules for Single Machine Scheduling with Stochastic Breakdowns
Directory of Open Access Journals (Sweden)
Jinwei Gu
2014-01-01
Full Text Available This paper studies the problem of scheduling a set of jobs on a single machine subject to stochastic breakdowns, where jobs have to be restarted if preemptions occur because of breakdowns. The breakdown process of the machine is independent of the jobs processed on the machine. The processing times required to complete the jobs are constants if no breakdown occurs. The machine uptimes are independently and identically distributed (i.i.d. and are subject to a uniform distribution. It is proved that the Longest Processing Time first (LPT rule minimizes the expected makespan. For the large-scale problem, it is also showed that the Shortest Processing Time first (SPT rule is optimal to minimize the expected total completion times of all jobs.
Petra, Cosmin G.; Schenk, Olaf; Lubin, Miles; Gä ertner, Klaus
2014-01-01
We present a scalable approach and implementation for solving stochastic optimization problems on high-performance computers. In this work we revisit the sparse linear algebra computations of the parallel solver PIPS with the goal of improving the shared-memory performance and decreasing the time to solution. These computations consist of solving sparse linear systems with multiple sparse right-hand sides and are needed in our Schur-complement decomposition approach to compute the contribution of each scenario to the Schur matrix. Our novel approach uses an incomplete augmented factorization implemented within the PARDISO linear solver and an outer BiCGStab iteration to efficiently absorb pivot perturbations occurring during factorization. This approach is capable of both efficiently using the cores inside a computational node and exploiting sparsity of the right-hand sides. We report on the performance of the approach on highperformance computers when solving stochastic unit commitment problems of unprecedented size (billions of variables and constraints) that arise in the optimization and control of electrical power grids. Our numerical experiments suggest that supercomputers can be efficiently used to solve power grid stochastic optimization problems with thousands of scenarios under the strict "real-time" requirements of power grid operators. To our knowledge, this has not been possible prior to the present work. © 2014 Society for Industrial and Applied Mathematics.
Intelligent stochastic optimization routine for in-core fuel cycle design
International Nuclear Information System (INIS)
Parks, G.T.
1988-01-01
Any reactor fuel management strategy must specify the fuel design, batch sizes, loading configurations, and operational procedures for each cycle. To permit detailed design studies, the complex core characteristics must necessarily be computer modeled. Thus, the identification of an optimal fuel cycle design represents an optimization problem with a nonlinear objective function (OF), nonlinear safety constraints, many control variables, and no direct derivative information. Most available library routines cannot tackle such problems; this paper introduces an intelligent stochastic optimization routine that can. There has been considerable interest recently in the application of stochastic methods to difficult optimization problems, based on the statistical mechanics algorithms originally attributed to Metropolis. Previous work showed that, in optimizing the performance of a British advanced gas-cooled reactor fuel stringer, a rudimentary version of the Metropolis algorithm performed as efficiently as the only suitable routine in the Numerical Algorithms Group library. Since then the performance of the Metropolis algorithm has been considerably enhanced by the introduction of self-tuning capabilities by which the routine adjusts its control parameters and search pattern as it progresses. Both features can be viewed as examples of artificial intelligence, in which the routine uses the accumulation of data, or experience, to guide its future actions
International Nuclear Information System (INIS)
Zhu, Zhiwen; Zhang, Qingxin; Xu, Jia
2014-01-01
Stochastic bifurcation and fractal and chaos control of a giant magnetostrictive film–shape memory alloy (GMF–SMA) composite cantilever plate subjected to in-plane harmonic and stochastic excitation were studied. Van der Pol items were improved to interpret the hysteretic phenomena of both GMF and SMA, and the nonlinear dynamic model of a GMF–SMA composite cantilever plate subjected to in-plane harmonic and stochastic excitation was developed. The probability density function of the dynamic response of the system was obtained, and the conditions of stochastic Hopf bifurcation were analyzed. The conditions of noise-induced chaotic response were obtained in the stochastic Melnikov integral method, and the fractal boundary of the safe basin of the system was provided. Finally, the chaos control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that stochastic Hopf bifurcation and chaos appear in the parameter variation process. The boundary of the safe basin of the system has fractal characteristics, and its area decreases when the noise intensifies. The system reliability was improved through stochastic optimal control, and the safe basin area of the system increased
Event-Triggered Faults Tolerant Control for Stochastic Systems with Time Delays
Directory of Open Access Journals (Sweden)
Ling Huang
2016-01-01
Full Text Available This paper is concerned with the state-feedback controller design for stochastic networked control systems (NCSs with random actuator failures and transmission delays. Firstly, an event-triggered scheme is introduced to optimize the performance of the stochastic NCSs. Secondly, stochastic NCSs under event-triggered scheme are modeled as stochastic time-delay systems. Thirdly, some less conservative delay-dependent stability criteria in terms of linear matrix inequalities for the codesign of both the controller gain and the trigger parameters are obtained by using delay-decomposition technique and convex combination approach. Finally, a numerical example is provided to show the less sampled data transmission and less conservatism of the proposed theory.
Kiesmüller, G.P.
2003-01-01
This paper addresses the control problem of a stochastic recovery system with two stocking points and different leadtimes for production and remanufacturing. For such systems the optimal control policy for a linear cost model is not known. Therefore, in the literature several heuristic policies are
DEFF Research Database (Denmark)
Sokoler, Leo Emil; Dammann, Bernd; Madsen, Henrik
2014-01-01
This paper presents a decomposition algorithm for solving the optimal control problem (OCP) that arises in Mean-Variance Economic Model Predictive Control of stochastic linear systems. The algorithm applies the alternating direction method of multipliers to a reformulation of the OCP...
Control of Networked Traffic Flow Distribution - A Stochastic Distribution System Perspective
Energy Technology Data Exchange (ETDEWEB)
Wang, Hong [Pacific Northwest National Laboratory (PNNL); Aziz, H M Abdul [ORNL; Young, Stan [National Renewable Energy Laboratory (NREL); Patil, Sagar [Pacific Northwest National Laboratory (PNNL)
2017-10-01
Networked traffic flow is a common scenario for urban transportation, where the distribution of vehicle queues either at controlled intersections or highway segments reflect the smoothness of the traffic flow in the network. At signalized intersections, the traffic queues are controlled by traffic signal control settings and effective traffic lights control would realize both smooth traffic flow and minimize fuel consumption. Funded by the Energy Efficient Mobility Systems (EEMS) program of the Vehicle Technologies Office of the US Department of Energy, we performed a preliminary investigation on the modelling and control framework in context of urban network of signalized intersections. In specific, we developed a recursive input-output traffic queueing models. The queue formation can be modeled as a stochastic process where the number of vehicles entering each intersection is a random number. Further, we proposed a preliminary B-Spline stochastic model for a one-way single-lane corridor traffic system based on theory of stochastic distribution control.. It has been shown that the developed stochastic model would provide the optimal probability density function (PDF) of the traffic queueing length as a dynamic function of the traffic signal setting parameters. Based upon such a stochastic distribution model, we have proposed a preliminary closed loop framework on stochastic distribution control for the traffic queueing system to make the traffic queueing length PDF follow a target PDF that potentially realizes the smooth traffic flow distribution in a concerned corridor.
Stochastic modelling of turbulent combustion for design optimization of gas turbine combustors
Mehanna Ismail, Mohammed Ali
The present work covers the development and the implementation of an efficient algorithm for the design optimization of gas turbine combustors. The purpose is to explore the possibilities and indicate constructive suggestions for optimization techniques as alternative methods for designing gas turbine combustors. The algorithm is general to the extent that no constraints are imposed on the combustion phenomena or on the combustor configuration. The optimization problem is broken down into two elementary problems: the first is the optimum search algorithm, and the second is the turbulent combustion model used to determine the combustor performance parameters. These performance parameters constitute the objective and physical constraints in the optimization problem formulation. The examination of both turbulent combustion phenomena and the gas turbine design process suggests that the turbulent combustion model represents a crucial part of the optimization algorithm. The basic requirements needed for a turbulent combustion model to be successfully used in a practical optimization algorithm are discussed. In principle, the combustion model should comply with the conflicting requirements of high fidelity, robustness and computational efficiency. To that end, the problem of turbulent combustion is discussed and the current state of the art of turbulent combustion modelling is reviewed. According to this review, turbulent combustion models based on the composition PDF transport equation are found to be good candidates for application in the present context. However, these models are computationally expensive. To overcome this difficulty, two different models based on the composition PDF transport equation were developed: an improved Lagrangian Monte Carlo composition PDF algorithm and the generalized stochastic reactor model. Improvements in the Lagrangian Monte Carlo composition PDF model performance and its computational efficiency were achieved through the
Filtering and control of stochastic jump hybrid systems
Yao, Xiuming; Zheng, Wei Xing
2016-01-01
This book presents recent research work on stochastic jump hybrid systems. Specifically, the considered stochastic jump hybrid systems include Markovian jump Ito stochastic systems, Markovian jump linear-parameter-varying (LPV) systems, Markovian jump singular systems, Markovian jump two-dimensional (2-D) systems, and Markovian jump repeated scalar nonlinear systems. Some sufficient conditions are first established respectively for the stability and performances of those kinds of stochastic jump hybrid systems in terms of solution of linear matrix inequalities (LMIs). Based on the derived analysis conditions, the filtering and control problems are addressed. The book presents up-to-date research developments and novel methodologies on stochastic jump hybrid systems. The contents can be divided into two parts: the first part is focused on robust filter design problem, while the second part is put the emphasis on robust control problem. These methodologies provide a framework for stability and performance analy...
Stochastic search, optimization and regression with energy applications
Hannah, Lauren A.
Designing clean energy systems will be an important task over the next few decades. One of the major roadblocks is a lack of mathematical tools to economically evaluate those energy systems. However, solutions to these mathematical problems are also of interest to the operations research and statistical communities in general. This thesis studies three problems that are of interest to the energy community itself or provide support for solution methods: R&D portfolio optimization, nonparametric regression and stochastic search with an observable state variable. First, we consider the one stage R&D portfolio optimization problem to avoid the sequential decision process associated with the multi-stage. The one stage problem is still difficult because of a non-convex, combinatorial decision space and a non-convex objective function. We propose a heuristic solution method that uses marginal project values---which depend on the selected portfolio---to create a linear objective function. In conjunction with the 0-1 decision space, this new problem can be solved as a knapsack linear program. This method scales well to large decision spaces. We also propose an alternate, provably convergent algorithm that does not exploit problem structure. These methods are compared on a solid oxide fuel cell R&D portfolio problem. Next, we propose Dirichlet Process mixtures of Generalized Linear Models (DPGLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We prove conditions for the asymptotic unbiasedness of the DP-GLM regression mean function estimate. We also give examples for when those conditions hold, including models for compactly supported continuous distributions and a model with continuous covariates and categorical response. We empirically analyze the properties of the DP-GLM and why it provides better results than existing Dirichlet process mixture regression
Risk-sensitive control of stochastic hybrid systems on infinite time horizon
Directory of Open Access Journals (Sweden)
Runolfsson Thordur
1999-01-01
Full Text Available A risk-sensitive optimal control problem is considered for a hybrid system that consists of continuous time diffusion process that depends on a discrete valued mode variable that is modeled as a Markov chain. Optimality conditions are presented and conditions for the existence of optimal controls are derived. It is shown that the optimal risk-sensitive control problem is equivalent to the upper value of an associated stochastic differential game, and insight into the contributions of the noise input and mode variable to the risk sensitivity of the cost functional is given. Furthermore, it is shown that due to the mode variable risk sensitivity, the equivalence relationship that has been observed between risk-sensitive and H ∞ control in the nonhybrid case does not hold for stochastic hybrid systems.
Stochastic Power Control for Time-Varying Long-Term Fading Wireless Networks
Directory of Open Access Journals (Sweden)
Charalambous Charalambos D
2006-01-01
Full Text Available A new time-varying (TV long-term fading (LTF channel model which captures both the space and time variations of wireless systems is developed. The proposed TV LTF model is based on a stochastic differential equation driven by Brownian motion. This model is more realistic than the static models usually encountered in the literature. It allows viewing the wireless channel as a dynamical system, thus enabling well-developed tools of adaptive and nonadaptive estimation and identification techniques to be applied to this class of problems. In contrast with the traditional models, the statistics of the proposed model are shown to be TV, but converge in steady state to their static counterparts. Moreover, optimal power control algorithms (PCAs based on the new model are proposed. A centralized PCA is shown to reduce to a simple linear programming problem if predictable power control strategies (PPCS are used. In addition, an iterative distributed stochastic PCA is used to solve for the optimization problem using stochastic approximations. The latter solely requires each mobile to know its received signal-to-interference ratio. Generalizations of the power control problem based on convex optimization techniques are provided if PPCS are not assumed. Numerical results show that there are potentially large gains to be achieved by using TV stochastic models, and the distributed stochastic PCA provides better power stability and consumption than the distributed deterministic PCA.
Convergence of Sample Path Optimal Policies for Stochastic Dynamic Programming
National Research Council Canada - National Science Library
Fu, Michael C; Jin, Xing
2005-01-01
.... These results have practical implications for Monte Carlo simulation-based solution approaches to stochastic dynamic programming problems where it is impractical to extract the explicit transition...
Qin, Xiaosheng; Huang, Guohe; Liu, Lei
2010-01-01
A genetic-algorithm-aided stochastic optimization (GASO) model was developed in this study for supporting regional air quality management under uncertainty. The model incorporated genetic algorithm (GA) and Monte Carlo simulation techniques into a general stochastic chance-constrained programming (CCP) framework and allowed uncertainties in simulation and optimization model parameters to be considered explicitly in the design of least-cost strategies. GA was used to seek the optimal solution of the management model by progressively evaluating the performances of individual solutions. Monte Carlo simulation was used to check the feasibility of each solution. A management problem in terms of regional air pollution control was studied to demonstrate the applicability of the proposed method. Results of the case study indicated the proposed model could effectively communicate uncertainties into the optimization process and generate solutions that contained a spectrum of potential air pollutant treatment options with risk and cost information. Decision alternatives could be obtained by analyzing tradeoffs between the overall pollutant treatment cost and the system-failure risk due to inherent uncertainties.
A stochastic programming approach to manufacturing flow control
Haurie, Alain; Moresino, Francesco
2012-01-01
This paper proposes and tests an approximation of the solution of a class of piecewise deterministic control problems, typically used in the modeling of manufacturing flow processes. This approximation uses a stochastic programming approach on a suitably discretized and sampled system. The method proceeds through two stages: (i) the Hamilton-Jacobi-Bellman (HJB) dynamic programming equations for the finite horizon continuous time stochastic control problem are discretized over a set of sample...
A theory of Markovian time-inconsistent stochastic control in discrete time
DEFF Research Database (Denmark)
Bjork, Tomas; Murgoci, Agatha
2014-01-01
We develop a theory for a general class of discrete-time stochastic control problems that, in various ways, are time-inconsistent in the sense that they do not admit a Bellman optimality principle. We attack these problems by viewing them within a game theoretic framework, and we look for subgame...
NN-Based Implicit Stochastic Optimization of Multi-Reservoir Systems Management
Directory of Open Access Journals (Sweden)
Matteo Sangiorgio
2018-03-01
Full Text Available Multi-reservoir systems management is complex because of the uncertainty on future events and the variety of purposes, usually conflicting, of the involved actors. An efficient management of these systems can help improving resource allocation, preventing political crisis and reducing the conflicts between the stakeholders. Bellman stochastic dynamic programming (SDP is the most famous among the many proposed approaches to solve this optimal control problem. Unfortunately, SDP is affected by the curse of dimensionality: computational effort increases exponentially with the complexity of the considered system (i.e., number of reservoirs, and the problem rapidly becomes intractable. This paper proposes an implicit stochastic optimization approach for the solution of the reservoir management problem. The core idea is using extremely flexible functions, such as artificial neural networks (NN, for designing release rules which approximate the optimal policies obtained by an open-loop approach. These trained NNs can then be used to take decisions in real time. The approach thus requires a sufficiently long series of historical or synthetic inflows, and the definition of a compromise solution to be approximated. This work analyzes with particular emphasis the importance of the information which represents the input of the control laws, investigating the effects of different degrees of completeness. The methodology is applied to the Nile River basin considering the main management objectives (minimization of the irrigation water deficit and maximization of the hydropower production, but can be easily adopted also in other cases.
Understanding and Optimizing Asynchronous Low-Precision Stochastic Gradient Descent
De Sa, Christopher; Feldman, Matthew; Ré, Christopher; Olukotun, Kunle
2018-01-01
Stochastic gradient descent (SGD) is one of the most popular numerical algorithms used in machine learning and other domains. Since this is likely to continue for the foreseeable future, it is important to study techniques that can make it run fast on parallel hardware. In this paper, we provide the first analysis of a technique called Buckwild! that uses both asynchronous execution and low-precision computation. We introduce the DMGC model, the first conceptualization of the parameter space that exists when implementing low-precision SGD, and show that it provides a way to both classify these algorithms and model their performance. We leverage this insight to propose and analyze techniques to improve the speed of low-precision SGD. First, we propose software optimizations that can increase throughput on existing CPUs by up to 11×. Second, we propose architectural changes, including a new cache technique we call an obstinate cache, that increase throughput beyond the limits of current-generation hardware. We also implement and analyze low-precision SGD on the FPGA, which is a promising alternative to the CPU for future SGD systems. PMID:29391770
OPTIMAL TRAINING POLICY FOR PROMOTION - STOCHASTIC MODELS OF MANPOWER SYSTEMS
Directory of Open Access Journals (Sweden)
V.S.S. Yadavalli
2012-01-01
Full Text Available In this paper, the optimal planning of manpower training programmes in a manpower system with two grades is discussed. The planning of manpower training within a given organization involves a trade-off between training costs and expected return. These planning problems are examined through models that reflect the random nature of manpower movement in two grades. To be specific, the system consists of two grades, grade 1 and grade 2. Any number of persons in grade 2 can be sent for training and after the completion of training, they will stay in grade 2 and will be given promotion as and when vacancies arise in grade 1. Vacancies arise in grade 1 only by wastage. A person in grade 1 can leave the system with probability p. Vacancies are filled with persons in grade 2 who have completed the training. It is assumed that there is a perfect passing rate and that the sizes of both grades are fixed. Assuming that the planning horizon is finite and is T, the underlying stochastic process is identified as a finite state Markov chain and using dynamic programming, a policy is evolved to determine how many persons should be sent for training at any time k so as to minimize the total expected cost for the entire planning period T.
Reliability-Based Shape Optimization using Stochastic Finite Element Methods
DEFF Research Database (Denmark)
Enevoldsen, Ib; Sørensen, John Dalsgaard; Sigurdsson, G.
1991-01-01
stochastic fields (e.g. loads and material parameters such as Young's modulus and the Poisson ratio). In this case stochastic finite element techniques combined with FORM analysis can be used to obtain measures of the reliability of the structural systems, see Der Kiureghian & Ke (6) and Liu & Der Kiureghian...
Halyo, Nesim
1987-01-01
A combined stochastic feedforward and feedback control design methodology was developed. The objective of the feedforward control law is to track the commanded trajectory, whereas the feedback control law tries to maintain the plant state near the desired trajectory in the presence of disturbances and uncertainties about the plant. The feedforward control law design is formulated as a stochastic optimization problem and is embedded into the stochastic output feedback problem where the plant contains unstable and uncontrollable modes. An algorithm to compute the optimal feedforward is developed. In this approach, the use of error integral feedback, dynamic compensation, control rate command structures are an integral part of the methodology. An incremental implementation is recommended. Results on the eigenvalues of the implemented versus designed control laws are presented. The stochastic feedforward/feedback control methodology is used to design a digital automatic landing system for the ATOPS Research Vehicle, a Boeing 737-100 aircraft. The system control modes include localizer and glideslope capture and track, and flare to touchdown. Results of a detailed nonlinear simulation of the digital control laws, actuator systems, and aircraft aerodynamics are presented.
Optimal decoupling controllers revisited
Czech Academy of Sciences Publication Activity Database
Kučera, Vladimír
2013-01-01
Roč. 42, č. 1 (2013), s. 1-16 ISSN 0324-8569 R&D Projects: GA TA ČR(CZ) TE01020197 Institutional support: RVO:67985556 Keywords : linear systems * fractional representations * decoupling control lers * stabilizing control lers * optimal control lers Subject RIV: BC - Control Systems Theory
Design and analysis of stochastic DSS query optimizers in a distributed database system
Directory of Open Access Journals (Sweden)
Manik Sharma
2016-07-01
Full Text Available Query optimization is a stimulating task of any database system. A number of heuristics have been applied in recent times, which proposed new algorithms for substantially improving the performance of a query. The hunt for a better solution still continues. The imperishable developments in the field of Decision Support System (DSS databases are presenting data at an exceptional rate. The massive volume of DSS data is consequential only when it is able to access and analyze by distinctive researchers. Here, an innovative stochastic framework of DSS query optimizer is proposed to further optimize the design of existing query optimization genetic approaches. The results of Entropy Based Restricted Stochastic Query Optimizer (ERSQO are compared with the results of Exhaustive Enumeration Query Optimizer (EAQO, Simple Genetic Query Optimizer (SGQO, Novel Genetic Query Optimizer (NGQO and Restricted Stochastic Query Optimizer (RSQO. In terms of Total Costs, EAQO outperforms SGQO, NGQO, RSQO and ERSQO. However, stochastic approaches dominate in terms of runtime. The Total Costs produced by ERSQO is better than SGQO, NGQO and RGQO by 12%, 8% and 5% respectively. Moreover, the effect of replicating data on the Total Costs of DSS query is also examined. In addition, the statistical analysis revealed a 2-tailed significant correlation between the number of join operations and the Total Costs of distributed DSS query. Finally, in regard to the consistency of stochastic query optimizers, the results of SGQO, NGQO, RSQO and ERSQO are 96.2%, 97.2%, 97.45 and 97.8% consistent respectively.
Nonlinear optimal control theory
Berkovitz, Leonard David
2012-01-01
Nonlinear Optimal Control Theory presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory. Many examples illustrate the mathematical issues that need to be addressed when using optimal control techniques in diverse areas. Drawing on classroom-tested material from Purdue University and North Carolina State University, the book gives a unified account of bounded state problems governed by ordinary, integrodifferential, and delay systems. It also dis
2017-07-04
This paper presents a stochastic multi-agent optimization model that supports energy infrastruc- : ture planning under uncertainty. The interdependence between dierent decision entities in the : system is captured in an energy supply chain network, w...
Stochastic optimization in insurance a dynamic programming approach
Azcue, Pablo
2014-01-01
The main purpose of the book is to show how a viscosity approach can be used to tackle control problems in insurance. The problems covered are the maximization of survival probability as well as the maximization of dividends in the classical collective risk model. The authors consider the possibility of controlling the risk process by reinsurance as well as by investments. They show that optimal value functions are characterized as either the unique or the smallest viscosity solution of the associated Hamilton-Jacobi-Bellman equation; they also study the structure of the optimal strategies and show how to find them. The viscosity approach was widely used in control problems related to mathematical finance but until quite recently it was not used to solve control problems related to actuarial mathematical science. This book is designed to familiarize the reader on how to use this approach. The intended audience is graduate students as well as researchers in this area.
International Nuclear Information System (INIS)
Hong, H.P.; Zhou, W.; Zhang, S.; Ye, W.
2014-01-01
Components in engineered systems are subjected to stochastic deterioration due to the operating environmental conditions, and the uncertainty in material properties. The components need to be inspected and possibly replaced based on preventive or failure replacement criteria to provide the intended and safe operation of the system. In the present study, we investigate the influence of dependent stochastic degradation of multiple components on the optimal maintenance decisions. We use copula to model the dependent stochastic degradation of components, and formulate the optimal decision problem based on the minimum expected cost rule and the stochastic dominance rules. The latter is used to cope with decision maker's risk attitude. We illustrate the developed probabilistic analysis approach and the influence of the dependency of the stochastic degradation on the preferred decisions through numerical examples
A Stochastic Maximum Principle for Risk-Sensitive Mean-Field Type Control
Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul
2015-01-01
In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle (SMP) for optimal control of stochastic differential equations (SDEs) of mean-field type, in which the drift and the diffusion coefficients as well as the performance functional depend not only on the state and the control but also on the mean of the distribution of the state. Our result extends the risk-sensitive SMP (without mean-field coupling) of Lim and Zhou (2005), derived for feedback (or Markov) type optimal controls, to optimal control problems for non-Markovian dynamics which may be time-inconsistent in the sense that the Bellman optimality principle does not hold. In our approach to the risk-sensitive SMP, the smoothness assumption on the value-function imposed in Lim and Zhou (2005) needs not be satisfied. For a general action space a Peng's type SMP is derived, specifying the necessary conditions for optimality. Two examples are carried out to illustrate the proposed risk-sensitive mean-field type SMP under linear stochastic dynamics with exponential quadratic cost function. Explicit solutions are given for both mean-field free and mean-field models.
A Stochastic Maximum Principle for Risk-Sensitive Mean-Field Type Control
Djehiche, Boualem
2015-02-24
In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle (SMP) for optimal control of stochastic differential equations (SDEs) of mean-field type, in which the drift and the diffusion coefficients as well as the performance functional depend not only on the state and the control but also on the mean of the distribution of the state. Our result extends the risk-sensitive SMP (without mean-field coupling) of Lim and Zhou (2005), derived for feedback (or Markov) type optimal controls, to optimal control problems for non-Markovian dynamics which may be time-inconsistent in the sense that the Bellman optimality principle does not hold. In our approach to the risk-sensitive SMP, the smoothness assumption on the value-function imposed in Lim and Zhou (2005) needs not be satisfied. For a general action space a Peng\\'s type SMP is derived, specifying the necessary conditions for optimality. Two examples are carried out to illustrate the proposed risk-sensitive mean-field type SMP under linear stochastic dynamics with exponential quadratic cost function. Explicit solutions are given for both mean-field free and mean-field models.
DEFF Research Database (Denmark)
Ding, Tao; Yang, Qingrun; Yang, Yongheng
2018-01-01
To address the uncertain output of distributed generators (DGs) for reactive power optimization in active distribution networks, the stochastic programming model is widely used. The model is employed to find an optimal control strategy with minimum expected network loss while satisfying all......, in this paper, a data-driven modeling approach is introduced to assume that the probability distribution from the historical data is uncertain within a confidence set. Furthermore, a data-driven stochastic programming model is formulated as a two-stage problem, where the first-stage variables find the optimal...... control for discrete reactive power compensation equipment under the worst probability distribution of the second stage recourse. The second-stage variables are adjusted to uncertain probability distribution. In particular, this two-stage problem has a special structure so that the second-stage problem...
An introduction to optimal control of FBSDE with incomplete information
Wang, Guangchen; Xiong, Jie
2018-01-01
This book focuses on maximum principle and verification theorem for incomplete information forward-backward stochastic differential equations (FBSDEs) and their applications in linear-quadratic optimal controls and mathematical finance. Lots of interesting phenomena arising from the area of mathematical finance can be described by FBSDEs. Optimal control problems of FBSDEs are theoretically important and practically relevant. A standard assumption in the literature is that the stochastic noises in the model are completely observed. However, this is rarely the case in real world situations. The optimal control problems under complete information are studied extensively. Nevertheless, very little is known about these problems when the information is not complete. The aim of this book is to fill this gap. This book is written in a style suitable for graduate students and researchers in mathematics and engineering with basic knowledge of stochastic process, optimal control and mathematical finance.
International Nuclear Information System (INIS)
Niknam, Taher; Azizipanah-Abarghooee, Rasoul; Narimani, Mohammad Rasoul
2012-01-01
Highlights: ► Proposes a stochastic model for optimal energy management. ► Consider uncertainties related to the forecasted values for load demand. ► Consider uncertainties of forecasted values of output power of wind and photovoltaic units. ► Consider uncertainties of forecasted values of market price. ► Present an improved multi-objective teaching–learning-based optimization. -- Abstract: This paper proposes a stochastic model for optimal energy management with the goal of cost and emission minimization. In this model, the uncertainties related to the forecasted values for load demand, available output power of wind and photovoltaic units and market price are modeled by a scenario-based stochastic programming. In the presented method, scenarios are generated by a roulette wheel mechanism based on probability distribution functions of the input random variables. Through this method, the inherent stochastic nature of the proposed problem is released and the problem is decomposed into a deterministic problem. An improved multi-objective teaching–learning-based optimization is implemented to yield the best expected Pareto optimal front. In the proposed stochastic optimization method, a novel self adaptive probabilistic modification strategy is offered to improve the performance of the presented algorithm. Also, a set of non-dominated solutions are stored in a repository during the simulation process. Meanwhile, the size of the repository is controlled by usage of a fuzzy-based clustering technique. The best expected compromise solution stored in the repository is selected via the niching mechanism in a way that solutions are encouraged to seek the lesser explored regions. The proposed framework is applied in a typical grid-connected micro grid in order to verify its efficiency and feasibility.
Asymptotically optimal production policies in dynamic stochastic jobshops with limited buffers
Hou, Yumei; Sethi, Suresh P.; Zhang, Hanqin; Zhang, Qing
2006-05-01
We consider a production planning problem for a jobshop with unreliable machines producing a number of products. There are upper and lower bounds on intermediate parts and an upper bound on finished parts. The machine capacities are modelled as finite state Markov chains. The objective is to choose the rate of production so as to minimize the total discounted cost of inventory and production. Finding an optimal control policy for this problem is difficult. Instead, we derive an asymptotic approximation by letting the rates of change of the machine states approach infinity. The asymptotic analysis leads to a limiting problem in which the stochastic machine capacities are replaced by their equilibrium mean capacities. The value function for the original problem is shown to converge to the value function of the limiting problem. The convergence rate of the value function together with the error estimate for the constructed asymptotic optimal production policies are established.
Probabilistic DHP adaptive critic for nonlinear stochastic control systems.
Herzallah, Randa
2013-06-01
Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work (Herzallah & Káarnáy, 2011; Kárný, 1996) by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained. Copyright © 2013 Elsevier Ltd. All rights reserved.
A numerical scheme for optimal transition paths of stochastic chemical kinetic systems
International Nuclear Information System (INIS)
Liu Di
2008-01-01
We present a new framework for finding the optimal transition paths of metastable stochastic chemical kinetic systems with large system size. The optimal transition paths are identified to be the most probable paths according to the Large Deviation Theory of stochastic processes. Dynamical equations for the optimal transition paths are derived using the variational principle. A modified Minimum Action Method (MAM) is proposed as a numerical scheme to solve the optimal transition paths. Applications to Gene Regulatory Networks such as the toggle switch model and the Lactose Operon Model in Escherichia coli are presented as numerical examples
Design Of Combined Stochastic Feedforward/Feedback Control
Halyo, Nesim
1989-01-01
Methodology accommodates variety of control structures and design techniques. In methodology for combined stochastic feedforward/feedback control, main objectives of feedforward and feedback control laws seen clearly. Inclusion of error-integral feedback, dynamic compensation, rate-command control structure, and like integral element of methodology. Another advantage of methodology flexibility to develop variety of techniques for design of feedback control with arbitrary structures to obtain feedback controller: includes stochastic output feedback, multiconfiguration control, decentralized control, or frequency and classical control methods. Control modes of system include capture and tracking of localizer and glideslope, crab, decrab, and flare. By use of recommended incremental implementation, control laws simulated on digital computer and connected with nonlinear digital simulation of aircraft and its systems.
Risk averse optimal operation of a virtual power plant using two stage stochastic programming
International Nuclear Information System (INIS)
Tajeddini, Mohammad Amin; Rahimi-Kian, Ashkan; Soroudi, Alireza
2014-01-01
VPP (Virtual Power Plant) is defined as a cluster of energy conversion/storage units which are centrally operated in order to improve the technical and economic performance. This paper addresses the optimal operation of a VPP considering the risk factors affecting its daily operation profits. The optimal operation is modelled in both day ahead and balancing markets as a two-stage stochastic mixed integer linear programming in order to maximize a GenCo (generation companies) expected profit. Furthermore, the CVaR (Conditional Value at Risk) is used as a risk measure technique in order to control the risk of low profit scenarios. The uncertain parameters, including the PV power output, wind power output and day-ahead market prices are modelled through scenarios. The proposed model is successfully applied to a real case study to show its applicability and the results are presented and thoroughly discussed. - Highlights: • Virtual power plant modelling considering a set of energy generating and conversion units. • Uncertainty modelling using two stage stochastic programming technique. • Risk modelling using conditional value at risk. • Flexible operation of renewable energy resources. • Electricity price uncertainty in day ahead energy markets
Energy Optimal Path Planning: Integrating Coastal Ocean Modelling with Optimal Control
Subramani, D. N.; Haley, P. J., Jr.; Lermusiaux, P. F. J.
2016-02-01
A stochastic optimization methodology is formulated for computing energy-optimal paths from among time-optimal paths of autonomous vehicles navigating in a dynamic flow field. To set up the energy optimization, the relative vehicle speed and headings are considered to be stochastic, and new stochastic Dynamically Orthogonal (DO) level-set equations that govern their stochastic time-optimal reachability fronts are derived. Their solution provides the distribution of time-optimal reachability fronts and corresponding distribution of time-optimal paths. An optimization is then performed on the vehicle's energy-time joint distribution to select the energy-optimal paths for each arrival time, among all stochastic time-optimal paths for that arrival time. The accuracy and efficiency of the DO level-set equations for solving the governing stochastic level-set reachability fronts are quantitatively assessed, including comparisons with independent semi-analytical solutions. Energy-optimal missions are studied in wind-driven barotropic quasi-geostrophic double-gyre circulations, and in realistic data-assimilative re-analyses of multiscale coastal ocean flows. The latter re-analyses are obtained from multi-resolution 2-way nested primitive-equation simulations of tidal-to-mesoscale dynamics in the Middle Atlantic Bight and Shelbreak Front region. The effects of tidal currents, strong wind events, coastal jets, and shelfbreak fronts on the energy-optimal paths are illustrated and quantified. Results showcase the opportunities for longer-duration missions that intelligently utilize the ocean environment to save energy, rigorously integrating ocean forecasting with optimal control of autonomous vehicles.
Distributed Adaptive Neural Control for Stochastic Nonlinear Multiagent Systems.
Wang, Fang; Chen, Bing; Lin, Chong; Li, Xuehua
2016-11-14
In this paper, a consensus tracking problem of nonlinear multiagent systems is investigated under a directed communication topology. All the followers are modeled by stochastic nonlinear systems in nonstrict feedback form, where nonlinearities and stochastic disturbance terms are totally unknown. Based on the structural characteristic of neural networks (in Lemma 4), a novel distributed adaptive neural control scheme is put forward. The raised control method not only effectively handles unknown nonlinearities in nonstrict feedback systems, but also copes with the interactions among agents and coupling terms. Based on the stochastic Lyapunov functional method, it is indicated that all the signals of the closed-loop system are bounded in probability and all followers' outputs are convergent to a neighborhood of the output of leader. At last, the efficiency of the control method is testified by a numerical example.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Xiaodong, E-mail: xiaodong.zhang@beg.utexas.edu [Bureau of Economic Geology, Jackson School of Geosciences, The University of Texas at Austin, Austin, TX 78713 (United States); Huang, Gordon [Institute of Energy, Environment and Sustainable Communities, University of Regina, Regina, Saskatchewan S4S 0A2 (Canada)
2013-02-15
Highlights: ► A dynamic stochastic possibilistic multiobjective programming model is developed. ► Greenhouse gas emission control is considered. ► Three planning scenarios are analyzed and compared. ► Optimal decision schemes under three scenarios and different p{sub i} levels are obtained. ► Tradeoffs between economics and environment are reflected. -- Abstract: Greenhouse gas (GHG) emissions from municipal solid waste (MSW) management facilities have become a serious environmental issue. In MSW management, not only economic objectives but also environmental objectives should be considered simultaneously. In this study, a dynamic stochastic possibilistic multiobjective programming (DSPMP) model is developed for supporting MSW management and associated GHG emission control. The DSPMP model improves upon the existing waste management optimization methods through incorporation of fuzzy possibilistic programming and chance-constrained programming into a general mixed-integer multiobjective linear programming (MOP) framework where various uncertainties expressed as fuzzy possibility distributions and probability distributions can be effectively reflected. Two conflicting objectives are integrally considered, including minimization of total system cost and minimization of total GHG emissions from waste management facilities. Three planning scenarios are analyzed and compared, representing different preferences of the decision makers for economic development and environmental-impact (i.e. GHG-emission) issues in integrated MSW management. Optimal decision schemes under three scenarios and different p{sub i} levels (representing the probability that the constraints would be violated) are generated for planning waste flow allocation and facility capacity expansions as well as GHG emission control. The results indicate that economic and environmental tradeoffs can be effectively reflected through the proposed DSPMP model. The generated decision variables can help
Model tracking dual stochastic controller design under irregular internal noises
International Nuclear Information System (INIS)
Lee, Jong Bok; Heo, Hoon; Cho, Yun Hyun; Ji, Tae Young
2006-01-01
Although many methods about the control of irregular external noise have been introduced and implemented, it is still necessary to design a controller that will be more effective and efficient methods to exclude for various noises. Accumulation of errors due to model tracking, internal noises (thermal noise, shot noise and l/f noise) that come from elements such as resistor, diode and transistor etc. in the circuit system and numerical errors due to digital process often destabilize the system and reduce the system performance. New stochastic controller is adopted to remove those noises using conventional controller simultaneously. Design method of a model tracking dual controller is proposed to improve the stability of system while removing external and internal noises. In the study, design process of the model tracking dual stochastic controller is introduced that improves system performance and guarantees robustness under irregular internal noises which can be created internally. The model tracking dual stochastic controller utilizing F-P-K stochastic control technique developed earlier is implemented to reveal its performance via simulation
Backward Stochastic H2/H∞ Control: Infinite Horizon Case
Directory of Open Access Journals (Sweden)
Zhen Wu
2014-01-01
Full Text Available The mixed H2/H∞ control problem is studied for systems governed by infinite horizon backward stochastic differential equations (BSDEs with exogenous disturbance signal. A necessary and sufficient condition for the existence of a unique solution to the H2/H∞ control problem is derived. The equivalent feedback solution is also discussed. Contrary to deterministic or stochastic forward case, the feedback solution is no longer feedback of the current state; rather, it is feedback of the entire history of the state.
Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost
International Nuclear Information System (INIS)
Bokanowski, Olivier; Picarelli, Athena; Zidani, Hasnaa
2015-01-01
This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton–Jacobi–Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system of controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach
Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost
Energy Technology Data Exchange (ETDEWEB)
Bokanowski, Olivier, E-mail: boka@math.jussieu.fr [Laboratoire Jacques-Louis Lions, Université Paris-Diderot (Paris 7) UFR de Mathématiques - Bât. Sophie Germain (France); Picarelli, Athena, E-mail: athena.picarelli@inria.fr [Projet Commands, INRIA Saclay & ENSTA ParisTech (France); Zidani, Hasnaa, E-mail: hasnaa.zidani@ensta.fr [Unité de Mathématiques appliquées (UMA), ENSTA ParisTech (France)
2015-02-15
This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton–Jacobi–Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system of controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach.
Optimal investment models with stochastic volatility: the time ...
African Journals Online (AJOL)
Therefore, a transform is primordial to express the value function in terms of a semilinear PDE with quadratic growth on the derivative term. Some proofs for the existence of smooth solution to this equation have been provided for this equation by Pham [11]. In that paper they illustrated some common stochastic volatility ...
Mortgage Loan Portfolio Optimization Using Multi-Stage Stochastic Programming
DEFF Research Database (Denmark)
Rasmussen, Kourosh Marjani; Clausen, Jens
2007-01-01
We consider the dynamics of the Danish mortgage loan system and propose several models to reflect the choices of a mortgagor as well as his attitude towards risk. The models are formulated as multi stage stochastic integer programs, which are difficult to solve for more than 10 stages. Scenario...
Optimal Stochastic Advertising Strategies for the U.S. Beef Industry
Kun C. Lee; Stanley Schraufnagel; Earl O. Heady
1982-01-01
An important decision variable in the promotional strategy for the beef sector is the optimal level of advertising expenditures over time. Optimal stochastic and deterministic advertising expenditures are derived for the U.S. beef industry for the period `1966 through 1980. They are compared with historical levels and gains realized by optimal advertising strategies are measured. Finally, the optimal advertising expenditures in the future are forecasted.
Keren, Baruch; Pliskin, Joseph S
2011-12-01
The optimal timing for performing radical medical procedures as joint (e.g., hip) replacement must be seriously considered. In this paper we show that under deterministic assumptions the optimal timing for joint replacement is a solution of a mathematical programming problem, and under stochastic assumptions the optimal timing can be formulated as a stochastic programming problem. We formulate deterministic and stochastic models that can serve as decision support tools. The results show that the benefit from joint replacement surgery is heavily dependent on timing. Moreover, for a special case where the patient's remaining life is normally distributed along with a normally distributed survival of the new joint, the expected benefit function from surgery is completely solved. This enables practitioners to draw the expected benefit graph, to find the optimal timing, to evaluate the benefit for each patient, to set priorities among patients and to decide if joint replacement should be performed and when.
Goel, R.; Kofman, I.; DeDios, Y. E.; Jeevarajan, J.; Stepanyan, V.; Nair, M.; Congdon, S.; Fregia, M.; Peters, B.; Cohen, H.;
2015-01-01
Sensorimotor changes such as postural and gait instabilities can affect the functional performance of astronauts when they transition across different gravity environments. We are developing a method, based on stochastic resonance (SR), to enhance information transfer by applying non-zero levels of external noise on the vestibular system (vestibular stochastic resonance, VSR). The goal of this project was to determine optimal levels of stimulation for SR applications by using a defined vestibular threshold of motion detection.
Continuous-Time Public Good Contribution Under Uncertainty: A Stochastic Control Approach
International Nuclear Information System (INIS)
Ferrari, Giorgio; Riedel, Frank; Steg, Jan-Henrik
2017-01-01
In this paper we study continuous-time stochastic control problems with both monotone and classical controls motivated by the so-called public good contribution problem. That is the problem of n economic agents aiming to maximize their expected utility allocating initial wealth over a given time period between private consumption and irreversible contributions to increase the level of some public good. We investigate the corresponding social planner problem and the case of strategic interaction between the agents, i.e. the public good contribution game. We show existence and uniqueness of the social planner’s optimal policy, we characterize it by necessary and sufficient stochastic Kuhn–Tucker conditions and we provide its expression in terms of the unique optional solution of a stochastic backward equation. Similar stochastic first order conditions prove to be very useful for studying any Nash equilibria of the public good contribution game. In the symmetric case they allow us to prove (qualitative) uniqueness of the Nash equilibrium, which we again construct as the unique optional solution of a stochastic backward equation. We finally also provide a detailed analysis of the so-called free rider effect.
Continuous-Time Public Good Contribution Under Uncertainty: A Stochastic Control Approach
Energy Technology Data Exchange (ETDEWEB)
Ferrari, Giorgio, E-mail: giorgio.ferrari@uni-bielefeld.de; Riedel, Frank, E-mail: frank.riedel@uni-bielefeld.de; Steg, Jan-Henrik, E-mail: jsteg@uni-bielefeld.de [Bielefeld University, Center for Mathematical Economics (Germany)
2017-06-15
In this paper we study continuous-time stochastic control problems with both monotone and classical controls motivated by the so-called public good contribution problem. That is the problem of n economic agents aiming to maximize their expected utility allocating initial wealth over a given time period between private consumption and irreversible contributions to increase the level of some public good. We investigate the corresponding social planner problem and the case of strategic interaction between the agents, i.e. the public good contribution game. We show existence and uniqueness of the social planner’s optimal policy, we characterize it by necessary and sufficient stochastic Kuhn–Tucker conditions and we provide its expression in terms of the unique optional solution of a stochastic backward equation. Similar stochastic first order conditions prove to be very useful for studying any Nash equilibria of the public good contribution game. In the symmetric case they allow us to prove (qualitative) uniqueness of the Nash equilibrium, which we again construct as the unique optional solution of a stochastic backward equation. We finally also provide a detailed analysis of the so-called free rider effect.
Optimization of accelerator control
International Nuclear Information System (INIS)
Vasiljev, N.D.; Mozin, I.V.; Shelekhov, V.A.; Efremov, D.V.
1992-01-01
Expensive exploitation of charged particle accelerators is inevitably concerned with requirements of effectively obtaining of the best characteristics of accelerated beams for physical experiments. One of these characteristics is intensity. Increase of intensity is hindered by a number of effects, concerned with the influence of the volume charge field on a particle motion dynamics in accelerator's chamber. However, ultimate intensity, determined by a volume charge, is almost not achieved for the most of the operating accelerators. This fact is caused by losses of particles during injection, at the initial stage of acceleration and during extraction. These losses are caused by deviations the optimal from real characteristics of the accelerating and magnetic system. This is due to a number of circumstances, including technological tolerances on structural elements of systems, influence of measuring and auxiliary equipment and beam consumers' installations, placed in the closed proximity to magnets, and instability in operation of technological systems of accelerator. Control task consists in compensation of deviations of characteristics of magnetic and electric fields by optimal selection of control actions. As for technical means, automatization of modern accelerators allows to solve optimal control problems in real time. Therefore, the report is devoted to optimal control methods and experimental results. (J.P.N.)
Stochastic control of Indian megadroughts and megafloods
Energy Technology Data Exchange (ETDEWEB)
Hunt, B.G. [CSIRO Marine and Atmospheric Research, Aspendale, VIC (Australia)
2012-10-15
A multi-millennial run of the CSIRO Mark2 coupled climatic model has been used to investigate megadroughts and megafloods during the Indian summer monsoon (June-September). These extreme events were defined as having rainfall anomalies at least two standard deviations from normal. More than ten megafloods and more than twenty megadroughts, so-defined, were found to occur in a 5,000-year period of the simulation. The simulation replicated most of the major features of the observed summer monsoon, but a comparison of observed and simulated probability density functions suggests that the limited observed rainfall time series to date does not adequately sample the possible range of Indian monsoonal rainfall. An investigation of causal mechanisms of Indian rainfall variability reproduced the observed negative correlation with ENSO events, but it was found that neither extreme ENSO events or extremes of a range of other climatic phenomena coincided with the simulated, extreme megadroughts and megafloods. This disconnect between these events is succinctly illustrated with examples related to ENSO events in particular. Autoregressive and FFT analysis of observed and simulated Indian summer monsoon rainfall time series revealed them to consist of white noise. Since these time series therefore consist of random outcomes, it is apparent that these Indian megadroughts and megafloods are the consequence of stochastic influences. Thus, it is concluded that the interannual variability of Indian summer monsoonal rainfall cannot be predicted in general, nor can megadroughts and megafloods in particular. (orig.)
Stochastic resonance in the presence of slowly varying control parameters
International Nuclear Information System (INIS)
Nicolis, C; Nicolis, G
2005-01-01
The kinetics of transitions between states in a noisy system is studied in the simultaneous presence of a periodic forcing and a ramp. It is shown that the interaction between stochastic resonance and the action of the ramp may give rise to a new method for the control of the transition rates
Stochastic Predictive Control of Multi-Microgrid Systems
DEFF Research Database (Denmark)
Bazmohammadi, Najmeh; Tahsiri, Ahmadreza; Anvari-Moghaddam, Amjad
2018-01-01
This paper presents a stochastic predictive control algorithm for a number of microgrids connected to the same distribution system. Each microgrid includes a variety of distributed resources such as wind turbine, photo voltaic units, energy storage devices and loads. Considering the uncertainty...
Nguyen, A; Yosinski, J; Clune, J
2016-01-01
The Achilles Heel of stochastic optimization algorithms is getting trapped on local optima. Novelty Search mitigates this problem by encouraging exploration in all interesting directions by replacing the performance objective with a reward for novel behaviors. This reward for novel behaviors has traditionally required a human-crafted, behavioral distance function. While Novelty Search is a major conceptual breakthrough and outperforms traditional stochastic optimization on certain problems, it is not clear how to apply it to challenging, high-dimensional problems where specifying a useful behavioral distance function is difficult. For example, in the space of images, how do you encourage novelty to produce hawks and heroes instead of endless pixel static? Here we propose a new algorithm, the Innovation Engine, that builds on Novelty Search by replacing the human-crafted behavioral distance with a Deep Neural Network (DNN) that can recognize interesting differences between phenotypes. The key insight is that DNNs can recognize similarities and differences between phenotypes at an abstract level, wherein novelty means interesting novelty. For example, a DNN-based novelty search in the image space does not explore in the low-level pixel space, but instead creates a pressure to create new types of images (e.g., churches, mosques, obelisks, etc.). Here, we describe the long-term vision for the Innovation Engine algorithm, which involves many technical challenges that remain to be solved. We then implement a simplified version of the algorithm that enables us to explore some of the algorithm's key motivations. Our initial results, in the domain of images, suggest that Innovation Engines could ultimately automate the production of endless streams of interesting solutions in any domain: for example, producing intelligent software, robot controllers, optimized physical components, and art.
International Nuclear Information System (INIS)
Sankaran, Sethuraman; Audet, Charles; Marsden, Alison L.
2010-01-01
Recent advances in coupling novel optimization methods to large-scale computing problems have opened the door to tackling a diverse set of physically realistic engineering design problems. A large computational overhead is associated with computing the cost function for most practical problems involving complex physical phenomena. Such problems are also plagued with uncertainties in a diverse set of parameters. We present a novel stochastic derivative-free optimization approach for tackling such problems. Our method extends the previously developed surrogate management framework (SMF) to allow for uncertainties in both simulation parameters and design variables. The stochastic collocation scheme is employed for stochastic variables whereas Kriging based surrogate functions are employed for the cost function. This approach is tested on four numerical optimization problems and is shown to have significant improvement in efficiency over traditional Monte-Carlo schemes. Problems with multiple probabilistic constraints are also discussed.
Uncertainty Aware Structural Topology Optimization Via a Stochastic Reduced Order Model Approach
Aguilo, Miguel A.; Warner, James E.
2017-01-01
This work presents a stochastic reduced order modeling strategy for the quantification and propagation of uncertainties in topology optimization. Uncertainty aware optimization problems can be computationally complex due to the substantial number of model evaluations that are necessary to accurately quantify and propagate uncertainties. This computational complexity is greatly magnified if a high-fidelity, physics-based numerical model is used for the topology optimization calculations. Stochastic reduced order model (SROM) methods are applied here to effectively 1) alleviate the prohibitive computational cost associated with an uncertainty aware topology optimization problem; and 2) quantify and propagate the inherent uncertainties due to design imperfections. A generic SROM framework that transforms the uncertainty aware, stochastic topology optimization problem into a deterministic optimization problem that relies only on independent calls to a deterministic numerical model is presented. This approach facilitates the use of existing optimization and modeling tools to accurately solve the uncertainty aware topology optimization problems in a fraction of the computational demand required by Monte Carlo methods. Finally, an example in structural topology optimization is presented to demonstrate the effectiveness of the proposed uncertainty aware structural topology optimization approach.
Static vs stochastic optimization: A case study of FTSE Bursa Malaysia sectorial indices
Mamat, Nur Jumaadzan Zaleha; Jaaman, Saiful Hafizah; Ahmad, Rokiah@Rozita
2014-06-01
Traditional portfolio optimization methods in the likes of Markowitz' mean-variance model and semi-variance model utilize static expected return and volatility risk from historical data to generate an optimal portfolio. The optimal portfolio may not truly be optimal in reality due to the fact that maximum and minimum values from the data may largely influence the expected return and volatility risk values. This paper considers distributions of assets' return and volatility risk to determine a more realistic optimized portfolio. For illustration purposes, the sectorial indices data in FTSE Bursa Malaysia is employed. The results show that stochastic optimization provides more stable information ratio.
Static vs stochastic optimization: A case study of FTSE Bursa Malaysia sectorial indices
Energy Technology Data Exchange (ETDEWEB)
Mamat, Nur Jumaadzan Zaleha; Jaaman, Saiful Hafizah; Ahmad, Rokiah Rozita [School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor (Malaysia)
2014-06-19
Traditional portfolio optimization methods in the likes of Markowitz' mean-variance model and semi-variance model utilize static expected return and volatility risk from historical data to generate an optimal portfolio. The optimal portfolio may not truly be optimal in reality due to the fact that maximum and minimum values from the data may largely influence the expected return and volatility risk values. This paper considers distributions of assets' return and volatility risk to determine a more realistic optimized portfolio. For illustration purposes, the sectorial indices data in FTSE Bursa Malaysia is employed. The results show that stochastic optimization provides more stable information ratio.
Static vs stochastic optimization: A case study of FTSE Bursa Malaysia sectorial indices
International Nuclear Information System (INIS)
Mamat, Nur Jumaadzan Zaleha; Jaaman, Saiful Hafizah; Ahmad, Rokiah Rozita
2014-01-01
Traditional portfolio optimization methods in the likes of Markowitz' mean-variance model and semi-variance model utilize static expected return and volatility risk from historical data to generate an optimal portfolio. The optimal portfolio may not truly be optimal in reality due to the fact that maximum and minimum values from the data may largely influence the expected return and volatility risk values. This paper considers distributions of assets' return and volatility risk to determine a more realistic optimized portfolio. For illustration purposes, the sectorial indices data in FTSE Bursa Malaysia is employed. The results show that stochastic optimization provides more stable information ratio
Lorig, Matthew; Sircar, Ronnie
2015-01-01
We study the finite horizon Merton portfolio optimization problem in a general local-stochastic volatility setting. Using model coefficient expansion techniques, we derive approximations for the both the value function and the optimal investment strategy. We also analyze the `implied Sharpe ratio' and derive a series approximation for this quantity. The zeroth-order approximation of the value function and optimal investment strategy correspond to those obtained by Merton (1969) when the risky...
International Nuclear Information System (INIS)
Kushner, Harold J.
2012-01-01
This is the second part of a work dealing with key issues that have not been addressed in the modeling and numerical optimization of nonlinear stochastic delay systems. We consider new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. Part I was concerned with issues concerning the class of admissible controls and their approximations, since the classical definitions are inadequate for our models. This part is concerned with transportation equation representations and their approximations. Such representations of nonlinear stochastic delay models have been crucial in the development of numerical algorithms with much reduced memory and computational requirements. The representations for the new models are not obvious and are developed. They also provide a template for the adaptation of the Markov chain approximation numerical methods.
A penalty guided stochastic fractal search approach for system reliability optimization
International Nuclear Information System (INIS)
Mellal, Mohamed Arezki; Zio, Enrico
2016-01-01
Modern industry requires components and systems with high reliability levels. In this paper, we address the system reliability optimization problem. A penalty guided stochastic fractal search approach is developed for solving reliability allocation, redundancy allocation, and reliability–redundancy allocation problems. Numerical results of ten case studies are presented as benchmark problems for highlighting the superiority of the proposed approach compared to others from literature. - Highlights: • System reliability optimization is investigated. • A penalty guided stochastic fractal search approach is developed. • Results of ten case studies are compared with previously published methods. • Performance of the approach is demonstrated.
Oil Reservoir Production Optimization using Optimal Control
DEFF Research Database (Denmark)
Völcker, Carsten; Jørgensen, John Bagterp; Stenby, Erling Halfdan
2011-01-01
Practical oil reservoir management involves solution of large-scale constrained optimal control problems. In this paper we present a numerical method for solution of large-scale constrained optimal control problems. The method is a single-shooting method that computes the gradients using the adjo...... reservoir using water ooding and smart well technology. Compared to the uncontrolled case, the optimal operation increases the Net Present Value of the oil field by 10%.......Practical oil reservoir management involves solution of large-scale constrained optimal control problems. In this paper we present a numerical method for solution of large-scale constrained optimal control problems. The method is a single-shooting method that computes the gradients using...
International Nuclear Information System (INIS)
Osmani, Atif; Zhang, Jun
2013-01-01
An integrated multi-feedstock (i.e. switchgrass and crop residue) lignocellulosic-based bioethanol supply chain is studied under jointly occurring uncertainties in switchgrass yield, crop residue purchase price, bioethanol demand and sales price. A two-stage stochastic mathematical model is proposed to maximize expected profit by optimizing the strategic and tactical decisions. A case study based on ND (North Dakota) state in the U.S. demonstrates that in a stochastic environment it is cost effective to meet 100% of ND's annual gasoline demand from bioethanol by using switchgrass as a primary and crop residue as a secondary biomass feedstock. Although results show that the financial performance is degraded as variability of the uncertain parameters increases, the proposed stochastic model increasingly outperforms the deterministic model under uncertainties. The locations of biorefineries (i.e. first-stage integer variables) are insensitive to the uncertainties. Sensitivity analysis shows that “mean” value of stochastic parameters has a significant impact on the expected profit and optimal values of first-stage continuous variables. Increase in level of mean ethanol demand and mean sale price results in higher bioethanol production. When mean switchgrass yield is at low level and mean crop residue price is at high level, all the available marginal land is used for switchgrass cultivation. - Highlights: • Two-stage stochastic MILP model for maximizing profit of a multi-feedstock lignocellulosic-based bioethanol supply chain. • Multiple uncertainties in switchgrass yield, crop residue purchase price, bioethanol demand, and bioethanol sale price. • Proposed stochastic model outperforms the traditional deterministic model under uncertainties. • Stochastic parameters significantly affect marginal land allocation for switchgrass cultivation and bioethanol production. • Location of biorefineries is found to be insensitive to the stochastic environment
A note on the strong formulation of stochastic control problems with model uncertainty
Sirbu, Mihai
2014-01-01
We consider a Markovian stochastic control problem with model uncertainty. The controller (intelligent player) observes only the state, and, therefore, uses feedback (closed-loop) strategies. The adverse player (nature) who does not have a direct interest in the payoff, chooses open-loop controls that parametrize Knightian uncertainty. This creates a two-step optimization problem (like half of a game) over feedback strategies and open-loop controls. The main result is to sh...
Numerical research of the optimal control problem in the semi-Markov inventory model
Energy Technology Data Exchange (ETDEWEB)
Gorshenin, Andrey K. [Institute of Informatics Problems, Russian Academy of Sciences, Vavilova str., 44/2, Moscow, Russia MIREA, Faculty of Information Technology (Russian Federation); Belousov, Vasily V. [Institute of Informatics Problems, Russian Academy of Sciences, Vavilova str., 44/2, Moscow (Russian Federation); Shnourkoff, Peter V.; Ivanov, Alexey V. [National research university Higher school of economics, Moscow (Russian Federation)
2015-03-10
This paper is devoted to the numerical simulation of stochastic system for inventory management products using controlled semi-Markov process. The results of a special software for the system’s research and finding the optimal control are presented.
Numerical research of the optimal control problem in the semi-Markov inventory model
International Nuclear Information System (INIS)
Gorshenin, Andrey K.; Belousov, Vasily V.; Shnourkoff, Peter V.; Ivanov, Alexey V.
2015-01-01
This paper is devoted to the numerical simulation of stochastic system for inventory management products using controlled semi-Markov process. The results of a special software for the system’s research and finding the optimal control are presented
Optimizing signal recycling for detecting a stochastic gravitational-wave background
Tao, Duo; Christensen, Nelson
2018-06-01
Signal recycling is applied in laser interferometers such as the Advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO) to increase their sensitivity to gravitational waves. In this study, signal recycling configurations for detecting a stochastic gravitational wave background are optimized based on aLIGO parameters. Optimal transmission of the signal recycling mirror (SRM) and detuning phase of the signal recycling cavity under a fixed laser power and low-frequency cutoff are calculated. Based on the optimal configurations, the compatibility with a binary neutron star (BNS) search is discussed. Then, different laser powers and low-frequency cutoffs are considered. Two models for the dimensionless energy density of gravitational waves , the flat model and the model, are studied. For a stochastic background search, it is found that an interferometer using signal recycling has a better sensitivity than an interferometer not using it. The optimal stochastic search configurations are typically found when both the SRM transmission and the signal recycling detuning phase are low. In this region, the BNS range mostly lies between 160 and 180 Mpc. When a lower laser power is used the optimal signal recycling detuning phase increases, the optimal SRM transmission increases and the optimal sensitivity improves. A reduced low-frequency cutoff gives a better sensitivity limit. For both models of , a typical optimal sensitivity limit on the order of 10‑10 is achieved at a reference frequency of Hz.
International Nuclear Information System (INIS)
Zare Oskouei, Morteza; Sadeghi Yazdankhah, Ahmad
2015-01-01
Highlights: • Two-stage objective function is proposed for optimization problem. • Hourly-based optimal contractual agreement is calculated. • Scenario-based stochastic optimization problem is solved. • Improvement of system frequency by utilizing PSH unit. - Abstract: This paper proposes the operating strategy of a micro grid connected wind farm, photovoltaic and pump-storage hybrid system. The strategy consists of two stages. In the first stage, the optimal hourly contractual agreement is determined. The second stage corresponds to maximizing its profit by adapting energy management strategy of wind and photovoltaic in coordination with optimum operating schedule of storage device under frequency based pricing for a day ahead electricity market. The pump-storage hydro plant is utilized to minimize unscheduled interchange flow and maximize the system benefit by participating in frequency control based on energy price. Because of uncertainties in power generation of renewable sources and market prices, generation scheduling is modeled by a stochastic optimization problem. Uncertainties of parameters are modeled by scenario generation and scenario reduction method. A powerful optimization algorithm is proposed using by General Algebraic Modeling System (GAMS)/CPLEX. In order to verify the efficiency of the method, the algorithm is applied to various scenarios with different wind and photovoltaic power productions in a day ahead electricity market. The numerical results demonstrate the effectiveness of the proposed approach.
Empirical Estimates in Stochastic Optimization via Distribution Tails
Czech Academy of Sciences Publication Activity Database
Kaňková, Vlasta
2010-01-01
Roč. 46, č. 3 (2010), s. 459-471 ISSN 0023-5954. [International Conference on Mathematical Methods in Economy and Industry. České Budějovice, 15.06.2009-18.06.2009] R&D Projects: GA ČR GA402/07/1113; GA ČR(CZ) GA402/08/0107; GA MŠk(CZ) LC06075 Institutional research plan: CEZ:AV0Z10750506 Keywords : Stochastic programming problems * Stability * Wasserstein metric * L_1 norm * Lipschitz property * Empirical estimates * Convergence rate * Exponential tails * Heavy tails * Pareto distribution * Risk functional * Empirical quantiles Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.461, year: 2010
Approximate Controllability for Linear Stochastic Differential Equations in Infinite Dimensions
International Nuclear Information System (INIS)
Goreac, D.
2009-01-01
The objective of the paper is to investigate the approximate controllability property of a linear stochastic control system with values in a separable real Hilbert space. In a first step we prove the existence and uniqueness for the solution of the dual linear backward stochastic differential equation. This equation has the particularity that in addition to an unbounded operator acting on the Y-component of the solution there is still another one acting on the Z-component. With the help of this dual equation we then deduce the duality between approximate controllability and observability. Finally, under the assumption that the unbounded operator acting on the state process of the forward equation is an infinitesimal generator of an exponentially stable semigroup, we show that the generalized Hautus test provides a necessary condition for the approximate controllability. The paper generalizes former results by Buckdahn, Quincampoix and Tessitore (Stochastic Partial Differential Equations and Applications, Series of Lecture Notes in Pure and Appl. Math., vol. 245, pp. 253-260, Chapman and Hall, London, 2006) and Goreac (Applied Analysis and Differential Equations, pp. 153-164, World Scientific, Singapore, 2007) from the finite dimensional to the infinite dimensional case
Zhang, Xiaodong; Huang, Gordon
2013-02-15
Greenhouse gas (GHG) emissions from municipal solid waste (MSW) management facilities have become a serious environmental issue. In MSW management, not only economic objectives but also environmental objectives should be considered simultaneously. In this study, a dynamic stochastic possibilistic multiobjective programming (DSPMP) model is developed for supporting MSW management and associated GHG emission control. The DSPMP model improves upon the existing waste management optimization methods through incorporation of fuzzy possibilistic programming and chance-constrained programming into a general mixed-integer multiobjective linear programming (MOP) framework where various uncertainties expressed as fuzzy possibility distributions and probability distributions can be effectively reflected. Two conflicting objectives are integrally considered, including minimization of total system cost and minimization of total GHG emissions from waste management facilities. Three planning scenarios are analyzed and compared, representing different preferences of the decision makers for economic development and environmental-impact (i.e. GHG-emission) issues in integrated MSW management. Optimal decision schemes under three scenarios and different p(i) levels (representing the probability that the constraints would be violated) are generated for planning waste flow allocation and facility capacity expansions as well as GHG emission control. The results indicate that economic and environmental tradeoffs can be effectively reflected through the proposed DSPMP model. The generated decision variables can help the decision makers justify and/or adjust their waste management strategies based on their implicit knowledge and preferences. Copyright © 2012 Elsevier B.V. All rights reserved.
Quality control system response to stochastic growth of amyloid fibrils
DEFF Research Database (Denmark)
Pigolotti, S.; Lizana, L.; Sneppen, K.
2013-01-01
We introduce a stochastic model describing aggregation of misfolded proteins and degradation by the protein quality control system in a single cell. Aggregate growth is contrasted by the cell quality control system, that attacks them at different stages of the growth process, with an efficiency...... that decreases with their size. Model parameters are estimated from experimental data. Two qualitatively different behaviors emerge: a homeostatic state, where the quality control system is stable and aggregates of large sizes are not formed, and an oscillatory state, where the quality control system...
P.A.N. Bosman (Peter); J.A. La Poutré (Han); D. Thierens (Dirk)
2007-01-01
htmlabstractThe focus of this paper is on how to design evolutionary algorithms (EAs) for solving stochastic dynamic optimization problems online, i.e. as time goes by. For a proper design, the EA must not only be capable of tracking shifting optima, it must also take into account the future
Optimal control for chemical engineers
Upreti, Simant Ranjan
2013-01-01
Optimal Control for Chemical Engineers gives a detailed treatment of optimal control theory that enables readers to formulate and solve optimal control problems. With a strong emphasis on problem solving, the book provides all the necessary mathematical analyses and derivations of important results, including multiplier theorems and Pontryagin's principle.The text begins by introducing various examples of optimal control, such as batch distillation and chemotherapy, and the basic concepts of optimal control, including functionals and differentials. It then analyzes the notion of optimality, de
Optimal Control of Hybrid Systems in Air Traffic Applications
Kamgarpour, Maryam
Growing concerns over the scalability of air traffic operations, air transportation fuel emissions and prices, as well as the advent of communication and sensing technologies motivate improvements to the air traffic management system. To address such improvements, in this thesis a hybrid dynamical model as an abstraction of the air traffic system is considered. Wind and hazardous weather impacts are included using a stochastic model. This thesis focuses on the design of algorithms for verification and control of hybrid and stochastic dynamical systems and the application of these algorithms to air traffic management problems. In the deterministic setting, a numerically efficient algorithm for optimal control of hybrid systems is proposed based on extensions of classical optimal control techniques. This algorithm is applied to optimize the trajectory of an Airbus 320 aircraft in the presence of wind and storms. In the stochastic setting, the verification problem of reaching a target set while avoiding obstacles (reach-avoid) is formulated as a two-player game to account for external agents' influence on system dynamics. The solution approach is applied to air traffic conflict prediction in the presence of stochastic wind. Due to the uncertainty in forecasts of the hazardous weather, and hence the unsafe regions of airspace for aircraft flight, the reach-avoid framework is extended to account for stochastic target and safe sets. This methodology is used to maximize the probability of the safety of aircraft paths through hazardous weather. Finally, the problem of modeling and optimization of arrival air traffic and runway configuration in dense airspace subject to stochastic weather data is addressed. This problem is formulated as a hybrid optimal control problem and is solved with a hierarchical approach that decouples safety and performance. As illustrated with this problem, the large scale of air traffic operations motivates future work on the efficient
Stochastic Model Predictive Control with Applications in Smart Energy Systems
DEFF Research Database (Denmark)
Sokoler, Leo Emil; Edlund, Kristian; Mølbak, Tommy
2012-01-01
to cover more than 50% of the total consumption by 2050. Energy systems based on significant amounts of renewable energy sources are subject to uncertainties. To accommodate the need for model predictive control (MPC) of such systems, the effect of the stochastic effects on the constraints must...... study, we consider a system consisting of fuel-fired thermal power plants, wind farms and electric vehicles....
Stochastic quasi-gradient based optimization algorithms for dynamic reliability applications
International Nuclear Information System (INIS)
Bourgeois, F.; Labeau, P.E.
2001-01-01
On one hand, PSA results are increasingly used in decision making, system management and optimization of system design. On the other hand, when severe accidental transients are considered, dynamic reliability appears appropriate to account for the complex interaction between the transitions between hardware configurations, the operator behavior and the dynamic evolution of the system. This paper presents an exploratory work in which the estimation of the system unreliability in a dynamic context is coupled with an optimization algorithm to determine the 'best' safety policy. Because some reliability parameters are likely to be distributed, the cost function to be minimized turns out to be a random variable. Stochastic programming techniques are therefore envisioned to determine an optimal strategy. Monte Carlo simulation is used at all stages of the computations, from the estimation of the system unreliability to that of the stochastic quasi-gradient. The optimization algorithm is illustrated on a HNO 3 supply system
Stochastic Modelling and Self Tuning Control of a Continuous Cement Raw Material Mixing System
Directory of Open Access Journals (Sweden)
Hannu T. Toivonen
1980-01-01
Full Text Available The control of a continuously operating system for cement raw material mixing is studied. The purpose of the mixing system is to maintain a constant composition of the cement raw meal for the kiln despite variations of the raw material compositions. Experimental knowledge of the process dynamics and the characteristics of the various disturbances is used for deriving a stochastic model of the system. The optimal control strategy is then obtained as a minimum variance strategy. The control problem is finally solved using a self-tuning minimum variance regulator, and results from a successful implementation of the regulator are given.
Power, control and optimization
Vasant, Pandian; Barsoum, Nader
2013-01-01
The book consists of chapters based on selected papers of international conference „Power, Control and Optimization 2012”, held in Las Vegas, USA. Readers can find interesting chapters discussing various topics from the field of power control, its distribution and related fields. Book discusses topics like energy consumption impacted by climate, mathematical modeling of the influence of thermal power plant on the aquatic environment, investigation of cost reduction in residential electricity bill using electric vehicle at peak times or allocation and size evaluation of distributed generation using ANN model and others. Chapter authors are to the best of our knowledge the originators or closely related to the originators of presented ideas and its applications. Hence, this book certainly is one of the few books discussing the benefit from intersection of those modern and fruitful scientific fields of research with very tight and deep impact on real life and industry. This book is devoted to the studies o...
DEFF Research Database (Denmark)
Sadegh, Payman
1997-01-01
This paper deals with a projection algorithm for stochastic approximation using simultaneous perturbation gradient approximation for optimization under inequality constraints where no direct gradient of the loss function is available and the inequality constraints are given as explicit functions...... of the optimization parameters. It is shown that, under application of the projection algorithm, the parameter iterate converges almost surely to a Kuhn-Tucker point, The procedure is illustrated by a numerical example, (C) 1997 Elsevier Science Ltd....
Modelling on optimal portfolio with exchange rate based on discontinuous stochastic process
Yan, Wei; Chang, Yuwen
2016-12-01
Considering the stochastic exchange rate, this paper is concerned with the dynamic portfolio selection in financial market. The optimal investment problem is formulated as a continuous-time mathematical model under mean-variance criterion. These processes follow jump-diffusion processes (Weiner process and Poisson process). Then the corresponding Hamilton-Jacobi-Bellman(HJB) equation of the problem is presented and its efferent frontier is obtained. Moreover, the optimal strategy is also derived under safety-first criterion.
Introduction to optimal control theory
International Nuclear Information System (INIS)
Agrachev, A.A.
2002-01-01
These are lecture notes of the introductory course in Optimal Control theory treated from the geometric point of view. Optimal Control Problem is reduced to the study of controls (and corresponding trajectories) leading to the boundary of attainable sets. We discuss Pontryagin Maximum Principle, basic existence results, and apply these tools to concrete simple optimal control problems. Special sections are devoted to the general theory of linear time-optimal problems and linear-quadratic problems. (author)
Existence of optimal controls for systems governed by mean-field ...
African Journals Online (AJOL)
In this paper, we study the existence of an optimal control for systems, governed by stochastic dierential equations of mean-eld type. For non linear systems, we prove the existence of an optimal relaxed control, by using tightness techniques and Skorokhod selection theorem. The optimal control is a measure valued process ...
Kim, U.; Parker, J.; Borden, R. C.
2014-12-01
In-situ chemical oxidation (ISCO) has been applied at many dense non-aqueous phase liquid (DNAPL) contaminated sites. A stirred reactor-type model was developed that considers DNAPL dissolution using a field-scale mass transfer function, instantaneous reaction of oxidant with aqueous and adsorbed contaminant and with readily oxidizable natural oxygen demand ("fast NOD"), and second-order kinetic reactions with "slow NOD." DNAPL dissolution enhancement as a function of oxidant concentration and inhibition due to manganese dioxide precipitation during permanganate injection are included in the model. The DNAPL source area is divided into multiple treatment zones with different areas, depths, and contaminant masses based on site characterization data. The performance model is coupled with a cost module that involves a set of unit costs representing specific fixed and operating costs. Monitoring of groundwater and/or soil concentrations in each treatment zone is employed to assess ISCO performance and make real-time decisions on oxidant reinjection or ISCO termination. Key ISCO design variables include the oxidant concentration to be injected, time to begin performance monitoring, groundwater and/or soil contaminant concentrations to trigger reinjection or terminate ISCO, number of monitoring wells or geoprobe locations per treatment zone, number of samples per sampling event and location, and monitoring frequency. Design variables for each treatment zone may be optimized to minimize expected cost over a set of Monte Carlo simulations that consider uncertainty in site parameters. The model is incorporated in the Stochastic Cost Optimization Toolkit (SCOToolkit) program, which couples the ISCO model with a dissolved plume transport model and with modules for other remediation strategies. An example problem is presented that illustrates design tradeoffs required to deal with characterization and monitoring uncertainty. Monitoring soil concentration changes during ISCO
Optimal Resource Management in a Stochastic Schaefer Model
Richard Hartman
2008-01-01
This paper incorporates uncertainty into the growth function of the Schaefer model for the optimal management of a biological resource. There is a critical value for the biological stock, and it is optimal to do no harvesting if the biological stock is below that critical value and to exert whatever harvesting effort is necessary to prevent the stock from rising above that critical value. The introduction of uncertainty increases the critical value of the stock.
Driving-behavior-aware stochastic model predictive control for plug-in hybrid electric buses
International Nuclear Information System (INIS)
Li, Liang; You, Sixiong; Yang, Chao; Yan, Bingjie; Song, Jian; Chen, Zheng
2016-01-01
Highlights: • The novel approximated global optimal energy management strategy has been proposed for hybrid powertrains. • Eight typical driving behaviors have been classified with K-means to deal with the multiplicative traffic conditions. • The stochastic driver models of different driving behaviors were established based on the Markov chains. • ECMS was used to modify the SMPC-based energy management strategy to improve its fuel economy. • The approximated global optimal energy management strategy for plug-in hybrid electric buses has been verified and analyzed. - Abstract: Driving cycles of a city bus is statistically characterized by some repetitive features, which makes the predictive energy management strategy very desirable to obtain approximate optimal fuel economy of a plug-in hybrid electric bus. But dealing with the complicated traffic conditions and finding an approximated global optimal strategy which is applicable to the plug-in hybrid electric bus still remains a challenging technique. To solve this problem, a novel driving-behavior-aware modified stochastic model predictive control method is proposed for the plug-in hybrid electric bus. Firstly, the K-means is employed to classify driving behaviors, and the driver models based on Markov chains is obtained under different kinds of driving behaviors. While the obtained driver behaviors are regarded as stochastic disturbance inputs, the local minimum fuel consumption might be obtained with a traditional stochastic model predictive control at each step, taking tracking the reference battery state of charge trajectory into consideration in the finite predictive horizons. However, this technique is still accompanied by some working points with reduced/worsened fuel economy. Thus, the stochastic model predictive control is modified with the equivalent consumption minimization strategy to eliminate these undesirable working points. The results in real-world city bus routines show that the
Stochastic optimal charging of electric-drive vehicles with renewable energy
International Nuclear Information System (INIS)
Pantoš, Miloš
2011-01-01
The paper presents the stochastic optimization algorithm that may eventually be used by electric energy suppliers to coordinate charging of electric-drive vehicles (EDVs) in order to maximize the use of renewable energy in transportation. Due to the stochastic nature of transportation patterns, the Monte Carlo simulation is applied to model uncertainties presented by numerous scenarios. To reduce the problem complexity, the simulated driving patterns are not individually considered in the optimization but clustered into fleets using the GAMS/SCENRED tool. Uncertainties of production of renewable energy sources (RESs) are presented by statistical central moments that are further considered in Hong’s 2-point + 1 estimation method in order to define estimate points considered in the optimization. Case studies illustrate the application of the proposed optimization in achieving maximal exploitation of RESs in transportation by EDVs. -- Highlights: ► Optimization model for EDV charging applying linear programming. ► Formation of EDV fleets based on the driving patterns assessment applying the GAMS/SCENRED. ► Consideration of uncertainties of RES production and energy prices in the market. ► Stochastic optimization. ► Application of Hong’s 2-point + 1 estimation method.
Stability and synchronization control of stochastic neural networks
Zhou, Wuneng; Zhou, Liuwei; Tong, Dongbing
2016-01-01
This book reports on the latest findings in the study of Stochastic Neural Networks (SNN). The book collects the novel model of the disturbance driven by Levy process, the research method of M-matrix, and the adaptive control method of the SNN in the context of stability and synchronization control. The book will be of interest to university researchers, graduate students in control science and engineering and neural networks who wish to learn the core principles, methods, algorithms and applications of SNN.
Energy-Based Controller Design of Stochastic Magnetic Levitation System
Directory of Open Access Journals (Sweden)
Weiwei Sun
2017-01-01
Full Text Available This paper investigates the control problem of magnetic levitation system, in which velocity feedback signal is influenced by stochastic disturbance. Firstly, single-degree-freedom magnetic levitation is regarded as an energy-transform action device. From the view of energy-balance relation, the magnetic levitation system is transformed into port-controlled Hamiltonian system model. Next, based on the Hamiltonian structure, the control law of magnetic levitation system is designed by applying Lyapunov theory. Finally, the simulation verifies the correctness of the proposed results.
Unit Stratified Sampling as a Tool for Approximation of Stochastic Optimization Problems
Czech Academy of Sciences Publication Activity Database
Šmíd, Martin
2012-01-01
Roč. 19, č. 30 (2012), s. 153-169 ISSN 1212-074X R&D Projects: GA ČR GAP402/11/0150; GA ČR GAP402/10/0956; GA ČR GA402/09/0965 Institutional research plan: CEZ:AV0Z10750506 Institutional support: RVO:67985556 Keywords : Stochastic programming * approximation * stratified sampling Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2013/E/smid-unit stratified sampling as a tool for approximation of stochastic optimization problems.pdf
Stochastic Optimization Model to STudy the Operational Impacts of High Wind Penetrations in Ireland
DEFF Research Database (Denmark)
Meibom, Peter; Barth, R.; Hasche, B.
2011-01-01
A stochastic mixed integer linear optimization scheduling model minimizing system operation costs and treating load and wind power production as stochastic inputs is presented. The schedules are updated in a rolling manner as more up-to-date information becomes available. This is a fundamental...... change relative to day-ahead unit commitment approaches. The need for reserves dependent on forecast horizon and share of wind power has been estimated with a statistical model combining load and wind power forecast errors with scenarios of forced outages. The model is used to study operational impacts...
International Nuclear Information System (INIS)
Yokose, Yoshio; Noguchi, So; Yamashita, Hideo
2002-01-01
Stochastic methods and deterministic methods are used for the problem of optimization of electromagnetic devices. The Genetic Algorithms (GAs) are used for one stochastic method in multivariable designs, and the deterministic method uses the gradient method, which is applied sensitivity of the objective function. These two techniques have benefits and faults. In this paper, the characteristics of those techniques are described. Then, research evaluates the technique by which two methods are used together. Next, the results of the comparison are described by applying each method to electromagnetic devices. (Author)
A stochastic programming approach towards optimization of biofuel supply chain
International Nuclear Information System (INIS)
Azadeh, Ali; Vafa Arani, Hamed; Dashti, Hossein
2014-01-01
Bioenergy has been recognized as an important source of energy that will reduce dependency on petroleum. It would have a positive impact on the economy, environment, and society. Production of bioenergy is expected to increase. As a result, we foresee an increase in the number of biorefineries in the near future. This paper analyzes challenges with supplying biomass to a biorefinery and shipping biofuel to demand centers. A stochastic linear programming model is proposed within a multi-period planning framework to maximize the expected profit. The model deals with a time-staged, multi-commodity, production/distribution system, facility locations and capacities, technologies, and material flows. We illustrate the model outputs and discuss the results through numerical examples considering disruptions in biofuel supply chain. Finally, sensitivity analyses are performed to gain managerial insights on how profit changes due to existing uncertainties. - Highlights: • A robust model of biofuel SC is proposed and a sensitivity analysis implemented. • Demand of products is a function of price and GBM (Geometric Brownian Motion) is used for prices of biofuels. • Uncertainties in SC network are captured through defining probabilistic scenarios. • Both traditional feedstock and lignocellulosic biomass are considered for biofuel production. • Developed model is applicable to any related biofuel supply chain regardless of region
Stochastic Averaging for Constrained Optimization With Application to Online Resource Allocation
Chen, Tianyi; Mokhtari, Aryan; Wang, Xin; Ribeiro, Alejandro; Giannakis, Georgios B.
2017-06-01
Existing approaches to resource allocation for nowadays stochastic networks are challenged to meet fast convergence and tolerable delay requirements. The present paper leverages online learning advances to facilitate stochastic resource allocation tasks. By recognizing the central role of Lagrange multipliers, the underlying constrained optimization problem is formulated as a machine learning task involving both training and operational modes, with the goal of learning the sought multipliers in a fast and efficient manner. To this end, an order-optimal offline learning approach is developed first for batch training, and it is then generalized to the online setting with a procedure termed learn-and-adapt. The novel resource allocation protocol permeates benefits of stochastic approximation and statistical learning to obtain low-complexity online updates with learning errors close to the statistical accuracy limits, while still preserving adaptation performance, which in the stochastic network optimization context guarantees queue stability. Analysis and simulated tests demonstrate that the proposed data-driven approach improves the delay and convergence performance of existing resource allocation schemes.
Liang, Faming
2014-04-03
Simulated annealing has been widely used in the solution of optimization problems. As known by many researchers, the global optima cannot be guaranteed to be located by simulated annealing unless a logarithmic cooling schedule is used. However, the logarithmic cooling schedule is so slow that no one can afford to use this much CPU time. This article proposes a new stochastic optimization algorithm, the so-called simulated stochastic approximation annealing algorithm, which is a combination of simulated annealing and the stochastic approximation Monte Carlo algorithm. Under the framework of stochastic approximation, it is shown that the new algorithm can work with a cooling schedule in which the temperature can decrease much faster than in the logarithmic cooling schedule, for example, a square-root cooling schedule, while guaranteeing the global optima to be reached when the temperature tends to zero. The new algorithm has been tested on a few benchmark optimization problems, including feed-forward neural network training and protein-folding. The numerical results indicate that the new algorithm can significantly outperform simulated annealing and other competitors. Supplementary materials for this article are available online.
Optimal Control of Mechanical Systems
Directory of Open Access Journals (Sweden)
Vadim Azhmyakov
2007-01-01
Full Text Available In the present work, we consider a class of nonlinear optimal control problems, which can be called “optimal control problems in mechanics.” We deal with control systems whose dynamics can be described by a system of Euler-Lagrange or Hamilton equations. Using the variational structure of the solution of the corresponding boundary-value problems, we reduce the initial optimal control problem to an auxiliary problem of multiobjective programming. This technique makes it possible to apply some consistent numerical approximations of a multiobjective optimization problem to the initial optimal control problem. For solving the auxiliary problem, we propose an implementable numerical algorithm.
Worst-Case Portfolio Optimization under Stochastic Interest Rate Risk
Directory of Open Access Journals (Sweden)
Tina Engler
2014-12-01
Full Text Available We investigate a portfolio optimization problem under the threat of a market crash, where the interest rate of the bond is modeled as a Vasicek process, which is correlated with the stock price process. We adopt a non-probabilistic worst-case approach for the height and time of the market crash. On a given time horizon [0; T], we then maximize the investor’s expected utility of terminal wealth in the worst-case crash scenario. Our main result is an explicit characterization of the worst-case optimal portfolio strategy for the class of HARA (hyperbolic absolute risk aversion utility functions.
Optimally eating a stochastic cake. A recursive utility approach
International Nuclear Information System (INIS)
Epaulard, Anne; Pommeret, Aude
2003-01-01
In this short paper, uncertainties on resource stock and on technical progress are introduced into an intertemporal equilibrium model of optimal extraction of a non-renewable resource. The representative consumer maximizes a recursive utility function which disentangles between intertemporal elasticity of substitution and risk aversion. A closed-form solution is derived for both the optimal extraction and price paths. The value of the intertemporal elasticity of substitution relative to unity is then crucial in understanding extraction. Moreover, this model leads to a non-renewable resource price following a geometric Brownian motion
Euler's fluid equations: Optimal control vs optimization
International Nuclear Information System (INIS)
Holm, Darryl D.
2009-01-01
An optimization method used in image-processing (metamorphosis) is found to imply Euler's equations for incompressible flow of an inviscid fluid, without requiring that the Lagrangian particle labels exactly follow the flow lines of the Eulerian velocity vector field. Thus, an optimal control problem and an optimization problem for incompressible ideal fluid flow both yield the same Euler fluid equations, although their Lagrangian parcel dynamics are different. This is a result of the gauge freedom in the definition of the fluid pressure for an incompressible flow, in combination with the symmetry of fluid dynamics under relabeling of their Lagrangian coordinates. Similar ideas are also illustrated for SO(N) rigid body motion.
Annealing evolutionary stochastic approximation Monte Carlo for global optimization
Liang, Faming
2010-04-08
In this paper, we propose a new algorithm, the so-called annealing evolutionary stochastic approximation Monte Carlo (AESAMC) algorithm as a general optimization technique, and study its convergence. AESAMC possesses a self-adjusting mechanism, whose target distribution can be adapted at each iteration according to the current samples. Thus, AESAMC falls into the class of adaptive Monte Carlo methods. This mechanism also makes AESAMC less trapped by local energy minima than nonadaptive MCMC algorithms. Under mild conditions, we show that AESAMC can converge weakly toward a neighboring set of global minima in the space of energy. AESAMC is tested on multiple optimization problems. The numerical results indicate that AESAMC can potentially outperform simulated annealing, the genetic algorithm, annealing stochastic approximation Monte Carlo, and some other metaheuristics in function optimization. © 2010 Springer Science+Business Media, LLC.
An Optimal Stochastic Investment and Consumption Strategy with ...
African Journals Online (AJOL)
This paper considers a single investor who owns a production plant that generates units of consumption goods in a capitalist economy. The goal is to choose optimal investment and consumption policies that maximize the finite horizon expected discounted logarithmic utility of consumption and terminal wealth. A dynamical ...
International Nuclear Information System (INIS)
Langrene, Nicolas
2014-01-01
This thesis deals with the numerical solution of general stochastic control problems, with notable applications for electricity markets. We first propose a structural model for the price of electricity, allowing for price spikes well above the marginal fuel price under strained market conditions. This model allows to price and partially hedge electricity derivatives, using fuel forwards as hedging instruments. Then, we propose an algorithm, which combines Monte-Carlo simulations with local basis regressions, to solve general optimal switching problems. A comprehensive rate of convergence of the method is provided. Moreover, we manage to make the algorithm parsimonious in memory (and hence suitable for high dimensional problems) by generalizing to this framework a memory reduction method that avoids the storage of the sample paths. We illustrate this on the problem of investments in new power plants (our structural power price model allowing the new plants to impact the price of electricity). Finally, we study more general stochastic control problems (the control can be continuous and impact the drift and volatility of the state process), the solutions of which belong to the class of fully nonlinear Hamilton-Jacobi-Bellman equations, and can be handled via constrained Backward Stochastic Differential Equations, for which we develop a backward algorithm based on control randomization and parametric optimizations. A rate of convergence between the constraPned BSDE and its discrete version is provided, as well as an estimate of the optimal control. This algorithm is then applied to the problem of super replication of options under uncertain volatilities (and correlations). (author)
Fully probabilistic control for stochastic nonlinear control systems with input dependent noise.
Herzallah, Randa
2015-03-01
Robust controllers for nonlinear stochastic systems with functional uncertainties can be consistently designed using probabilistic control methods. In this paper a generalised probabilistic controller design for the minimisation of the Kullback-Leibler divergence between the actual joint probability density function (pdf) of the closed loop control system, and an ideal joint pdf is presented emphasising how the uncertainty can be systematically incorporated in the absence of reliable systems models. To achieve this objective all probabilistic models of the system are estimated from process data using mixture density networks (MDNs) where all the parameters of the estimated pdfs are taken to be state and control input dependent. Based on this dependency of the density parameters on the input values, explicit formulations to the construction of optimal generalised probabilistic controllers are obtained through the techniques of dynamic programming and adaptive critic methods. Using the proposed generalised probabilistic controller, the conditional joint pdfs can be made to follow the ideal ones. A simulation example is used to demonstrate the implementation of the algorithm and encouraging results are obtained. Copyright © 2014 Elsevier Ltd. All rights reserved.
Keçeci, Neslihan Fidan; Kuzmenko, Viktor; Uryasev, Stan
2016-01-01
The paper compares portfolio optimization with the Second-Order Stochastic Dominance (SSD) constraints with mean-variance and minimum variance portfolio optimization. As a distribution-free decision rule, stochastic dominance takes into account the entire distribution of return rather than some specific characteristic, such as variance. The paper is focused on practical applications of the portfolio optimization and uses the Portfolio Safeguard (PSG) package, which has precoded modules for op...
Neslihan Fidan Keçeci; Viktor Kuzmenko; Stan Uryasev
2016-01-01
The paper compares portfolio optimization with the Second-Order Stochastic Dominance (SSD) constraints with mean-variance and minimum variance portfolio optimization. As a distribution-free decision rule, stochastic dominance takes into account the entire distribution of return rather than some specific characteristic, such as variance. The paper is focused on practical applications of the portfolio optimization and uses the Portfolio Safeguard (PSG) package, which has precoded modules for op...
Adaptive Decision Making Using Probabilistic Programming and Stochastic Optimization
2018-01-01
world optimization problems (and hence 16 Approved for Public Release (PA); Distribution Unlimited Pred. demand (uncertain; discrete ...simplify the setting, we further assume that the demands are discrete , taking on values d1, . . . , dk with probabilities (conditional on x) (pθ)i ≡ p...Tyrrell Rockafellar. Implicit functions and solution mappings. Springer Monogr. Math ., 2009. Anthony V Fiacco and Yo Ishizuka. Sensitivity and stability
A remark on multiobjective stochastic optimization via strongly convex functions
Czech Academy of Sciences Publication Activity Database
Kaňková, Vlasta
2016-01-01
Roč. 24, č. 2 (2016), s. 309-333 ISSN 1435-246X R&D Projects: GA ČR GA13-14445S Institutional support: RVO:67985556 Keywords : Stochasticmultiobjective optimization problem * Efficient solution * Wasserstein metric and L_1 norm * Stability and empirical estimates Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.659, year: 2016 http://library.utia.cas.cz/separaty/2015/E/kankova-0450553.pdf
Stochastic optimization under risk constraint and utility functions
International Nuclear Information System (INIS)
Seck, B.
2008-09-01
In a context of concurrence and emergence of energy markets, the production of electricity is affected by the new sources of risks which are the price variations on the energy markets. These new sources of risks generate a new risk: the market risk. In this research, the author explores the possibility of introducing constraints, expressed by measurements of risk, into the process of optimization of electricity production when financial contracts are signed on the energy market. The author makes the distinction between the engineering approach (taking the risk into account by risk measurements) and the economist approach (taking the risk into account by utility functions). After an overview of these both approaches in a static framework, he gives an economical formulation (a Maccheroni type one) for a static optimization problem under a risk constraint when the risk measurement is written under the form of an expected infimum like the variance, the 'conditional value at risk', and so on. The obtained results are then extended to a dynamic optimization framework under risk constraints. A numerical application of this approach is presented to solve a problem of electricity production management under a constraint of 'conditional value at risk' on a middle term
International Nuclear Information System (INIS)
Khorramdel, Benyamin; Raoofat, Mahdi
2012-01-01
Distributed Generators (DGs) in a microgrid may operate in three different reactive power control strategies, including PV, PQ and voltage droop schemes. This paper proposes a new stochastic programming approach for reactive power scheduling of a microgrid, considering the uncertainty of wind farms. The proposed algorithm firstly finds the expected optimal operating point of each DG in V-Q plane while the wind speed is a probabilistic variable. A multi-objective function with goals of loss minimization, reactive power reserve maximization and voltage security margin maximization is optimized using a four-stage multi-objective nonlinear programming. Then, using Monte Carlo simulation enhanced by scenario reduction technique, the proposed algorithm simulates actual condition and finds optimal operating strategy of DGs. Also, if any DGs are scheduled to operate in voltage droop scheme, the optimum droop is determined. Also, in the second part of the research, to enhance the optimality of the results, PSO algorithm is used for the multi-objective optimization problem. Numerical examples on IEEE 34-bus test system including two wind turbines are studied. The results show the benefits of voltage droop scheme for mitigating the impacts of the uncertainty of wind. Also, the results show preference of PSO method in the proposed approach. -- Highlights: ► Reactive power scheduling in a microgrid considering loss and voltage security. ► Stochastic nature of wind farms affects reactive power scheduling and is considered. ► Advantages of using the voltage droop characteristics of DGs in voltage security are shown. ► Power loss, voltage security and VAR reserve are three goals of a multi-objective optimization. ► Monte Carlo method with scenario reduction is used to determine optimal control strategy of DGs.
International Nuclear Information System (INIS)
Tahvili, Sahar; Österberg, Jonas; Silvestrov, Sergei; Biteus, Jonas
2014-01-01
One of the most important factors in the operations of many cooperations today is to maximize profit and one important tool to that effect is the optimization of maintenance activities. Maintenance activities is at the largest level divided into two major areas, corrective maintenance (CM) and preventive maintenance (PM). When optimizing maintenance activities, by a maintenance plan or policy, we seek to find the best activities to perform at each point in time, be it PM or CM. We explore the use of stochastic simulation, genetic algorithms and other tools for solving complex maintenance planning optimization problems in terms of a suggested framework model based on discrete event simulation
Energy Technology Data Exchange (ETDEWEB)
Tahvili, Sahar [Mälardalen University (Sweden); Österberg, Jonas; Silvestrov, Sergei [Division of Applied Mathematics, Mälardalen University (Sweden); Biteus, Jonas [Scania CV (Sweden)
2014-12-10
One of the most important factors in the operations of many cooperations today is to maximize profit and one important tool to that effect is the optimization of maintenance activities. Maintenance activities is at the largest level divided into two major areas, corrective maintenance (CM) and preventive maintenance (PM). When optimizing maintenance activities, by a maintenance plan or policy, we seek to find the best activities to perform at each point in time, be it PM or CM. We explore the use of stochastic simulation, genetic algorithms and other tools for solving complex maintenance planning optimization problems in terms of a suggested framework model based on discrete event simulation.
Directory of Open Access Journals (Sweden)
Emmanuel Okewu
2017-10-01
Full Text Available The role of automation in sustainable development is not in doubt. Computerization in particular has permeated every facet of human endeavour, enhancing the provision of information for decision-making that reduces cost of operation, promotes productivity and socioeconomic prosperity and cohesion. Hence, a new field called information and communication technology for development (ICT4D has emerged. Nonetheless, the need to ensure environmentally friendly computing has led to this research study with particular focus on green computing in Africa. This is against the backdrop that the continent is feared to suffer most from the vulnerability of climate change and the impact of environmental risk. Using Nigeria as a test case, this paper gauges the green computing awareness level of Africans via sample survey. It also attempts to institutionalize green computing maturity model with a view to optimizing the level of citizens awareness amid inherent uncertainties like low bandwidth, poor network and erratic power in an emerging African market. Consequently, we classified the problem as a stochastic optimization problem and applied metaheuristic search algorithm to determine the best sensitization strategy. Although there are alternative ways of promoting green computing education, the metaheuristic search we conducted indicated that an online real-time solution that not only drives but preserves timely conversations on electronic waste (e-waste management and energy saving techniques among the citizenry is cutting edge. The authors therefore reviewed literature, gathered requirements, modelled the proposed solution using Universal Modelling Language (UML and developed a prototype. The proposed solution is a web-based multi-tier e-Green computing system that educates computer users on innovative techniques of managing computers and accessories in an environmentally friendly way. We found out that such a real-time web-based interactive forum does not
Directory of Open Access Journals (Sweden)
Farid Chighoub
2014-01-01
the stochastic calculus of jump diffusions and some properties of singular controls. Then, we give, under smoothness conditions, a useful verification theorem and we show that the solution of the adjoint equation coincides with the spatial gradient of the value function, evaluated along the optimal trajectory of the state equation. Finally, using these theoretical results, we solve explicitly an example, on optimal harvesting strategy, for a geometric Brownian motion with jumps.
Stochastic optimization of laboratory test workflow at metallurgical testing centers
Directory of Open Access Journals (Sweden)
F. Tošenovský
2016-10-01
Full Text Available The objective of the paper is to present a way to shorten the time required to perform laboratory tests of materials in metallurgy. The paper finds a relation between the time to perform a test of materials and the number of technicians carrying out the test. The relation can be used to optimize the number of technicians. The approach is based on probability theory, as the amount of material to be tested is unknown in advance, and uses powerful modelling techniques involving the generalized estimating equations.
Time dependent optimal switching controls in online selling models
Energy Technology Data Exchange (ETDEWEB)
Bradonjic, Milan [Los Alamos National Laboratory; Cohen, Albert [MICHIGAN STATE UNIV
2010-01-01
We present a method to incorporate dishonesty in online selling via a stochastic optimal control problem. In our framework, the seller wishes to maximize her average wealth level W at a fixed time T of her choosing. The corresponding Hamilton-Jacobi-Bellmann (HJB) equation is analyzed for a basic case. For more general models, the admissible control set is restricted to a jump process that switches between extreme values. We propose a new approach, where the optimal control problem is reduced to a multivariable optimization problem.
Robust Topology Optimization Based on Stochastic Collocation Methods under Loading Uncertainties
Directory of Open Access Journals (Sweden)
Qinghai Zhao
2015-01-01
Full Text Available A robust topology optimization (RTO approach with consideration of loading uncertainties is developed in this paper. The stochastic collocation method combined with full tensor product grid and Smolyak sparse grid transforms the robust formulation into a weighted multiple loading deterministic problem at the collocation points. The proposed approach is amenable to implementation in existing commercial topology optimization software package and thus feasible to practical engineering problems. Numerical examples of two- and three-dimensional topology optimization problems are provided to demonstrate the proposed RTO approach and its applications. The optimal topologies obtained from deterministic and robust topology optimization designs under tensor product grid and sparse grid with different levels are compared with one another to investigate the pros and cons of optimization algorithm on final topologies, and an extensive Monte Carlo simulation is also performed to verify the proposed approach.
Control of open end plasma flow utilizing orbital stochasticity
International Nuclear Information System (INIS)
Hojo, Hitoshi
1995-01-01
It has been known that the control of plasma outside the confinement region of diverter plasma and others in a magnetic field confinement device is very important for improveing the confinement of bulk plasma. The control of plasma outside a confinement region bears two roles, one is the reduction of the thermal load on a diverter plate and others due to the plasma particles lost from the confinement region, and another is the restriction of the back flow of cold plasma and impurities generated outside the confinement region to a bulk plasma region. In this study, the new method of controlling plasma outside a confinement region called magnetic diverter is considered. To the plasma particles advancing along magnetic force lines, the reflection and capture of the plasma particles occur in the region of orbital stochasticity, and the thermal load on an end plate and the reverse flow to a bulk plasma region are restricted. The numerical computation model used regarding the particle control utilizing the orbital stochasticity and the results of calculating the orbit of plasma particles in a magnetic field are reported. (K.I.)
Evaluation of the need for stochastic optimization of out-of-core nuclear fuel management decisions
International Nuclear Information System (INIS)
Thomas, R.L. Jr.
1989-01-01
Work has been completed on utilizing mathematical optimization techniques to optimize out-of-core nuclear fuel management decisions. The objective of such optimization is to minimize the levelized fuel cycle cost over some planning horizon. Typical decision variables include feed enrichments and number of assemblies, burnable poison requirements, and burned fuel to reinsert for every cycle in the planning horizon. Engineering constraints imposed consist of such items as discharge burnup limits, maximum enrichment limit, and target cycle energy productions. Earlier the authors reported on the development of the OCEON code, which employs the integer Monte Carlo Programming method as the mathematical optimization method. The discharge burnpups, and feed enrichment and burnable poison requirements are evaluated, initially employing a linear reactivity core physics model and refined using a coarse mesh nodal model. The economic evaluation is completed using a modification of the CINCAS methodology. Interest now is to assess the need for stochastic optimization, which will account for cost components and cycle energy production uncertainties. The implication of the present studies is that stochastic optimization in regard to cost component uncertainties need not be completed since deterministic optimization will identify nearly the same family of near-optimum cycling schemes
The stochastic goodwill problem
Marinelli, Carlo
2003-01-01
Stochastic control problems related to optimal advertising under uncertainty are considered. In particular, we determine the optimal strategies for the problem of maximizing the utility of goodwill at launch time and minimizing the disutility of a stream of advertising costs that extends until the launch time for some classes of stochastic perturbations of the classical Nerlove-Arrow dynamics. We also consider some generalizations such as problems with constrained budget and with discretionar...
Beck, Joakim; Nobile, Fabio; Tamellini, Lorenzo; Tempone, Raul
2014-01-01
In this work we consider quasi-optimal versions of the Stochastic Galerkin method for solving linear elliptic PDEs with stochastic coefficients. In particular, we consider the case of a finite number N of random inputs and an analytic dependence of the solution of the PDE with respect to the parameters in a polydisc of the complex plane CN. We show that a quasi-optimal approximation is given by a Galerkin projection on a weighted (anisotropic) total degree space and prove a (sub)exponential convergence rate. As a specific application we consider a thermal conduction problem with non-overlapping inclusions of random conductivity. Numerical results show the sharpness of our estimates. © 2013 Elsevier Ltd. All rights reserved.
Beck, Joakim
2014-03-01
In this work we consider quasi-optimal versions of the Stochastic Galerkin method for solving linear elliptic PDEs with stochastic coefficients. In particular, we consider the case of a finite number N of random inputs and an analytic dependence of the solution of the PDE with respect to the parameters in a polydisc of the complex plane CN. We show that a quasi-optimal approximation is given by a Galerkin projection on a weighted (anisotropic) total degree space and prove a (sub)exponential convergence rate. As a specific application we consider a thermal conduction problem with non-overlapping inclusions of random conductivity. Numerical results show the sharpness of our estimates. © 2013 Elsevier Ltd. All rights reserved.
ALOPEX stochastic optimization for pumping management in fresh water coastal aquifers
International Nuclear Information System (INIS)
Stratis, P N; Saridakis, Y G; Zakynthinaki, M S; Papadopoulou, E P
2014-01-01
Saltwater intrusion in freshwater aquifers is a problem of increasing significance in areas nearby the coastline. Apart from natural disastrous phenomena, such as earthquakes or floods, intense pumping human activities over the aquifer areas may change the chemical composition of the freshwater aquifer. Working towards the direction of real time management of freshwater pumping from coastal aquifers, we have considered the deployment of the stochastic optimization Algorithm of Pattern Extraction (ALOPEX), coupled with several penalty strategies that produce convenient management policies. The present study, which further extents recently derived results, considers the analytical solution of a classical model for underground flow and the ALOPEX stochastic optimization technique to produce an efficient approach for pumping management over coastal aquifers. Numerical experimentation also includes a case study at Vathi area on the Greek island of Kalymnos, to compare with known results in the literature as well as to demonstrate different management strategies
Tehrani, Kayvan F; Zhang, Yiwen; Shen, Ping; Kner, Peter
2017-11-01
Stochastic optical reconstruction microscopy (STORM) can achieve resolutions of better than 20nm imaging single fluorescently labeled cells. However, when optical aberrations induced by larger biological samples degrade the point spread function (PSF), the localization accuracy and number of localizations are both reduced, destroying the resolution of STORM. Adaptive optics (AO) can be used to correct the wavefront, restoring the high resolution of STORM. A challenge for AO-STORM microscopy is the development of robust optimization algorithms which can efficiently correct the wavefront from stochastic raw STORM images. Here we present the implementation of a particle swarm optimization (PSO) approach with a Fourier metric for real-time correction of wavefront aberrations during STORM acquisition. We apply our approach to imaging boutons 100 μm deep inside the central nervous system (CNS) of Drosophila melanogaster larvae achieving a resolution of 146 nm.
Nonlinear stochastic systems with incomplete information filtering and control
Shen, Bo; Shu, Huisheng
2013-01-01
Nonlinear Stochastic Processes addresses the frequently-encountered problem of incomplete information. The causes of this problem considered here include: missing measurements; sensor delays and saturation; quantization effects; and signal sampling. Divided into three parts, the text begins with a focus on H∞ filtering and control problems associated with general classes of nonlinear stochastic discrete-time systems. Filtering problems are considered in the second part, and in the third the theory and techniques previously developed are applied to the solution of issues arising in complex networks with the design of sampled-data-based controllers and filters. Among its highlights, the text provides: · a unified framework for handling filtering and control problems in complex communication networks with limited bandwidth; · new concepts such as random sensor and signal saturations for more realistic modeling; and · demonstration of the use of techniques such...
Haberko, Jakub; Wasylczyk, Piotr
2018-03-01
We demonstrate that a stochastic optimization algorithm with a properly chosen, weighted fitness function, following a global variation of parameters upon each step can be used to effectively design reflective polarizing optical elements. Two sub-wavelength metallic metasurfaces, corresponding to broadband half- and quarter-waveplates are demonstrated with simple structure topology, a uniform metallic coating and with the design suited for the currently available microfabrication techniques, such as ion milling or 3D printing.
Optimization of advanced gas-cooled reactor fuel performance by a stochastic method
International Nuclear Information System (INIS)
Parks, G.T.
1987-01-01
A brief description is presented of a model representing the in-core behaviour of a single advanced gas-cooled reactor fuel channel, developed specifically for optimization studies. The performances of the only suitable Numerical Algorithms Group (NAG) library package and a Metropolis algorithm routine on this problem are discussed and contrasted. It is concluded that, for the problem in question, the stochastic Metropolis algorithm has distinct advantages over the deterministic NAG routine. (author)
Røstad, Lars Dybsjord; Erichsen, Jeanette Christine
2012-01-01
In this thesis, we have developed a strategic optimization model of investments in infrastructure in the LNG value chain. The focus is on floating LNG production units: when they are a viable solution and what value they add to the LNG value chain. First a deterministic model is presented with focus on describing the value chain, before it is expanded to a multistage stochastic model with uncertain field sizes and gas prices. The objective is to maximize expected discounted profits through op...
International Nuclear Information System (INIS)
Karan, Ebrahim; Asadi, Somayeh; Ntaimo, Lewis
2016-01-01
The magnitude of building- and transportation-related GHG (greenhouse gas) emissions makes the adoption of all-EVs (electric vehicles) powered with renewable power as one of the most effective strategies to reduce emission of GHGs. This paper formulates the problem of GHG mitigation strategy under uncertain conditions and optimizes the strategies in which EVs are powered by solar energy. Under a pre-specified budget, the objective is to determine the type of EV and power generation capacity of the solar system in such a way as to maximize GHG emissions reductions. The model supports the three primary solar systems: off-grid, grid-tied, and hybrid. First, a stochastic optimization model using probability distributions of stochastic variables and EV and solar system specifications is developed. The model is then validated by comparing the estimated values of the optimal strategies and actual values. It is found that the mitigation strategies in which EVs are powered by a hybrid solar system lead to the best cost-expected reduction of CO_2 emissions ratio. The results show an accuracy of about 4% for mitigation strategies in which EVs are powered by a grid-tied or hybrid solar system and 11% when applied to estimate the CO_2 emissions reductions of an off-grid system. - Highlights: • The problem of GHG mitigation is formulated as a stochastic optimization problem. • The objective is to maximize CO_2 emissions reductions within a specified budget. • The stochastic model is validated using actual data. • The results show an estimation accuracy of 4–11%.
Tuning of Controller for Type 1 Diabetes Treatment with Stochastic Differential Equations
DEFF Research Database (Denmark)
Duun-Henriksen, Anne Katrine; Boiroux, Dimitri; Schmidt, Signe
2012-01-01
due to the noise corrupted observations from the CGM. In this paper we present a method to estimate the optimal Kalman gain in the controller based on stochastic differential equation modeling. With this model type we could estimate the process noise and observation noise separately based on data from......People with type 1 diabetes need several insulin injections every day to keep their blood glucose level in the normal range and thereby avoiding the acute and long term complications of diabetes. One of the recent treatments consists of a pump injecting insulin into the subcutaneous layer combined...
International Nuclear Information System (INIS)
Sturm, R.
1991-01-01
Two aspects of performance are of main concern: plant availability and plant reliability (defined as the conditional probability of an unplanned shutdown). The goal of the research is a unified framework that combines behavioral models of optimizing agents with models of complex technical systems that take into account the dynamic and stochastic features of the system. In order to achieve this synthesis, two liens of work are necessary. One line requires a deeper understanding of complex production systems and the type of data they give rise to; the other line involves the specification and estimation of a rigorously specified behavioral model. Plant operations are modeled as a controlled stochastic process, and the sequence of up and downtime spells is analyzed during failure time and point process models. Similar to work on rational expectations and structural econometric models, the behavior model of how the plant process is controlled is formulated at the level of basic processes, i.e., the objective function of the plant manager, technical constraints, and stochastic disturbances
Stochastic optimized life cycle models for risk mitigation in power system applications
International Nuclear Information System (INIS)
Sageder, A.
1998-01-01
This ork shows the relevance of stochastic optimization in complex power system applications. It was proven that usual deterministic mean value models not only predict inaccurate results but are also most often on the risky side. The change in the market effects all kind of evaluation processes (e.g. fuel type and technology but especially financial engineering evaluations) in the endeavor of a strict risk mitigation comparison. But not only IPPs also traditional Utilities dash for risk/return optimized investment opportunities. In this study I developed a 2-phase model which can support a decision-maker in finding optimal solutions on investment and profitability. It has to be stated, that in this study no objective function will be optimized in an algorithmically way. On the one hand focus is laid on finding optimal solutions out of different choices (highest return at lowest possible risk); on the other hand the endeavor was to provide a decision makers with a better assessment of the likelihood of outcomes on investment considerations. The first (deterministic) phase computes in a Total Cost of Ownership (TCO) approach (Life cycle Calculation; DCF method). Most of the causal relations (day of operation, escalation of personal expanses, inflation, depreciation period, etc.) are defined within this phase. The second (stochastic) phase is a total new way in optimizing risk/return relations. With the some decision theory mathematics an expected value of stochastic solutions can be calculated. Furthermore probability function have to be defined out of historical data. The model not only supports profitability analysis (including regress and sensitivity analysis) but also supports a decision-maker in a decision process. Emphasis was laid on risk-return analysis, which can give the decision-maker first hand informations of the type of risk return problem (risk concave, averse or linear). Five important parameters were chosen which have the characteristics of typical
Optimal design of distributed energy resource systems based on two-stage stochastic programming
International Nuclear Information System (INIS)
Yang, Yun; Zhang, Shijie; Xiao, Yunhan
2017-01-01
Highlights: • A two-stage stochastic programming model is built to design DER systems under uncertainties. • Uncertain energy demands have a significant effect on the optimal design. • Uncertain energy prices and renewable energy intensity have little effect on the optimal design. • The economy is overestimated if the system is designed without considering the uncertainties. • The uncertainty in energy prices has the significant and greatest effect on the economy. - Abstract: Multiple uncertainties exist in the optimal design of distributed energy resource (DER) systems. The expected energy, economic, and environmental benefits may not be achieved and a deficit in energy supply may occur if the uncertainties are not handled properly. This study focuses on the optimal design of DER systems with consideration of the uncertainties. A two-stage stochastic programming model is built in consideration of the discreteness of equipment capacities, equipment partial load operation and output bounds as well as of the influence of ambient temperature on gas turbine performance. The stochastic model is then transformed into its deterministic equivalent and solved. For an illustrative example, the model is applied to a hospital in Lianyungang, China. Comparative studies are performed to evaluate the effect of the uncertainties in load demands, energy prices, and renewable energy intensity separately and simultaneously on the system’s economy and optimal design. Results show that the uncertainties in load demands have a significant effect on the optimal system design, whereas the uncertainties in energy prices and renewable energy intensity have almost no effect. Results regarding economy show that it is obviously overestimated if the system is designed without considering the uncertainties.
LIBRJMCMC: AN OPEN-SOURCE GENERIC C++ LIBRARY FOR STOCHASTIC OPTIMIZATION
Directory of Open Access Journals (Sweden)
M. Brédif
2012-07-01
Full Text Available The librjmcmc is an open source C++ library that solves optimization problems using a stochastic framework. The library is primarily intended for but not limited to research purposes in computer vision, photogrammetry and remote sensing, as it has initially been developed in the context of extracting building footprints from digital elevation models using a marked point process of rectangles. It has been designed to be both highly modular and extensible, and have computational times comparable to a code specifically designed for a particular application, thanks to the powerful paradigms of metaprogramming and generic programming. The proposed stochastic optimization is built on the coupling of a stochastic Reversible-Jump Markov Chain Monte Carlo (RJMCMC sampler and a simulated annealing relaxation. This framework allows, with theoretical guarantees, the optimization of an unrestricted objective function without requiring any initial solution. The modularity of our library allows the processing of any kind of input data, whether they are 1D signals (e.g. LiDAR or SAR waveforms, 2D images, 3D point clouds... The library user has just to define a few modules describing its domain specific context: the encoding of a configuration (e.g. its object type in a marked point process context, reversible jump kernels (e.g. birth, death, modifications..., the optimized energies (e.g. data and regularization terms and the probabilized search space given by the reference process. Similar to this extensibility in the application domain, concepts are clearly and orthogonally separated such that it is straightforward to customize the convergence test, the temperature schedule, or to add visitors enabling visual feedback during the optimization. The library offers dedicated modules for marked point processes, allowing the user to optimize a Maximum A Posteriori (MAP criterion with an image data term energy on a marked point process of rectangles.
Max-Plus Stochastic Control and Risk-Sensitivity
International Nuclear Information System (INIS)
Fleming, Wendell H.; Kaise, Hidehiro; Sheu, Shuenn-Jyi
2010-01-01
In the Maslov idempotent probability calculus, expectations of random variables are defined so as to be linear with respect to max-plus addition and scalar multiplication. This paper considers control problems in which the objective is to minimize the max-plus expectation of some max-plus additive running cost. Such problems arise naturally as limits of some types of risk sensitive stochastic control problems. The value function is a viscosity solution to a quasivariational inequality (QVI) of dynamic programming. Equivalence of this QVI to a nonlinear parabolic PDE with discontinuous Hamiltonian is used to prove a comparison theorem for viscosity sub- and super-solutions. An example from mathematical finance is given, and an application in nonlinear H-infinity control is sketched.
Darmon, David
2018-03-01
In the absence of mechanistic or phenomenological models of real-world systems, data-driven models become necessary. The discovery of various embedding theorems in the 1980s and 1990s motivated a powerful set of tools for analyzing deterministic dynamical systems via delay-coordinate embeddings of observations of their component states. However, in many branches of science, the condition of operational determinism is not satisfied, and stochastic models must be brought to bear. For such stochastic models, the tool set developed for delay-coordinate embedding is no longer appropriate, and a new toolkit must be developed. We present an information-theoretic criterion, the negative log-predictive likelihood, for selecting the embedding dimension for a predictively optimal data-driven model of a stochastic dynamical system. We develop a nonparametric estimator for the negative log-predictive likelihood and compare its performance to a recently proposed criterion based on active information storage. Finally, we show how the output of the model selection procedure can be used to compare candidate predictors for a stochastic system to an information-theoretic lower bound.
Directory of Open Access Journals (Sweden)
Mourad Kerboua
2014-12-01
Full Text Available We introduce a new notion called fractional stochastic nonlocal condition, and then we study approximate controllability of class of fractional stochastic nonlinear differential equations of Sobolev type in Hilbert spaces. We use Hölder's inequality, fixed point technique, fractional calculus, stochastic analysis and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions is formulated and proved for the fractional stochastic control system to be approximately controllable. An example is given to illustrate the abstract results.
International Nuclear Information System (INIS)
Mitra, Tapan; Roy, Santanu
1992-11-01
This paper analyzes the possibilities of extinction and survival of a renewable resource whose technology of reproduction is both stochastic and nonconvex. In particular, the production function is subject to random shocks over time and is allowed to be nonconcave, though it eventually exhibits bounded growth. The existence of a minimum biomass below which the resource can only decrease, is allowed for. Society harvests a part of the current stock every time period over an infinite horizon so as to maximize the expected discounted sum of one period social utilities from the harvested resource. The social utility function is strictly concave. The stochastic process of optimal stocks generated by the optimal stationary policy is analyzed. The nonconvexity in the optimization problem implies that the optimal policy functions are not 'well behaved'. The behaviour of the probability of extinction (and the expected time to extinction), as a function of initial stock, is characterized for various possible configurations of the optimal policy and the technology. Sufficient conditions on the utility and production functions and the rate of impatience, are specified in order to ensure survival of the resource with probability one from some stock level (the minimum safe standard of conservation). Sufficient conditions for almost sure extinction and almost sure survival from all stock levels are also specified. These conditions are related to the corresponding conditions derived in models with deterministic and/or convex technology. 4 figs., 29 refs
A two-stage stochastic programming model for the optimal design of distributed energy systems
International Nuclear Information System (INIS)
Zhou, Zhe; Zhang, Jianyun; Liu, Pei; Li, Zheng; Georgiadis, Michael C.; Pistikopoulos, Efstratios N.
2013-01-01
Highlights: ► The optimal design of distributed energy systems under uncertainty is studied. ► A stochastic model is developed using genetic algorithm and Monte Carlo method. ► The proposed system possesses inherent robustness under uncertainty. ► The inherent robustness is due to energy storage facilities and grid connection. -- Abstract: A distributed energy system is a multi-input and multi-output energy system with substantial energy, economic and environmental benefits. The optimal design of such a complex system under energy demand and supply uncertainty poses significant challenges in terms of both modelling and corresponding solution strategies. This paper proposes a two-stage stochastic programming model for the optimal design of distributed energy systems. A two-stage decomposition based solution strategy is used to solve the optimization problem with genetic algorithm performing the search on the first stage variables and a Monte Carlo method dealing with uncertainty in the second stage. The model is applied to the planning of a distributed energy system in a hotel. Detailed computational results are presented and compared with those generated by a deterministic model. The impacts of demand and supply uncertainty on the optimal design of distributed energy systems are systematically investigated using proposed modelling framework and solution approach.
Energy Technology Data Exchange (ETDEWEB)
Mitra, Tapan [Department of Economics, Cornell University, Ithaca, NY (United States); Roy, Santanu [Econometric Institute, Erasmus University, Rotterdam (Netherlands)
1992-11-01
This paper analyzes the possibilities of extinction and survival of a renewable resource whose technology of reproduction is both stochastic and nonconvex. In particular, the production function is subject to random shocks over time and is allowed to be nonconcave, though it eventually exhibits bounded growth. The existence of a minimum biomass below which the resource can only decrease, is allowed for. Society harvests a part of the current stock every time period over an infinite horizon so as to maximize the expected discounted sum of one period social utilities from the harvested resource. The social utility function is strictly concave. The stochastic process of optimal stocks generated by the optimal stationary policy is analyzed. The nonconvexity in the optimization problem implies that the optimal policy functions are not `well behaved`. The behaviour of the probability of extinction (and the expected time to extinction), as a function of initial stock, is characterized for various possible configurations of the optimal policy and the technology. Sufficient conditions on the utility and production functions and the rate of impatience, are specified in order to ensure survival of the resource with probability one from some stock level (the minimum safe standard of conservation). Sufficient conditions for almost sure extinction and almost sure survival from all stock levels are also specified. These conditions are related to the corresponding conditions derived in models with deterministic and/or convex technology. 4 figs., 29 refs.
Patnaik, Surya N.; Pai, Shantaram S.; Coroneos, Rula M.
2010-01-01
Structural design generated by traditional method, optimization method and the stochastic design concept are compared. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties, and other parameters and solution is obtained by solving a design optimization problem for a specified reliability. Acceptable solutions were produced by all the three methods. The variation in the weight calculated by the methods was modest. Some variation was noticed in designs calculated by the methods. The variation may be attributed to structural indeterminacy. It is prudent to develop design by all three methods prior to its fabrication. The traditional design method can be improved when the simplified sensitivities of the behavior constraint is used. Such sensitivity can reduce design calculations and may have a potential to unify the traditional and optimization methods. Weight versus reliabilitytraced out an inverted-S-shaped graph. The center of the graph corresponded to mean valued design. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Weight can be reduced to a small value for a most failure-prone design. Probabilistic modeling of load and material properties remained a challenge.
Directory of Open Access Journals (Sweden)
Timo Pukkala
2015-03-01
Full Text Available Background Decisions on forest management are made under risk and uncertainty because the stand development cannot be predicted exactly and future timber prices are unknown. Deterministic calculations may lead to biased advice on optimal forest management. The study optimized continuous cover management of boreal forest in a situation where tree growth, regeneration, and timber prices include uncertainty. Methods Both anticipatory and adaptive optimization approaches were used. The adaptive approach optimized the reservation price function instead of fixed cutting years. The future prices of different timber assortments were described by cross-correlated auto-regressive models. The high variation around ingrowth model was simulated using a model that describes the cross- and autocorrelations of the regeneration results of different species and years. Tree growth was predicted with individual tree models, the predictions of which were adjusted on the basis of a climate-induced growth trend, which was stochastic. Residuals of the deterministic diameter growth model were also simulated. They consisted of random tree factors and cross- and autocorrelated temporal terms. Results Of the analyzed factors, timber price caused most uncertainty in the calculation of the net present value of a certain management schedule. Ingrowth and climate trend were less significant sources of risk and uncertainty than tree growth. Stochastic anticipatory optimization led to more diverse post-cutting stand structures than obtained in deterministic optimization. Cutting interval was shorter when risk and uncertainty were included in the analyses. Conclusions Adaptive optimization and management led to 6%–14% higher net present values than obtained in management that was based on anticipatory optimization. Increasing risk aversion of the forest landowner led to earlier cuttings in a mature stand. The effect of risk attitude on optimization results was small.
Zhou, Bao-Rong; Liu, Si-Liang; Zhang, Yong-Jun; Yi, Ying-Qi; Lin, Xiao-Ming
2017-05-01
To mitigate the impact on the distribution networks caused by the stochastic characteristic and high penetration of photovoltaic, a multi-objective optimal power flow model is proposed in this paper. The regulation capability of capacitor, inverter of photovoltaic and energy storage system embedded in active distribution network are considered to minimize the expected value of active power the T loss and probability of voltage violation in this model. Firstly, a probabilistic power flow based on cumulant method is introduced to calculate the value of the objectives. Secondly, NSGA-II algorithm is adopted for optimization to obtain the Pareto optimal solutions. Finally, the best compromise solution can be achieved through fuzzy membership degree method. By the multi-objective optimization calculation of IEEE34-node distribution network, the results show that the model can effectively improve the voltage security and economy of the distribution network on different levels of photovoltaic penetration.
Energy Technology Data Exchange (ETDEWEB)
Rana, Swapan; Parashar, Preeti [Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 BT Road, Kolkata (India)
2011-11-15
We show that all multipartite pure states that are stochastic local operation and classical communication (SLOCC) equivalent to the N-qubit W state can be uniquely determined (among arbitrary states) from their bipartite marginals. We also prove that only (N-1) of the bipartite marginals are sufficient and that this is also the optimal number. Thus, contrary to the Greenberger-Horne-Zeilinger (GHZ) class, W-type states preserve their reducibility under SLOCC. We also study the optimal reducibility of some larger classes of states. The generic Dicke states |GD{sub N}{sup l}> are shown to be optimally determined by their (l+1)-partite marginals. The class of ''G'' states (superposition of W and W) are shown to be optimally determined by just two (N-2)-partite marginals.
Adaptive Urban Stormwater Management Using a Two-stage Stochastic Optimization Model
Hung, F.; Hobbs, B. F.; McGarity, A. E.
2014-12-01
In many older cities, stormwater results in combined sewer overflows (CSOs) and consequent water quality impairments. Because of the expense of traditional approaches for controlling CSOs, cities are considering the use of green infrastructure (GI) to reduce runoff and pollutants. Examples of GI include tree trenches, rain gardens, green roofs, and rain barrels. However, the cost and effectiveness of GI are uncertain, especially at the watershed scale. We present a two-stage stochastic extension of the Stormwater Investment Strategy Evaluation (StormWISE) model (A. McGarity, JWRPM, 2012, 111-24) to explicitly model and optimize these uncertainties in an adaptive management framework. A two-stage model represents the immediate commitment of resources ("here & now") followed by later investment and adaptation decisions ("wait & see"). A case study is presented for Philadelphia, which intends to extensively deploy GI over the next two decades (PWD, "Green City, Clean Water - Implementation and Adaptive Management Plan," 2011). After first-stage decisions are made, the model updates the stochastic objective and constraints (learning). We model two types of "learning" about GI cost and performance. One assumes that learning occurs over time, is automatic, and does not depend on what has been done in stage one (basic model). The other considers learning resulting from active experimentation and learning-by-doing (advanced model). Both require expert probability elicitations, and learning from research and monitoring is modelled by Bayesian updating (as in S. Jacobi et al., JWRPM, 2013, 534-43). The model allocates limited financial resources to GI investments over time to achieve multiple objectives with a given reliability. Objectives include minimizing construction and O&M costs; achieving nutrient, sediment, and runoff volume targets; and community concerns, such as aesthetics, CO2 emissions, heat islands, and recreational values. CVaR (Conditional Value at Risk) and
NLP model and stochastic multi-start optimization approach for heat exchanger networks
International Nuclear Information System (INIS)
Núñez-Serna, Rosa I.; Zamora, Juan M.
2016-01-01
Highlights: • An NLP model for the optimal design of heat exchanger networks is proposed. • The NLP model is developed from a stage-wise grid diagram representation. • A two-phase stochastic multi-start optimization methodology is utilized. • Improved network designs are obtained with different heat load distributions. • Structural changes and reductions in the number of heat exchangers are produced. - Abstract: Heat exchanger network synthesis methodologies frequently identify good network structures, which nevertheless, might be accompanied by suboptimal values of design variables. The objective of this work is to develop a nonlinear programming (NLP) model and an optimization approach that aim at identifying the best values for intermediate temperatures, sub-stream flow rate fractions, heat loads and areas for a given heat exchanger network topology. The NLP model that minimizes the total annual cost of the network is constructed based on a stage-wise grid diagram representation. To improve the possibilities of obtaining global optimal designs, a two-phase stochastic multi-start optimization algorithm is utilized for the solution of the developed model. The effectiveness of the proposed optimization approach is illustrated with the optimization of two network designs proposed in the literature for two well-known benchmark problems. Results show that from the addressed base network topologies it is possible to achieve improved network designs, with redistributions in exchanger heat loads that lead to reductions in total annual costs. The results also show that the optimization of a given network design sometimes leads to structural simplifications and reductions in the total number of heat exchangers of the network, thereby exposing alternative viable network topologies initially not anticipated.
Kucza, Witold
2013-07-25
Stochastic and deterministic simulations of dispersion in cylindrical channels on the Poiseuille flow have been presented. The random walk (stochastic) and the uniform dispersion (deterministic) models have been used for computations of flow injection analysis responses. These methods coupled with the genetic algorithm and the Levenberg-Marquardt optimization methods, respectively, have been applied for determination of diffusion coefficients. The diffusion coefficients of fluorescein sodium, potassium hexacyanoferrate and potassium dichromate have been determined by means of the presented methods and FIA responses that are available in literature. The best-fit results agree with each other and with experimental data thus validating both presented approaches. Copyright © 2013 The Author. Published by Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Fathi Abid
2014-05-01
Full Text Available This paper applies the mean-variance portfolio optimization (PO approach and the stochastic dominance (SD test to examine preferences for international diversification versus domestic diversification from American investors’ viewpoints. Our PO results imply that the domestic diversification strategy dominates the international diversification strategy at a lower risk level and the reverse is true at a higher risk level. Our SD analysis shows that there is no arbitrage opportunity between international and domestic stock markets; domestically diversified portfolios with smaller risk dominate internationally diversified portfolios with larger risk and vice versa; and at the same risk level, there is no difference between the domestically and internationally diversified portfolios. Nonetheless, we cannot find any domestically diversified portfolios that stochastically dominate all internationally diversified portfolios, but we find some internationally diversified portfolios with small risk that dominate all the domestically diversified portfolios.
On Stochastic Finite-Time Control of Discrete-Time Fuzzy Systems with Packet Dropout
Directory of Open Access Journals (Sweden)
Yingqi Zhang
2012-01-01
Full Text Available This paper is concerned with the stochastic finite-time stability and stochastic finite-time boundedness problems for one family of fuzzy discrete-time systems over networks with packet dropout, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, we present the dynamic model description studied, in which the discrete-time fuzzy T-S systems with packet loss can be described by one class of fuzzy Markovian jump systems. Then, the concepts of stochastic finite-time stability and stochastic finite-time boundedness and problem formulation are given. Based on Lyapunov function approach, sufficient conditions on stochastic finite-time stability and stochastic finite-time boundedness are established for the resulting closed-loop fuzzy discrete-time system with Markovian jumps, and state-feedback controllers are designed to ensure stochastic finite-time stability and stochastic finite-time boundedness of the class of fuzzy systems. The stochastic finite-time stability and stochastic finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the stochastic stability of the class of fuzzy T-S systems with packet loss. Finally, two illustrative examples are presented to show the validity of the developed methodology.
Optimal magnetic attitude control
DEFF Research Database (Denmark)
Wisniewski, Rafal; Markley, F.L.
1999-01-01
because control torques can only be generated perpendicular to the local geomagnetic field vector. This has been a serious obstacle for using magnetorquer based control for three-axis stabilization of a low earth orbit satellite. The problem of controlling the spacecraft attitude using only magnetic...
International Nuclear Information System (INIS)
Vahid-Pakdel, M.J.; Nojavan, Sayyad; Mohammadi-ivatloo, B.; Zare, Kazem
2017-01-01
Highlights: • Studying heating market impact on energy hub operation considering price uncertainty. • Investigating impact of implementation of heat demand response on hub operation. • Presenting stochastic method to consider wind generation and prices uncertainties. - Abstract: Multi carrier energy systems or energy hubs has provided more flexibility for energy management systems. On the other hand, due to mutual impact of different energy carriers in energy hubs, energy management studies become more challengeable. The initial patterns of energy demands from grids point of view can be modified by optimal scheduling of energy hubs. In this work, optimal operation of multi carrier energy system has been studied in the presence of wind farm, electrical and thermal storage systems, electrical and thermal demand response programs, electricity market and thermal energy market. Stochastic programming is implemented for modeling the system uncertainties such as demands, market prices and wind speed. It is shown that adding new source of heat energy for providing demand of consumers with market mechanism changes the optimal operation point of multi carrier energy system. Presented mixed integer linear formulation for the problem has been solved by executing CPLEX solver of GAMS optimization software. Simulation results shows that hub’s operation cost reduces up to 4.8% by enabling the option of using thermal energy market for meeting heat demand.
Robust Performance And Dissipation of Stochastic Control Systems
DEFF Research Database (Denmark)
Thygesen, Uffe Høgsbro
and topology on the space of supply rates. For instance, we give conditions under which the available storage is a continuous convex function of the supply rate. Dissipation theory in the existing literature applies only to deterministic systems. This is unfortunate since robust control applications typically...... is a prototype of robust adaptive control problems. We show that the optimal (minimax) controller for this problem is finite dimensional but not based on certainty equivalence, and we discuss the heuristic certainty equivalence controller....
Online prediction and control in nonlinear stochastic systems
DEFF Research Database (Denmark)
Nielsen, Torben Skov
2002-01-01
speed and the relationship between (primarily) wind speed and wind power (the power curve). In paper G the model parameters are estimated using a RLS algorithm and any systematic time-variation of the model parameters is disregarded. Two di erent parameterizations of the power curve is considered...... are estimated using the algorithm proposed in paper C. The power curve and the diurnal variation of wind speed is estimated separately using the local polynomial regression procedure described in paper A . In paper J the parameters of the prediction model is assumed to be smooth functions of wind direction (and......The present thesis consists of a summary report and ten research papers. The subject of the thesis is on-line prediction and control of non-linear and non-stationary systems based on stochastic modelling. The thesis consists of three parts where the rst part deals with on-line estimation in linear...
Johnson, Paul; Howell, Sydney; Duck, Peter
2017-08-13
A mixed financial/physical partial differential equation (PDE) can optimize the joint earnings of a single wind power generator (WPG) and a generic energy storage device (ESD). Physically, the PDE includes constraints on the ESD's capacity, efficiency and maximum speeds of charge and discharge. There is a mean-reverting daily stochastic cycle for WPG power output. Physically, energy can only be produced or delivered at finite rates. All suppliers must commit hourly to a finite rate of delivery C , which is a continuous control variable that is changed hourly. Financially, we assume heavy 'system balancing' penalties in continuous time, for deviations of output rate from the commitment C Also, the electricity spot price follows a mean-reverting stochastic cycle with a strong evening peak, when system balancing penalties also peak. Hence the economic goal of the WPG plus ESD, at each decision point, is to maximize expected net present value (NPV) of all earnings (arbitrage) minus the NPV of all expected system balancing penalties, along all financially/physically feasible future paths through state space. Given the capital costs for the various combinations of the physical parameters, the design and operating rules for a WPG plus ESD in a finite market may be jointly optimizable.This article is part of the themed issue 'Energy management: flexibility, risk and optimization'. © 2017 The Author(s).
Optimal control in thermal engineering
Badescu, Viorel
2017-01-01
This book is the first major work covering applications in thermal engineering and offering a comprehensive introduction to optimal control theory, which has applications in mechanical engineering, particularly aircraft and missile trajectory optimization. The book is organized in three parts: The first part includes a brief presentation of function optimization and variational calculus, while the second part presents a summary of the optimal control theory. Lastly, the third part describes several applications of optimal control theory in solving various thermal engineering problems. These applications are grouped in four sections: heat transfer and thermal energy storage, solar thermal engineering, heat engines and lubrication.Clearly presented and easy-to-use, it is a valuable resource for thermal engineers and thermal-system designers as well as postgraduate students.
Alirezaei, M.; Kanarachos, S.A.; Scheepers, B.T.M.; Maurice, J.P.
2013-01-01
The Integrated Vehicle Safety Department of TNO (Dutch Organization for Applied Scientific Research) investigates the application of modern control methods in the Integrated Vehicle Dynamics Control (IVDC) field, as a strategic research topic of the Beyond Safe framework. The aim of IVDC is to
DEFF Research Database (Denmark)
Davidsen, Claus; Liu, Suxia; Mo, Xingguo
2015-01-01
Few studies address water quality in hydro-economic models, which often focus primarily on optimal allocation of water quantities. Water quality and water quantity are closely coupled, and optimal management with focus solely on either quantity or quality may cause large costs in terms of the oth......-er component. In this study, we couple water quality and water quantity in a joint hydro-economic catchment-scale optimization problem. Stochastic dynamic programming (SDP) is used to minimize the basin-wide total costs arising from water allocation, water curtailment and water treatment. The simple water...... quality module can handle conservative pollutants, first order depletion and non-linear reactions. For demonstration purposes, we model pollutant releases as biochemical oxygen demand (BOD) and use the Streeter-Phelps equation for oxygen deficit to compute the resulting min-imum dissolved oxygen...
Stochastic Optimal Wind Power Bidding Strategy in Short-Term Electricity Market
DEFF Research Database (Denmark)
Hu, Weihao; Chen, Zhe; Bak-Jensen, Birgitte
2012-01-01
Due to the fluctuating nature and non-perfect forecast of the wind power, the wind power owners are penalized for the imbalance costs of the regulation, when they trade wind power in the short-term liberalized electricity market. Therefore, in this paper a formulation of an imbalance cost...... minimization problem for trading wind power in the short-term electricity market is described, to help the wind power owners optimize their bidding strategy. Stochastic optimization and a Monte Carlo method are adopted to find the optimal bidding strategy for trading wind power in the short-term electricity...... market in order to deal with the uncertainty of the regulation price, the activated regulation of the power system and the forecasted wind power generation. The Danish short-term electricity market and a wind farm in western Denmark are chosen as study cases due to the high wind power penetration here...
Directory of Open Access Journals (Sweden)
Heba-Allah I. ElAzab
2018-05-01
Full Text Available This paper presents a trustworthy unit commitment study to schedule both Renewable Energy Resources (RERs with conventional power plants to potentially decarbonize the electrical network. The study has employed a system with three IEEE thermal (coal-fired power plants as dispatchable distributed generators, one wind plant, one solar plant as stochastic distributed generators, and Plug-in Electric Vehicles (PEVs which can work either loads or generators based on their charging schedule. This paper investigates the unit commitment scheduling objective to minimize the Combined Economic Emission Dispatch (CEED. To reduce combined emission costs, integrating more renewable energy resources (RER and PEVs, there is an essential need to decarbonize the existing system. Decarbonizing the system means reducing the percentage of CO2 emissions. The uncertain behavior of wind and solar energies causes imbalance penalty costs. PEVs are proposed to overcome the intermittent nature of wind and solar energies. It is important to optimally integrate and schedule stochastic resources including the wind and solar energies, and PEVs charge and discharge processes with dispatched resources; the three IEEE thermal (coal-fired power plants. The Water Cycle Optimization Algorithm (WCOA is an efficient and intelligent meta-heuristic technique employed to solve the economically emission dispatch problem for both scheduling dispatchable and stochastic resources. The goal of this study is to obtain the solution for unit commitment to minimize the combined cost function including CO2 emission costs applying the Water Cycle Optimization Algorithm (WCOA. To validate the WCOA technique, the results are compared with the results obtained from applying the Dynamic Programming (DP algorithm, which is considered as a conventional numerical technique, and with the Genetic Algorithm (GA as a meta-heuristic technique.
Wu, Xiaohua; Hu, Xiaosong; Moura, Scott; Yin, Xiaofeng; Pickert, Volker
2016-11-01
Energy management strategies are instrumental in the performance and economy of smart homes integrating renewable energy and energy storage. This article focuses on stochastic energy management of a smart home with PEV (plug-in electric vehicle) energy storage and photovoltaic (PV) array. It is motivated by the challenges associated with sustainable energy supplies and the local energy storage opportunity provided by vehicle electrification. This paper seeks to minimize a consumer's energy charges under a time-of-use tariff, while satisfying home power demand and PEV charging requirements, and accommodating the variability of solar power. First, the random-variable models are developed, including Markov Chain model of PEV mobility, as well as predictive models of home power demand and PV power supply. Second, a stochastic optimal control problem is mathematically formulated for managing the power flow among energy sources in the smart home. Finally, based on time-varying electricity price, we systematically examine the performance of the proposed control strategy. As a result, the electric cost is 493.6% less for a Tesla Model S with optimal stochastic dynamic programming (SDP) control relative to the no optimal control case, and it is by 175.89% for a Nissan Leaf.
Analytical study on the criticality of the stochastic optimal velocity model
International Nuclear Information System (INIS)
Kanai, Masahiro; Nishinari, Katsuhiro; Tokihiro, Tetsuji
2006-01-01
In recent works, we have proposed a stochastic cellular automaton model of traffic flow connecting two exactly solvable stochastic processes, i.e., the asymmetric simple exclusion process and the zero range process, with an additional parameter. It is also regarded as an extended version of the optimal velocity model, and moreover it shows particularly notable properties. In this paper, we report that when taking optimal velocity function to be a step function, all of the flux-density graph (i.e. the fundamental diagram) can be estimated. We first find that the fundamental diagram consists of two line segments resembling an inversed-λ form, and next identify their end-points from a microscopic behaviour of vehicles. It is notable that by using a microscopic parameter which indicates a driver's sensitivity to the traffic situation, we give an explicit formula for the critical point at which a traffic jam phase arises. We also compare these analytical results with those of the optimal velocity model, and point out the crucial differences between them
Application of stochastic optimization to nuclear power plant asset management decisions
International Nuclear Information System (INIS)
Morton, D.; Koc, A.; Hess, S. M.
2013-01-01
We describe the development and application of stochastic optimization models and algorithms to address an issue of critical importance in the strategic allocation of resources; namely, the selection of a portfolio of capital investment projects under the constraints of a limited and uncertain budget. This issue is significant and one that faces decision-makers across all industries. The objective of this strategic decision process is generally self evident - to maximize the value obtained from the portfolio of selected projects (with value usually measured in terms of the portfolio's net present value). However, heretofore, many organizations have developed processes to make these investment decisions using simplistic rule-based rank-ordering schemes. This approach has the significant limitation of not accounting for the (often large) uncertainties in the costs or economic benefits associated with the candidate projects or in the uncertainties in the actual funds available to be expended over the projected period of time. As a result, the simple heuristic approaches that typically are employed in industrial practice generate outcomes that are non-optimal and do not achieve the level of benefits intended. In this paper we describe the results of research performed to utilize stochastic optimization models and algorithms to address this limitation by explicitly incorporating the evaluation of uncertainties in the analysis and decision making process. (authors)
Directory of Open Access Journals (Sweden)
Angel A. Juan
2015-12-01
Full Text Available Many combinatorial optimization problems (COPs encountered in real-world logistics, transportation, production, healthcare, financial, telecommunication, and computing applications are NP-hard in nature. These real-life COPs are frequently characterized by their large-scale sizes and the need for obtaining high-quality solutions in short computing times, thus requiring the use of metaheuristic algorithms. Metaheuristics benefit from different random-search and parallelization paradigms, but they frequently assume that the problem inputs, the underlying objective function, and the set of optimization constraints are deterministic. However, uncertainty is all around us, which often makes deterministic models oversimplified versions of real-life systems. After completing an extensive review of related work, this paper describes a general methodology that allows for extending metaheuristics through simulation to solve stochastic COPs. ‘Simheuristics’ allow modelers for dealing with real-life uncertainty in a natural way by integrating simulation (in any of its variants into a metaheuristic-driven framework. These optimization-driven algorithms rely on the fact that efficient metaheuristics already exist for the deterministic version of the corresponding COP. Simheuristics also facilitate the introduction of risk and/or reliability analysis criteria during the assessment of alternative high-quality solutions to stochastic COPs. Several examples of applications in different fields illustrate the potential of the proposed methodology.
Application of stochastic optimization to nuclear power plant asset management decisions
Energy Technology Data Exchange (ETDEWEB)
Morton, D. [Graduate Program in Operations Research and Industrial Engineering, University of Texas at Austin, Austin, TX, 78712 (United States); Koc, A. [IBM T.J. Watson Research Center, Business Analytics and Mathematical Sciences Dept., 1101 Kitchawan Rd., Yorktown Heights, NY, 10598 (United States); Hess, S. M. [Electric Power Research Institute, 300 Baywood Road, West Chester, PA, 19382 (United States)
2013-07-01
We describe the development and application of stochastic optimization models and algorithms to address an issue of critical importance in the strategic allocation of resources; namely, the selection of a portfolio of capital investment projects under the constraints of a limited and uncertain budget. This issue is significant and one that faces decision-makers across all industries. The objective of this strategic decision process is generally self evident - to maximize the value obtained from the portfolio of selected projects (with value usually measured in terms of the portfolio's net present value). However, heretofore, many organizations have developed processes to make these investment decisions using simplistic rule-based rank-ordering schemes. This approach has the significant limitation of not accounting for the (often large) uncertainties in the costs or economic benefits associated with the candidate projects or in the uncertainties in the actual funds available to be expended over the projected period of time. As a result, the simple heuristic approaches that typically are employed in industrial practice generate outcomes that are non-optimal and do not achieve the level of benefits intended. In this paper we describe the results of research performed to utilize stochastic optimization models and algorithms to address this limitation by explicitly incorporating the evaluation of uncertainties in the analysis and decision making process. (authors)
International Nuclear Information System (INIS)
Chertkov, Michael; Kolokolov, Igor; Lebedev, Vladimir
2012-01-01
The standard definition of the stochastic risk-sensitive linear–quadratic (RS-LQ) control depends on the risk parameter, which is normally left to be set exogenously. We reconsider the classical approach and suggest two alternatives, resolving the spurious freedom naturally. One approach consists in seeking for the minimum of the tail of the probability distribution function (PDF) of the cost functional at some large fixed value. Another option suggests minimizing the expectation value of the cost functional under a constraint on the value of the PDF tail. Under the assumption of resulting control stability, both problems are reduced to static optimizations over a stationary control matrix. The solutions are illustrated using the examples of scalar and 1D chain (string) systems. The large deviation self-similar asymptotic of the cost functional PDF is analyzed. (paper)
DEFF Research Database (Denmark)
Zhang, Baohua; Hu, Weihao; Chen, Zhe
2015-01-01
in the stochastic optimization to deal with the uncertainty of the up regulation price and the up regulation activation of the power system.The Danish short-term electricity market and a wind farm in western Denmark are chosen to evaluate the effect of the proposed strategy. Simulation results showthe proposed......As modern wind farmshave the ability to provideregulation service for the power system, wind power plant operators may be motivated to participate in the regulating market to maximize their profit.In this paper, anoptimal regulation servicestrategy for a wind farm to participate...... strategy can increase the revenue of wind farms by leavinga certain amount of wind powerfor regulation service....
Energy Technology Data Exchange (ETDEWEB)
Araujo, Leonardo Rodrigues de [Instituto Federal do Espirito Santo, Vitoria, ES (Brazil)], E-mail: leoaraujo@ifes.edu.br; Donatelli, Joao Luiz Marcon [Universidade Federal do Espirito Santo (UFES), Vitoria, ES (Brazil)], E-mail: joaoluiz@npd.ufes.br; Silva, Edmar Alino da Cruz [Instituto Tecnologico de Aeronautica (ITA/CTA), Sao Jose dos Campos, SP (Brazil); Azevedo, Joao Luiz F. [Instituto de Aeronautica e Espaco (CTA/IAE/ALA), Sao Jose dos Campos, SP (Brazil)
2010-07-01
Thermal systems are essential in facilities such as thermoelectric plants, cogeneration plants, refrigeration systems and air conditioning, among others, in which much of the energy consumed by humanity is processed. In a world with finite natural sources of fuels and growing energy demand, issues related with thermal system design, such as cost estimative, design complexity, environmental protection and optimization are becoming increasingly important. Therefore the need to understand the mechanisms that degrade energy, improve energy sources use, reduce environmental impacts and also reduce project, operation and maintenance costs. In recent years, a consistent development of procedures and techniques for computational design of thermal systems has occurred. In this context, the fundamental objective of this study is a performance comparative analysis of structural and parametric optimization of a cogeneration system using stochastic methods: genetic algorithm and simulated annealing. This research work uses a superstructure, modelled in a process simulator, IPSEpro of SimTech, in which the appropriate design case studied options are included. Accordingly, the cogeneration system optimal configuration is determined as a consequence of the optimization process, restricted within the configuration options included in the superstructure. The optimization routines are written in MsExcel Visual Basic, in order to work perfectly coupled to the simulator process. At the end of the optimization process, the system optimal configuration, given the characteristics of each specific problem, should be defined. (author)
Multistage Stochastic Programming and its Applications in Energy Systems Modeling and Optimization
Golari, Mehdi
Electric energy constitutes one of the most crucial elements to almost every aspect of life of people. The modern electric power systems face several challenges such as efficiency, economics, sustainability, and reliability. Increase in electrical energy demand, distributed generations, integration of uncertain renewable energy resources, and demand side management are among the main underlying reasons of such growing complexity. Additionally, the elements of power systems are often vulnerable to failures because of many reasons, such as system limits, weak conditions, unexpected events, hidden failures, human errors, terrorist attacks, and natural disasters. One common factor complicating the operation of electrical power systems is the underlying uncertainties from the demands, supplies and failures of system components. Stochastic programming provides a mathematical framework for decision making under uncertainty. It enables a decision maker to incorporate some knowledge of the intrinsic uncertainty into the decision making process. In this dissertation, we focus on application of two-stage and multistage stochastic programming approaches to electric energy systems modeling and optimization. Particularly, we develop models and algorithms addressing the sustainability and reliability issues in power systems. First, we consider how to improve the reliability of power systems under severe failures or contingencies prone to cascading blackouts by so called islanding operations. We present a two-stage stochastic mixed-integer model to find optimal islanding operations as a powerful preventive action against cascading failures in case of extreme contingencies. Further, we study the properties of this problem and propose efficient solution methods to solve this problem for large-scale power systems. We present the numerical results showing the effectiveness of the model and investigate the performance of the solution methods. Next, we address the sustainability issue
Optimal control theory an introduction
Kirk, Donald E
2004-01-01
Optimal control theory is the science of maximizing the returns from and minimizing the costs of the operation of physical, social, and economic processes. Geared toward upper-level undergraduates, this text introduces three aspects of optimal control theory: dynamic programming, Pontryagin's minimum principle, and numerical techniques for trajectory optimization.Chapters 1 and 2 focus on describing systems and evaluating their performances. Chapter 3 deals with dynamic programming. The calculus of variations and Pontryagin's minimum principle are the subjects of chapters 4 and 5, and chapter
Control of stochastic resonance in bistable systems by using periodic signals
International Nuclear Information System (INIS)
Min, Lin; Li-Min, Fang; Yong-Jun, Zheng
2009-01-01
According to the characteristic structure of double wells in bistable systems, this paper analyses stochastic fluctuations in the single potential well and probability transitions between the two potential wells and proposes a method of controlling stochastic resonance by using a periodic signal. Results of theoretical analysis and numerical simulation show that the phenomenon of stochastic resonance happens when the time scales of the periodic signal and the noise-induced probability transitions between the two potential wells achieve stochastic synchronization. By adding a bistable system with a controllable periodic signal, fluctuations in the single potential well can be effectively controlled, thus affecting the probability transitions between the two potential wells. In this way, an effective control can be achieved which allows one to either enhance or realize stochastic resonance
Optimal control of gene mutation in DNA replication.
Yu, Juanyi; Li, Jr-Shin; Tarn, Tzyh-Jong
2012-01-01
We propose a molecular-level control system view of the gene mutations in DNA replication from the finite field concept. By treating DNA sequences as state variables, chemical mutagens and radiation as control inputs, one cell cycle as a step increment, and the measurements of the resulting DNA sequence as outputs, we derive system equations for both deterministic and stochastic discrete-time, finite-state systems of different scales. Defining the cost function as a summation of the costs of applying mutagens and the off-trajectory penalty, we solve the deterministic and stochastic optimal control problems by dynamic programming algorithm. In addition, given that the system is completely controllable, we find that the global optimum of both base-to-base and codon-to-codon deterministic mutations can always be achieved within a finite number of steps.
a Stochastic Approach to Multiobjective Optimization of Large-Scale Water Reservoir Networks
Bottacin-Busolin, A.; Worman, A. L.
2013-12-01
A main challenge for the planning and management of water resources is the development of multiobjective strategies for operation of large-scale water reservoir networks. The optimal sequence of water releases from multiple reservoirs depends on the stochastic variability of correlated hydrologic inflows and on various processes that affect water demand and energy prices. Although several methods have been suggested, large-scale optimization problems arising in water resources management are still plagued by the high dimensional state space and by the stochastic nature of the hydrologic inflows. In this work, the optimization of reservoir operation is approached using approximate dynamic programming (ADP) with policy iteration and function approximators. The method is based on an off-line learning process in which operating policies are evaluated for a number of stochastic inflow scenarios, and the resulting value functions are used to design new, improved policies until convergence is attained. A case study is presented of a multi-reservoir system in the Dalälven River, Sweden, which includes 13 interconnected reservoirs and 36 power stations. Depending on the late spring and summer peak discharges, the lowlands adjacent to Dalälven can often be flooded during the summer period, and the presence of stagnating floodwater during the hottest months of the year is the cause of a large proliferation of mosquitos, which is a major problem for the people living in the surroundings. Chemical pesticides are currently being used as a preventive countermeasure, which do not provide an effective solution to the problem and have adverse environmental impacts. In this study, ADP was used to analyze the feasibility of alternative operating policies for reducing the flood risk at a reasonable economic cost for the hydropower companies. To this end, mid-term operating policies were derived by combining flood risk reduction with hydropower production objectives. The performance
Panda, Satyasen
2018-05-01
This paper proposes a modified artificial bee colony optimization (ABC) algorithm based on levy flight swarm intelligence referred as artificial bee colony levy flight stochastic walk (ABC-LFSW) optimization for optical code division multiple access (OCDMA) network. The ABC-LFSW algorithm is used to solve asset assignment problem based on signal to noise ratio (SNR) optimization in OCDM networks with quality of service constraints. The proposed optimization using ABC-LFSW algorithm provides methods for minimizing various noises and interferences, regulating the transmitted power and optimizing the network design for improving the power efficiency of the optical code path (OCP) from source node to destination node. In this regard, an optical system model is proposed for improving the network performance with optimized input parameters. The detailed discussion and simulation results based on transmitted power allocation and power efficiency of OCPs are included. The experimental results prove the superiority of the proposed network in terms of power efficiency and spectral efficiency in comparison to networks without any power allocation approach.
Achieving control and synchronization merely through a stochastically adaptive feedback coupling
Lin, Wei; Chen, Xin; Zhou, Shijie
2017-07-01
Techniques of deterministically adaptive feedback couplings have been successfully and extensively applied to realize control or/and synchronization in chaotic dynamical systems and even in complex dynamical networks. In this article, a technique of stochastically adaptive feedback coupling is novelly proposed to not only realize control in chaotic dynamical systems but also achieve synchronization in unidirectionally coupled systems. Compared with those deterministically adaptive couplings, the proposed stochastic technique interestingly shows some advantages from a physical viewpoint of time and energy consumptions. More significantly, the usefulness of the proposed stochastic technique is analytically validated by the theory of stochastic processes. It is anticipated that the proposed stochastic technique will be widely used in achieving system control and network synchronization.
Agha-mohammadi, Ali-akbar
2013-06-01
This paper is concerned with the problem of stochastic optimal control (possibly with imperfect measurements) in the presence of constraints. We propose a computationally tractable framework to address this problem. The method lends itself to sampling-based methods where we construct a graph in the state space of the problem, on which a Dynamic Programming (DP) is solved and a closed-loop feedback policy is computed. The constraints are seamlessly incorporated to the control policy selection by including their effect on the transition probabilities of the graph edges. We present a unified framework that is applicable both in the state space (with perfect measurements) and in the information space (with imperfect measurements).
Practice of contemporary dance promotes stochastic postural control in aging
Directory of Open Access Journals (Sweden)
Lena eFerrufino
2011-12-01
Full Text Available As society ages and the frequency of falls increases, counteracting gait and posture decline is a challenging issue for countries of the developed world. Previous studies have shown that exercise and hazard management help to improve balance and/or decrease the risks for falling in normal aging. Motor activity based on motor-skill learning, particularly dance, can also benefit balance and decreases falls with age. Recent studies have suggested that older dancers had better balance, posture, or gait than non-dancers. Additionally, clinical or laboratory measures have shown improvements in some aspects of balance after dance interventions in elderly trainees. This study examined the impact of contemporary dance (CD and of fall prevention (FP programs on postural control of older adults. Posturography of quiet upright stance was performed in forty-one participants aged 59-86 years before and after 4.4-month training in either CD or FP once a week. Though classical statistic scores failed to show any effect, dynamic analyses of the center-of-pressure displacements revealed significant changes after training. Specifically, practice of CD enhanced the critical time interval in diffusion analysis, and reduced recurrence and mathematical stability in recurrence quantification analysis, whereas practice of FP induced or tended to induce the reverse patterns. We suggest that CD training based on motor improvisation favored stochastic posture inducing plasticity in motor control, while FP training based on more stereotyped behaviors did not.
Optimal control of quantum measurement
Energy Technology Data Exchange (ETDEWEB)
Egger, Daniel; Wilhelm, Frank [Theoretical Physics, Saarland University, 66123 Saarbruecken (Germany)
2015-07-01
Pulses to steer the time evolution of quantum systems can be designed with optimal control theory. In most cases it is the coherent processes that can be controlled and one optimizes the time evolution towards a target unitary process, sometimes also in the presence of non-controllable incoherent processes. Here we show how to extend the GRAPE algorithm in the case where the incoherent processes are controllable and the target time evolution is a non-unitary quantum channel. We perform a gradient search on a fidelity measure based on Choi matrices. We illustrate our algorithm by optimizing a measurement pulse for superconducting phase qubits. We show how this technique can lead to large measurement contrast close to 99%. We also show, within the validity of our model, that this algorithm can produce short 1.4 ns pulses with 98.2% contrast.
International Nuclear Information System (INIS)
Biswas, Imran H.; Jakobsen, Espen R.; Karlsen, Kenneth H.
2010-01-01
We develop a viscosity solution theory for a system of nonlinear degenerate parabolic integro-partial differential equations (IPDEs) related to stochastic optimal switching and control problems or stochastic games. In the case of stochastic optimal switching and control, we prove via dynamic programming methods that the value function is a viscosity solution of the IPDEs. In our setting the value functions or the solutions of the IPDEs are not smooth, so classical verification theorems do not apply.
Adaptive Near-Optimal Multiuser Detection Using a Stochastic and Hysteretic Hopfield Net Receiver
Directory of Open Access Journals (Sweden)
Gábor Jeney
2003-01-01
Full Text Available This paper proposes a novel adaptive MUD algorithm for a wide variety (practically any kind of interference limited systems, for example, code division multiple access (CDMA. The algorithm is based on recently developed neural network techniques and can perform near optimal detection in the case of unknown channel characteristics. The proposed algorithm consists of two main blocks; one estimates the symbols sent by the transmitters, the other identifies each channel of the corresponding communication links. The estimation of symbols is carried out either by a stochastic Hopfield net (SHN or by a hysteretic neural network (HyNN or both. The channel identification is based on either the self-organizing feature map (SOM or the learning vector quantization (LVQ. The combination of these two blocks yields a powerful real-time detector with near optimal performance. The performance is analyzed by extensive simulations.
Directory of Open Access Journals (Sweden)
L. Ji
2015-01-01
Full Text Available The main goal of this paper is to provide a novel risk aversion model for long-term electric power system planning from the manager’s perspective with the consideration of various uncertainties. In the proposed method, interval parameter programming and two-stage stochastic programming are integrated to deal with the technical, economics, and policy uncertainties. Moreover, downside risk theory is introduced to balance the trade-off between the profit and risk according to the decision-maker’s risk aversion attitude. To verify the effectiveness and practical application of this approach, an inexact stochastic risk aversion model is developed for regional electric system planning and management in Ningxia Hui Autonomous Region, China. The series of solutions provide the decision-maker with the optimal investment strategy and operation management under different future emission reduction scenarios and risk-aversion levels. The results indicated that pollution control devices are still the main measures to achieve the current mitigation goal and the adjustment of generation structure would play an important role in the future cleaner electricity system with the stricter environmental policy. In addition, the model can be used for generating decision alternatives and helping decision-makers identify desired energy structure adjustment and pollutants/carbon mitigation abatement policies under various economic and system-reliability constraints.
Heterogeneous recurrence monitoring and control of nonlinear stochastic processes
Energy Technology Data Exchange (ETDEWEB)
Yang, Hui, E-mail: huiyang@usf.edu; Chen, Yun [Complex Systems Monitoring, Modeling and Analysis Laboratory, University of South Florida, Tampa, Florida 33620 (United States)
2014-03-15
Recurrence is one of the most common phenomena in natural and engineering systems. Process monitoring of dynamic transitions in nonlinear and nonstationary systems is more concerned with aperiodic recurrences and recurrence variations. However, little has been done to investigate the heterogeneous recurrence variations and link with the objectives of process monitoring and anomaly detection. Notably, nonlinear recurrence methodologies are based on homogeneous recurrences, which treat all recurrence states in the same way as black dots, and non-recurrence is white in recurrence plots. Heterogeneous recurrences are more concerned about the variations of recurrence states in terms of state properties (e.g., values and relative locations) and the evolving dynamics (e.g., sequential state transitions). This paper presents a novel approach of heterogeneous recurrence analysis that utilizes a new fractal representation to delineate heterogeneous recurrence states in multiple scales, including the recurrences of both single states and multi-state sequences. Further, we developed a new set of heterogeneous recurrence quantifiers that are extracted from fractal representation in the transformed space. To that end, we integrated multivariate statistical control charts with heterogeneous recurrence analysis to simultaneously monitor two or more related quantifiers. Experimental results on nonlinear stochastic processes show that the proposed approach not only captures heterogeneous recurrence patterns in the fractal representation but also effectively monitors the changes in the dynamics of a complex system.
Directory of Open Access Journals (Sweden)
S. Aberkane
2007-01-01
Full Text Available This paper deals with dynamic output feedback control of continuous-time active fault tolerant control systems with Markovian parameters (AFTCSMP and state-dependent noise. The main contribution is to formulate conditions for multiperformance design, related to this class of stochastic hybrid systems, that take into account the problematic resulting from the fact that the controller only depends on the fault detection and isolation (FDI process. The specifications and objectives under consideration include stochastic stability, ℋ2 and ℋ∞ (or more generally, stochastic integral quadratic constraints performances. Results are formulated as matrix inequalities. The theoretical results are illustrated using a classical example from literature.
Optimal control linear quadratic methods
Anderson, Brian D O
2007-01-01
This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the
Optimal control of motorsport differentials
Tremlett, A. J.; Massaro, M.; Purdy, D. J.; Velenis, E.; Assadian, F.; Moore, A. P.; Halley, M.
2015-12-01
Modern motorsport limited slip differentials (LSD) have evolved to become highly adjustable, allowing the torque bias that they generate to be tuned in the corner entry, apex and corner exit phases of typical on-track manoeuvres. The task of finding the optimal torque bias profile under such varied vehicle conditions is complex. This paper presents a nonlinear optimal control method which is used to find the minimum time optimal torque bias profile through a lane change manoeuvre. The results are compared to traditional open and fully locked differential strategies, in addition to considering related vehicle stability and agility metrics. An investigation into how the optimal torque bias profile changes with reduced track-tyre friction is also included in the analysis. The optimal LSD profile was shown to give a performance gain over its locked differential counterpart in key areas of the manoeuvre where a quick direction change is required. The methodology proposed can be used to find both optimal passive LSD characteristics and as the basis of a semi-active LSD control algorithm.
Optimal control of native predators
Martin, Julien; O'Connell, Allan F.; Kendall, William L.; Runge, Michael C.; Simons, Theodore R.; Waldstein, Arielle H.; Schulte, Shiloh A.; Converse, Sarah J.; Smith, Graham W.; Pinion, Timothy; Rikard, Michael; Zipkin, Elise F.
2010-01-01
We apply decision theory in a structured decision-making framework to evaluate how control of raccoons (Procyon lotor), a native predator, can promote the conservation of a declining population of American Oystercatchers (Haematopus palliatus) on the Outer Banks of North Carolina. Our management objective was to maintain Oystercatcher productivity above a level deemed necessary for population recovery while minimizing raccoon removal. We evaluated several scenarios including no raccoon removal, and applied an adaptive optimization algorithm to account for parameter uncertainty. We show how adaptive optimization can be used to account for uncertainties about how raccoon control may affect Oystercatcher productivity. Adaptive management can reduce this type of uncertainty and is particularly well suited for addressing controversial management issues such as native predator control. The case study also offers several insights that may be relevant to the optimal control of other native predators. First, we found that stage-specific removal policies (e.g., yearling versus adult raccoon removals) were most efficient if the reproductive values among stage classes were very different. Second, we found that the optimal control of raccoons would result in higher Oystercatcher productivity than the minimum levels recommended for this species. Third, we found that removing more raccoons initially minimized the total number of removals necessary to meet long term management objectives. Finally, if for logistical reasons managers cannot sustain a removal program by removing a minimum number of raccoons annually, managers may run the risk of creating an ecological trap for Oystercatchers.
A Stochastic Inversion Method for Potential Field Data: Ant Colony Optimization
Liu, Shuang; Hu, Xiangyun; Liu, Tianyou
2014-07-01
Simulating natural ants' foraging behavior, the ant colony optimization (ACO) algorithm performs excellently in combinational optimization problems, for example the traveling salesman problem and the quadratic assignment problem. However, the ACO is seldom used to inverted for gravitational and magnetic data. On the basis of the continuous and multi-dimensional objective function for potential field data optimization inversion, we present the node partition strategy ACO (NP-ACO) algorithm for inversion of model variables of fixed shape and recovery of physical property distributions of complicated shape models. We divide the continuous variables into discrete nodes and ants directionally tour the nodes by use of transition probabilities. We update the pheromone trails by use of Gaussian mapping between the objective function value and the quantity of pheromone. It can analyze the search results in real time and promote the rate of convergence and precision of inversion. Traditional mapping, including the ant-cycle system, weaken the differences between ant individuals and lead to premature convergence. We tested our method by use of synthetic data and real data from scenarios involving gravity and magnetic anomalies. The inverted model variables and recovered physical property distributions were in good agreement with the true values. The ACO algorithm for binary representation imaging and full imaging can recover sharper physical property distributions than traditional linear inversion methods. The ACO has good optimization capability and some excellent characteristics, for example robustness, parallel implementation, and portability, compared with other stochastic metaheuristics.
A review on condition-based maintenance optimization models for stochastically deteriorating system
International Nuclear Information System (INIS)
Alaswad, Suzan; Xiang, Yisha
2017-01-01
Condition-based maintenance (CBM) is a maintenance strategy that collects and assesses real-time information, and recommends maintenance decisions based on the current condition of the system. In recent decades, research on CBM has been rapidly growing due to the rapid development of computer-based monitoring technologies. Research studies have proven that CBM, if planned properly, can be effective in improving equipment reliability at reduced costs. This paper presents a review of CBM literature with emphasis on mathematical modeling and optimization approaches. We focus this review on important aspects of the CBM, such as optimization criteria, inspection frequency, maintenance degree, solution methodology, etc. Since the modeling choice for the stochastic deterioration process greatly influences CBM strategy decisions, this review classifies the literature on CBM models based on the underlying deterioration processes, namely discrete- and continuous-state deterioration, and proportional hazard model. CBM models for multi-unit systems are also reviewed in this paper. This paper provides useful references for CBM management professionals and researchers working on CBM modeling and optimization. - Highlights: • A review on Condition-based maintenance (CBM) optimization models is presented. • The CBM models are classified based on the underlying deterioration processes. • Existing CBM models for both single- and multi-unit systems are reviewed. • Future essential research directions on CBM are identified.
International Nuclear Information System (INIS)
Zhang Xiaobing; Fan Ying; Wei Yiming
2009-01-01
China's Strategic Petroleum Reserve (SPR) is currently being prepared. But how large the optimal stockpile size for China should be, what the best acquisition strategies are, how to release the reserve if a disruption occurs, and other related issues still need to be studied in detail. In this paper, we develop a stochastic dynamic programming model based on a total potential cost function of establishing SPRs to evaluate the optimal SPR policy for China. Using this model, empirical results are presented for the optimal size of China's SPR and the best acquisition and drawdown strategies for a few specific cases. The results show that with comprehensive consideration, the optimal SPR size for China is around 320 million barrels. This size is equivalent to about 90 days of net oil import amount in 2006 and should be reached in the year 2017, three years earlier than the national goal, which implies that the need for China to fill the SPR is probably more pressing; the best stockpile release action in a disruption is related to the disruption levels and expected continuation probabilities. The information provided by the results will be useful for decision makers.
Stochastic Optimization in The Power Management of Bottled Water Production Planning
Antoro, Budi; Nababan, Esther; Mawengkang, Herman
2018-01-01
This paper review a model developed to minimize production costs on bottled water production planning through stochastic optimization. As we know, that planning a management means to achieve the goal that have been applied, since each management level in the organization need a planning activities. The built models is a two-stage stochastic models that aims to minimize the cost on production of bottled water by observing that during the production process, neither interfernce nor vice versa occurs. The models were develop to minimaze production cost, assuming the availability of packing raw materials used considered to meet for each kind of bottles. The minimum cost for each kind production of bottled water are expressed in the expectation of each production with a scenario probability. The probability of uncertainly is a representation of the number of productions and the timing of power supply interruption. This is to ensure that the number of interruption that occur does not exceed the limit of the contract agreement that has been made by the company with power suppliers.
International Nuclear Information System (INIS)
Bouzid, M.; Benkherouf, H.; Benzadi, K.
2011-01-01
In this paper, we propose a stochastic joint source-channel scheme developed for efficient and robust encoding of spectral speech LSF parameters. The encoding system, named LSF-SSCOVQ-RC, is an LSF encoding scheme based on a reduced complexity stochastic split vector quantizer optimized for noisy channel. For transmissions over noisy channel, we will show first that our LSF-SSCOVQ-RC encoder outperforms the conventional LSF encoder designed by the split vector quantizer. After that, we applied the LSF-SSCOVQ-RC encoder (with weighted distance) for the robust encoding of LSF parameters of the 2.4 Kbits/s MELP speech coder operating over a noisy/noiseless channel. The simulation results will show that the proposed LSF encoder, incorporated in the MELP, ensure better performances than the original MELP MSVQ of 25 bits/frame; especially when the transmission channel is highly disturbed. Indeed, we will show that the LSF-SSCOVQ-RC yields significant improvement to the LSFs encoding performances by ensuring reliable transmissions over noisy channel.
The role of stochasticity in an information-optimal neural population code
International Nuclear Information System (INIS)
Stocks, N G; Nikitin, A P; McDonnell, M D; Morse, R P
2009-01-01
In this paper we consider the optimisation of Shannon mutual information (MI) in the context of two model neural systems. The first is a stochastic pooling network (population) of McCulloch-Pitts (MP) type neurons (logical threshold units) subject to stochastic forcing; the second is (in a rate coding paradigm) a population of neurons that each displays Poisson statistics (the so called 'Poisson neuron'). The mutual information is optimised as a function of a parameter that characterises the 'noise level'-in the MP array this parameter is the standard deviation of the noise; in the population of Poisson neurons it is the window length used to determine the spike count. In both systems we find that the emergent neural architecture and, hence, code that maximises the MI is strongly influenced by the noise level. Low noise levels leads to a heterogeneous distribution of neural parameters (diversity), whereas, medium to high noise levels result in the clustering of neural parameters into distinct groups that can be interpreted as subpopulations. In both cases the number of subpopulations increases with a decrease in noise level. Our results suggest that subpopulations are a generic feature of an information optimal neural population.
The role of stochasticity in an information-optimal neural population code
Energy Technology Data Exchange (ETDEWEB)
Stocks, N G; Nikitin, A P [School of Engineering, University of Warwick, Coventry CV4 7AL (United Kingdom); McDonnell, M D [Institute for Telecommunications Research, University of South Australia, SA 5095 (Australia); Morse, R P, E-mail: n.g.stocks@warwick.ac.u [School of Life and Health Sciences, Aston University, Birmingham B4 7ET (United Kingdom)
2009-12-01
In this paper we consider the optimisation of Shannon mutual information (MI) in the context of two model neural systems. The first is a stochastic pooling network (population) of McCulloch-Pitts (MP) type neurons (logical threshold units) subject to stochastic forcing; the second is (in a rate coding paradigm) a population of neurons that each displays Poisson statistics (the so called 'Poisson neuron'). The mutual information is optimised as a function of a parameter that characterises the 'noise level'-in the MP array this parameter is the standard deviation of the noise; in the population of Poisson neurons it is the window length used to determine the spike count. In both systems we find that the emergent neural architecture and, hence, code that maximises the MI is strongly influenced by the noise level. Low noise levels leads to a heterogeneous distribution of neural parameters (diversity), whereas, medium to high noise levels result in the clustering of neural parameters into distinct groups that can be interpreted as subpopulations. In both cases the number of subpopulations increases with a decrease in noise level. Our results suggest that subpopulations are a generic feature of an information optimal neural population.
Directory of Open Access Journals (Sweden)
Neslihan Fidan Keçeci
2016-10-01
Full Text Available The paper compares portfolio optimization with the Second-Order Stochastic Dominance (SSD constraints with mean-variance and minimum variance portfolio optimization. As a distribution-free decision rule, stochastic dominance takes into account the entire distribution of return rather than some specific characteristic, such as variance. The paper is focused on practical applications of the portfolio optimization and uses the Portfolio Safeguard (PSG package, which has precoded modules for optimization with SSD constraints, mean-variance and minimum variance portfolio optimization. We have done in-sample and out-of-sample simulations for portfolios of stocks from the Dow Jones, S&P 100 and DAX indices. The considered portfolios’ SSD dominate the Dow Jones, S&P 100 and DAX indices. Simulation demonstrated a superior performance of portfolios with SD constraints, versus mean-variance and minimum variance portfolios.
International Nuclear Information System (INIS)
Pazsit, I.; Glockler, O.
1984-01-01
In an earlier publication, using the theory of neutron fluctuations induced by a vibrating control rod, a complete formal solution of rod vibration diagnostics based on neutron noise measurements was given in terms of Fourier-transformed neutron detector time signals. The suggested procedure was checked in numerical simulation tests where only periodic vibrations could be considered. The procedure and its numerical testing are elaborated for stochastic two-dimensional vibrations. A simple stochastic theory of two-dimensional flow-induced vibrations is given; then the diagnostic method is formulated in the stochastic case, that is, in terms of neutron detector auto- and crosspower spectra. A previously suggested approximate rod localization technique is also formulated in the stochastic case. Applicability of the methods is then investigated in numerical simulation tests, using the proposed model of stochastic two-dimensional vibrations when generating neutron detector spectra that simulate measured data
Optimal control with aerospace applications
Longuski, James M; Prussing, John E
2014-01-01
Want to know not just what makes rockets go up but how to do it optimally? Optimal control theory has become such an important field in aerospace engineering that no graduate student or practicing engineer can afford to be without a working knowledge of it. This is the first book that begins from scratch to teach the reader the basic principles of the calculus of variations, develop the necessary conditions step-by-step, and introduce the elementary computational techniques of optimal control. This book, with problems and an online solution manual, provides the graduate-level reader with enough introductory knowledge so that he or she can not only read the literature and study the next level textbook but can also apply the theory to find optimal solutions in practice. No more is needed than the usual background of an undergraduate engineering, science, or mathematics program: namely calculus, differential equations, and numerical integration. Although finding optimal solutions for these problems is a...
Elsawy, Hesham; Hossain, Ekram
2014-01-01
Using stochastic geometry, we develop a tractable uplink modeling paradigm for outage probability and spectral efficiency in both single and multi-tier cellular wireless networks. The analysis accounts for per user equipment (UE) power control
Optimization and optimal control in automotive systems
Kolmanovsky, Ilya; Steinbuch, Maarten; Re, Luigi
2014-01-01
This book demonstrates the use of the optimization techniques that are becoming essential to meet the increasing stringency and variety of requirements for automotive systems. It shows the reader how to move away from earlier approaches, based on some degree of heuristics, to the use of more and more common systematic methods. Even systematic methods can be developed and applied in a large number of forms so the text collects contributions from across the theory, methods and real-world automotive applications of optimization. Greater fuel economy, significant reductions in permissible emissions, new drivability requirements and the generally increasing complexity of automotive systems are among the criteria that the contributing authors set themselves to meet. In many cases multiple and often conflicting requirements give rise to multi-objective constrained optimization problems which are also considered. Some of these problems fall into the domain of the traditional multi-disciplinary optimization applie...
Control and optimal control theories with applications
Burghes, D N
2004-01-01
This sound introduction to classical and modern control theory concentrates on fundamental concepts. Employing the minimum of mathematical elaboration, it investigates the many applications of control theory to varied and important present-day problems, e.g. economic growth, resource depletion, disease epidemics, exploited population, and rocket trajectories. An original feature is the amount of space devoted to the important and fascinating subject of optimal control. The work is divided into two parts. Part one deals with the control of linear time-continuous systems, using both transfer fun
Study on Stochastic Optimal Electric Power Procurement Strategies with Uncertain Market Prices
Sakchai, Siripatanakulkhajorn; Saisho, Yuichi; Fujii, Yasumasa; Yamaji, Kenji
The player in deregulated electricity markets can be categorized into three groups of GENCO (Generator Companies), TRNASCO (Transmission Companies), DISCO (Distribution Companies). This research focuses on the role of Distribution Companies, which purchase electricity from market at randomly fluctuating prices, and provide it to their customers at given fixed prices. Therefore Distribution companies have to take the risk stemming from price fluctuation of electricity instead of the customers. This entails the necessity to develop a certain method to make an optimal strategy for electricity procurement. In such a circumstance, this research has the purpose for proposing the mathematical method based on stochastic dynamic programming to evaluate the value of a long-term bilateral contract of electricity trade, and also a project of combination of the bilateral contract and power generation with their own generators for procuring electric power in deregulated market.
Optimal control of hybrid vehicles
Jager, Bram; Kessels, John
2013-01-01
Optimal Control of Hybrid Vehicles provides a description of power train control for hybrid vehicles. The background, environmental motivation and control challenges associated with hybrid vehicles are introduced. The text includes mathematical models for all relevant components in the hybrid power train. The power split problem in hybrid power trains is formally described and several numerical solutions detailed, including dynamic programming and a novel solution for state-constrained optimal control problems based on Pontryagin’s maximum principle. Real-time-implementable strategies that can approximate the optimal solution closely are dealt with in depth. Several approaches are discussed and compared, including a state-of-the-art strategy which is adaptive for vehicle conditions like velocity and mass. Two case studies are included in the book: · a control strategy for a micro-hybrid power train; and · experimental results obtained with a real-time strategy implemented in...
Towards Stochastic Optimization-Based Electric Vehicle Penetration in a Novel Archipelago Microgrid
Directory of Open Access Journals (Sweden)
Qingyu Yang
2016-06-01
Full Text Available Due to the advantage of avoiding upstream disturbance and voltage fluctuation from a power transmission system, Islanded Micro-Grids (IMG have attracted much attention. In this paper, we first propose a novel self-sufficient Cyber-Physical System (CPS supported by Internet of Things (IoT techniques, namely “archipelago micro-grid (MG”, which integrates the power grid and sensor networks to make the grid operation effective and is comprised of multiple MGs while disconnected with the utility grid. The Electric Vehicles (EVs are used to replace a portion of Conventional Vehicles (CVs to reduce CO 2 emission and operation cost. Nonetheless, the intermittent nature and uncertainty of Renewable Energy Sources (RESs remain a challenging issue in managing energy resources in the system. To address these issues, we formalize the optimal EV penetration problem as a two-stage Stochastic Optimal Penetration (SOP model, which aims to minimize the emission and operation cost in the system. Uncertainties coming from RESs (e.g., wind, solar, and load demand are considered in the stochastic model and random parameters to represent those uncertainties are captured by the Monte Carlo-based method. To enable the reasonable deployment of EVs in each MGs, we develop two scheduling schemes, namely Unlimited Coordinated Scheme (UCS and Limited Coordinated Scheme (LCS, respectively. An extensive simulation study based on a modified 9 bus system with three MGs has been carried out to show the effectiveness of our proposed schemes. The evaluation data indicates that our proposed strategy can reduce both the environmental pollution created by CO 2 emissions and operation costs in UCS and LCS.
Towards Stochastic Optimization-Based Electric Vehicle Penetration in a Novel Archipelago Microgrid.
Yang, Qingyu; An, Dou; Yu, Wei; Tan, Zhengan; Yang, Xinyu
2016-06-17
Due to the advantage of avoiding upstream disturbance and voltage fluctuation from a power transmission system, Islanded Micro-Grids (IMG) have attracted much attention. In this paper, we first propose a novel self-sufficient Cyber-Physical System (CPS) supported by Internet of Things (IoT) techniques, namely "archipelago micro-grid (MG)", which integrates the power grid and sensor networks to make the grid operation effective and is comprised of multiple MGs while disconnected with the utility grid. The Electric Vehicles (EVs) are used to replace a portion of Conventional Vehicles (CVs) to reduce CO 2 emission and operation cost. Nonetheless, the intermittent nature and uncertainty of Renewable Energy Sources (RESs) remain a challenging issue in managing energy resources in the system. To address these issues, we formalize the optimal EV penetration problem as a two-stage Stochastic Optimal Penetration (SOP) model, which aims to minimize the emission and operation cost in the system. Uncertainties coming from RESs (e.g., wind, solar, and load demand) are considered in the stochastic model and random parameters to represent those uncertainties are captured by the Monte Carlo-based method. To enable the reasonable deployment of EVs in each MGs, we develop two scheduling schemes, namely Unlimited Coordinated Scheme (UCS) and Limited Coordinated Scheme (LCS), respectively. An extensive simulation study based on a modified 9 bus system with three MGs has been carried out to show the effectiveness of our proposed schemes. The evaluation data indicates that our proposed strategy can reduce both the environmental pollution created by CO 2 emissions and operation costs in UCS and LCS.
Yang, Tao; Cao, Qingjie
2018-03-01
This work presents analytical studies of the stiffness nonlinearities SD (smooth and discontinuous) oscillator under displacement and velocity feedback control with a time delay. The SD oscillator can capture the qualitative characteristics of quasi-zero-stiffness and negative-stiffness. We focus mainly on the primary resonance of the quasi-zero-stiffness SD oscillator and the stochastic resonance (SR) of the negative-stiffness SD oscillator. Using the averaging method, we have been analyzed the amplitude response of the quasi-zero-stiffness SD oscillator. In this regard, the optimum time delay for changing the control intensity according to the optimization standard proposed can be obtained. For the optimum time delay, increasing the displacement feedback intensity is advantageous to suppress the vibrations in resonant regime where vibration isolation is needed, however, increasing the velocity feedback intensity is advantageous to strengthen the vibrations. Moreover, the effects of time-delayed feedback on the SR of the negative-stiffness SD oscillator are investigated under harmonic forcing and Gaussian white noise, based on the Langevin and Fokker-Planck approaches. The time-delayed feedback can enhance the SR phenomenon where vibrational energy harvesting is needed. This paper established the relationship between the parameters and vibration properties of a stiffness nonlinearities SD which provides the guidance for optimizing time-delayed control for vibration isolation and vibrational energy harvesting of the nonlinear systems.
Directory of Open Access Journals (Sweden)
Liudong Zhang
2014-01-01
Full Text Available An uncertain monthly reservoirs operation and multicrop deficit irrigation model was proposed under conjunctive use of underground and surface water for water resources optimization management. The objective is to maximize the total crop yield of the entire irrigation districts. Meanwhile, ecological water remained for the downstream demand. Because of the shortage of water resources, the monthly crop water production function was adopted for multiperiod deficit irrigation management. The model reflects the characteristics of water resources repetitive transformation in typical inland rivers irrigation system. The model was used as an example for water resources optimization management in Shiyang River Basin, China. Uncertainties in reservoir management shown as fuzzy probability were treated through chance-constraint parameter for decision makers. Necessity of dominance (ND was used to analyse the advantages of the method. The optimization results including reservoirs real-time operation policy, deficit irrigation management, and the available water resource allocation could be used to provide decision support for local irrigation management. Besides, the strategies obtained could help with the risk analysis of reservoirs operation stochastically.
Directory of Open Access Journals (Sweden)
Qinghai Zhao
2015-01-01
Full Text Available A mathematical framework is developed which integrates the reliability concept into topology optimization to solve reliability-based topology optimization (RBTO problems under uncertainty. Two typical methodologies have been presented and implemented, including the performance measure approach (PMA and the sequential optimization and reliability assessment (SORA. To enhance the computational efficiency of reliability analysis, stochastic response surface method (SRSM is applied to approximate the true limit state function with respect to the normalized random variables, combined with the reasonable design of experiments generated by sparse grid design, which was proven to be an effective and special discretization technique. The uncertainties such as material property and external loads are considered on three numerical examples: a cantilever beam, a loaded knee structure, and a heat conduction problem. Monte-Carlo simulations are also performed to verify the accuracy of the failure probabilities computed by the proposed approach. Based on the results, it is demonstrated that application of SRSM with SGD can produce an efficient reliability analysis in RBTO which enables a more reliable design than that obtained by DTO. It is also found that, under identical accuracy, SORA is superior to PMA in view of computational efficiency.
Analysis of novel stochastic switched SILI epidemic models with continuous and impulsive control
Gao, Shujing; Zhong, Deming; Zhang, Yan
2018-04-01
In this paper, we establish two new stochastic switched epidemic models with continuous and impulsive control. The stochastic perturbations are considered for the natural death rate in each equation of the models. Firstly, a stochastic switched SILI model with continuous control schemes is investigated. By using Lyapunov-Razumikhin method, the sufficient conditions for extinction in mean are established. Our result shows that the disease could be die out theoretically if threshold value R is less than one, regardless of whether the disease-free solutions of the corresponding subsystems are stable or unstable. Then, a stochastic switched SILI model with continuous control schemes and pulse vaccination is studied. The threshold value R is derived. The global attractivity of the model is also obtained. At last, numerical simulations are carried out to support our results.
Directory of Open Access Journals (Sweden)
Mingzhu Song
2016-01-01
Full Text Available We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time-varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time-varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.
Optimization and Optimal Control in Automotive Systems
Waschl, H.; Kolmanovsky, I.V.; Steinbuch, M.; Re, del L.
2014-01-01
This book demonstrates the use of the optimization techniques that are becoming essential to meet the increasing stringency and variety of requirements for automotive systems. It shows the reader how to move away from earlier approaches, based on some degree of heuristics, to the use of more and
Directory of Open Access Journals (Sweden)
Jianlei Zhang
Full Text Available We study the evolution of cooperation among selfish individuals in the stochastic strategy spatial prisoner's dilemma game. We equip players with the particle swarm optimization technique, and find that it may lead to highly cooperative states even if the temptations to defect are strong. The concept of particle swarm optimization was originally introduced within a simple model of social dynamics that can describe the formation of a swarm, i.e., analogous to a swarm of bees searching for a food source. Essentially, particle swarm optimization foresees changes in the velocity profile of each player, such that the best locations are targeted and eventually occupied. In our case, each player keeps track of the highest payoff attained within a local topological neighborhood and its individual highest payoff. Thus, players make use of their own memory that keeps score of the most profitable strategy in previous actions, as well as use of the knowledge gained by the swarm as a whole, to find the best available strategy for themselves and the society. Following extensive simulations of this setup, we find a significant increase in the level of cooperation for a wide range of parameters, and also a full resolution of the prisoner's dilemma. We also demonstrate extreme efficiency of the optimization algorithm when dealing with environments that strongly favor the proliferation of defection, which in turn suggests that swarming could be an important phenomenon by means of which cooperation can be sustained even under highly unfavorable conditions. We thus present an alternative way of understanding the evolution of cooperative behavior and its ubiquitous presence in nature, and we hope that this study will be inspirational for future efforts aimed in this direction.
Stochastic optimal foraging: tuning intensive and extensive dynamics in random searches.
Directory of Open Access Journals (Sweden)
Frederic Bartumeus
Full Text Available Recent theoretical developments had laid down the proper mathematical means to understand how the structural complexity of search patterns may improve foraging efficiency. Under information-deprived scenarios and specific landscape configurations, Lévy walks and flights are known to lead to high search efficiencies. Based on a one-dimensional comparative analysis we show a mechanism by which, at random, a searcher can optimize the encounter with close and distant targets. The mechanism consists of combining an optimal diffusivity (optimally enhanced diffusion with a minimal diffusion constant. In such a way the search dynamics adequately balances the tension between finding close and distant targets, while, at the same time, shifts the optimal balance towards relatively larger close-to-distant target encounter ratios. We find that introducing a multiscale set of reorientations ensures both a thorough local space exploration without oversampling and a fast spreading dynamics at the large scale. Lévy reorientation patterns account for these properties but other reorientation strategies providing similar statistical signatures can mimic or achieve comparable efficiencies. Hence, the present work unveils general mechanisms underlying efficient random search, beyond the Lévy model. Our results suggest that animals could tune key statistical movement properties (e.g. enhanced diffusivity, minimal diffusion constant to cope with the very general problem of balancing out intensive and extensive random searching. We believe that theoretical developments to mechanistically understand stochastic search strategies, such as the one here proposed, are crucial to develop an empirically verifiable and comprehensive animal foraging theory.
Partial Finite-Time Synchronization of Switched Stochastic Chua's Circuits via Sliding-Mode Control
Directory of Open Access Journals (Sweden)
Zhang-Lin Wan
2011-01-01
Full Text Available This paper considers the problem of partial finite-time synchronization between switched stochastic Chua's circuits accompanied by a time-driven switching law. Based on the Ito formula and Lyapunov stability theory, a sliding-mode controller is developed to guarantee the synchronization of switched stochastic master-slave Chua's circuits and for the mean of error states to obtain the partial finite-time stability. Numerical simulations demonstrate the effectiveness of the proposed methods.
Directory of Open Access Journals (Sweden)
Lin Wang
2013-01-01
Full Text Available As a practical inventory and transportation problem, it is important to synthesize several objectives for the joint replenishment and delivery (JRD decision. In this paper, a new multiobjective stochastic JRD (MSJRD of the one-warehouse and n-retailer systems considering the balance of service level and total cost simultaneously is proposed. The goal of this problem is to decide the reasonable replenishment interval, safety stock factor, and traveling routing. Secondly, two approaches are designed to handle this complex multi-objective optimization problem. Linear programming (LP approach converts the multi-objective to single objective, while a multi-objective evolution algorithm (MOEA solves a multi-objective problem directly. Thirdly, three intelligent optimization algorithms, differential evolution algorithm (DE, hybrid DE (HDE, and genetic algorithm (GA, are utilized in LP-based and MOEA-based approaches. Results of the MSJRD with LP-based and MOEA-based approaches are compared by a contrastive numerical example. To analyses the nondominated solution of MOEA, a metric is also used to measure the distribution of the last generation solution. Results show that HDE outperforms DE and GA whenever LP or MOEA is adopted.
International Nuclear Information System (INIS)
Ramirez-Marquez, Jose Emmanuel; Rocco S, Claudio M.
2009-01-01
This paper introduces an evolutionary optimization approach that can be readily applied to solve stochastic network interdiction problems (SNIP). The network interdiction problem solved considers the minimization of the cost associated with an interdiction strategy such that the maximum flow that can be transmitted between a source node and a sink node for a fixed network design is greater than or equal to a given reliability requirement. Furthermore, the model assumes that the nominal capacity of each network link and the cost associated with their interdiction can change from link to link and that such interdiction has a probability of being successful. This version of the SNIP is for the first time modeled as a capacitated network reliability problem allowing for the implementation of computation and solution techniques previously unavailable. The solution process is based on an evolutionary algorithm that implements: (1) Monte-Carlo simulation, to generate potential network interdiction strategies, (2) capacitated network reliability techniques to analyze strategies' source-sink flow reliability and, (3) an evolutionary optimization technique to define, in probabilistic terms, how likely a link is to appear in the final interdiction strategy. Examples for different sizes of networks are used throughout the paper to illustrate the approach
Directory of Open Access Journals (Sweden)
Muhammad Imran
2014-01-01
Full Text Available One of the major challenges for the CBIR is to bridge the gap between low level features and high level semantics according to the need of the user. To overcome this gap, relevance feedback (RF coupled with support vector machine (SVM has been applied successfully. However, when the feedback sample is small, the performance of the SVM based RF is often poor. To improve the performance of RF, this paper has proposed a new technique, namely, PSO-SVM-RF, which combines SVM based RF with particle swarm optimization (PSO. The aims of this proposed technique are to enhance the performance of SVM based RF and also to minimize the user interaction with the system by minimizing the RF number. The PSO-SVM-RF was tested on the coral photo gallery containing 10908 images. The results obtained from the experiments showed that the proposed PSO-SVM-RF achieved 100% accuracy in 8 feedback iterations for top 10 retrievals and 80% accuracy in 6 iterations for 100 top retrievals. This implies that with PSO-SVM-RF technique high accuracy rate is achieved at a small number of iterations.
Parasuraman, Ramviyas; Fabry, Thomas; Molinari, Luca; Kershaw, Keith; Di Castro, Mario; Masi, Alessandro; Ferre, Manuel
2014-01-01
The reliability of wireless communication in a network of mobile wireless robot nodes depends on the received radio signal strength (RSS). When the robot nodes are deployed in hostile environments with ionizing radiations (such as in some scientific facilities), there is a possibility that some electronic components may fail randomly (due to radiation effects), which causes problems in wireless connectivity. The objective of this paper is to maximize robot mission capabilities by maximizing the wireless network capacity and to reduce the risk of communication failure. Thus, in this paper, we consider a multi-node wireless tethering structure called the “server-relay-client” framework that uses (multiple) relay nodes in between a server and a client node. We propose a robust stochastic optimization (RSO) algorithm using a multi-sensor-based RSS sampling method at the relay nodes to efficiently improve and balance the RSS between the source and client nodes to improve the network capacity and to provide redundant networking abilities. We use pre-processing techniques, such as exponential moving averaging and spatial averaging filters on the RSS data for smoothing. We apply a receiver spatial diversity concept and employ a position controller on the relay node using a stochastic gradient ascent method for self-positioning the relay node to achieve the RSS balancing task. The effectiveness of the proposed solution is validated by extensive simulations and field experiments in CERN facilities. For the field trials, we used a youBot mobile robot platform as the relay node, and two stand-alone Raspberry Pi computers as the client and server nodes. The algorithm has been proven to be robust to noise in the radio signals and to work effectively even under non-line-of-sight conditions. PMID:25615734
Directory of Open Access Journals (Sweden)
Ramviyas Parasuraman
2014-12-01
Full Text Available The reliability of wireless communication in a network of mobile wireless robot nodes depends on the received radio signal strength (RSS. When the robot nodes are deployed in hostile environments with ionizing radiations (such as in some scientific facilities, there is a possibility that some electronic components may fail randomly (due to radiation effects, which causes problems in wireless connectivity. The objective of this paper is to maximize robot mission capabilities by maximizing the wireless network capacity and to reduce the risk of communication failure. Thus, in this paper, we consider a multi-node wireless tethering structure called the “server-relay-client” framework that uses (multiple relay nodes in between a server and a client node. We propose a robust stochastic optimization (RSO algorithm using a multi-sensor-based RSS sampling method at the relay nodes to efficiently improve and balance the RSS between the source and client nodes to improve the network capacity and to provide redundant networking abilities. We use pre-processing techniques, such as exponential moving averaging and spatial averaging filters on the RSS data for smoothing. We apply a receiver spatial diversity concept and employ a position controller on the relay node using a stochastic gradient ascent method for self-positioning the relay node to achieve the RSS balancing task. The effectiveness of the proposed solution is validated by extensive simulations and field experiments in CERN facilities. For the field trials, we used a youBot mobile robot platform as the relay node, and two stand-alone Raspberry Pi computers as the client and server nodes. The algorithm has been proven to be robust to noise in the radio signals and to work effectively even under non-line-of-sight conditions.
DEFF Research Database (Denmark)
Ghoreishi, Maryam
2018-01-01
Many models within the field of optimal dynamic pricing and lot-sizing models for deteriorating items assume everything is deterministic and develop a differential equation as the core of analysis. Two prominent examples are the papers by Rajan et al. (Manag Sci 38:240–262, 1992) and Abad (Manag......, we will try to expose the model by Abad (1996) and Rajan et al. (1992) to stochastic inputs; however, designing these stochastic inputs such that they as closely as possible are aligned with the assumptions of those papers. We do our investigation through a numerical test where we test the robustness...... of the numerical results reported in Rajan et al. (1992) and Abad (1996) in a simulation model. Our numerical results seem to confirm that the results stated in these papers are indeed robust when being imposed to stochastic inputs....
He, L; Huang, G H; Lu, H W
2010-04-15
Solving groundwater remediation optimization problems based on proxy simulators can usually yield optimal solutions differing from the "true" ones of the problem. This study presents a new stochastic optimization model under modeling uncertainty and parameter certainty (SOMUM) and the associated solution method for simultaneously addressing modeling uncertainty associated with simulator residuals and optimizing groundwater remediation processes. This is a new attempt different from the previous modeling efforts. The previous ones focused on addressing uncertainty in physical parameters (i.e. soil porosity) while this one aims to deal with uncertainty in mathematical simulator (arising from model residuals). Compared to the existing modeling approaches (i.e. only parameter uncertainty is considered), the model has the advantages of providing mean-variance analysis for contaminant concentrations, mitigating the effects of modeling uncertainties on optimal remediation strategies, offering confidence level of optimal remediation strategies to system designers, and reducing computational cost in optimization processes. 2009 Elsevier B.V. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
He, L., E-mail: li.he@ryerson.ca [Department of Civil Engineering, Faculty of Engineering, Architecture and Science, Ryerson University, 350 Victoria Street, Toronto, Ontario, M5B 2K3 (Canada); Huang, G.H. [Environmental Systems Engineering Program, Faculty of Engineering, University of Regina, Regina, Saskatchewan, S4S 0A2 (Canada); College of Urban Environmental Sciences, Peking University, Beijing 100871 (China); Lu, H.W. [Environmental Systems Engineering Program, Faculty of Engineering, University of Regina, Regina, Saskatchewan, S4S 0A2 (Canada)
2010-04-15
Solving groundwater remediation optimization problems based on proxy simulators can usually yield optimal solutions differing from the 'true' ones of the problem. This study presents a new stochastic optimization model under modeling uncertainty and parameter certainty (SOMUM) and the associated solution method for simultaneously addressing modeling uncertainty associated with simulator residuals and optimizing groundwater remediation processes. This is a new attempt different from the previous modeling efforts. The previous ones focused on addressing uncertainty in physical parameters (i.e. soil porosity) while this one aims to deal with uncertainty in mathematical simulator (arising from model residuals). Compared to the existing modeling approaches (i.e. only parameter uncertainty is considered), the model has the advantages of providing mean-variance analysis for contaminant concentrations, mitigating the effects of modeling uncertainties on optimal remediation strategies, offering confidence level of optimal remediation strategies to system designers, and reducing computational cost in optimization processes.
Directory of Open Access Journals (Sweden)
Zengyun Wang
2013-01-01
Full Text Available This paper investigates the problem of synchronization for two different stochastic chaotic systems with unknown parameters and uncertain terms. The main work of this paper consists of the following aspects. Firstly, based on the Lyapunov theory in stochastic differential equations and the theory of sliding mode control, we propose a simple sliding surface and discuss the occurrence of the sliding motion. Secondly, we design an adaptive sliding mode controller to realize the asymptotical synchronization in mean squares. Thirdly, we design an adaptive sliding mode controller to realize the almost surely synchronization. Finally, the designed adaptive sliding mode controllers are used to achieve synchronization between two pairs of different stochastic chaos systems (Lorenz-Chen and Chen-Lu in the presence of the uncertainties and unknown parameters. Numerical simulations are given to demonstrate the robustness and efficiency of the proposed robust adaptive sliding mode controller.
Modified Convolutional Neural Network Based on Dropout and the Stochastic Gradient Descent Optimizer
Directory of Open Access Journals (Sweden)
Jing Yang
2018-03-01
Full Text Available This study proposes a modified convolutional neural network (CNN algorithm that is based on dropout and the stochastic gradient descent (SGD optimizer (MCNN-DS, after analyzing the problems of CNNs in extracting the convolution features, to improve the feature recognition rate and reduce the time-cost of CNNs. The MCNN-DS has a quadratic CNN structure and adopts the rectified linear unit as the activation function to avoid the gradient problem and accelerate convergence. To address the overfitting problem, the algorithm uses an SGD optimizer, which is implemented by inserting a dropout layer into the all-connected and output layers, to minimize cross entropy. This study used the datasets MNIST, HCL2000, and EnglishHand as the benchmark data, analyzed the performance of the SGD optimizer under different learning parameters, and found that the proposed algorithm exhibited good recognition performance when the learning rate was set to [0.05, 0.07]. The performances of WCNN, MLP-CNN, SVM-ELM, and MCNN-DS were compared. Statistical results showed the following: (1 For the benchmark MNIST, the MCNN-DS exhibited a high recognition rate of 99.97%, and the time-cost of the proposed algorithm was merely 21.95% of MLP-CNN, and 10.02% of SVM-ELM; (2 Compared with SVM-ELM, the average improvement in the recognition rate of MCNN-DS was 2.35% for the benchmark HCL2000, and the time-cost of MCNN-DS was only 15.41%; (3 For the EnglishHand test set, the lowest recognition rate of the algorithm was 84.93%, the highest recognition rate was 95.29%, and the average recognition rate was 89.77%.
Stochastic ℋ∞ Finite-Time Control of Discrete-Time Systems with Packet Loss
Directory of Open Access Journals (Sweden)
Yingqi Zhang
2012-01-01
Full Text Available This paper investigates the stochastic finite-time stabilization and ℋ∞ control problem for one family of linear discrete-time systems over networks with packet loss, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the dynamic model description studied is given, which, if the packet dropout is assumed to be a discrete-time homogenous Markov process, the class of discrete-time linear systems with packet loss can be regarded as Markovian jump systems. Based on Lyapunov function approach, sufficient conditions are established for the resulting closed-loop discrete-time system with Markovian jumps to be stochastic ℋ∞ finite-time boundedness and then state feedback controllers are designed to guarantee stochastic ℋ∞ finite-time stabilization of the class of stochastic systems. The stochastic ℋ∞ finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the robust stochastic stabilization of the class of linear systems with packet loss. Finally, simulation examples are presented to illustrate the validity of the developed scheme.
Sandell, N. R., Jr.; Athans, M.
1975-01-01
The development of the theory of the finite - state, finite - memory (FSFM) stochastic control problem is discussed. The sufficiency of the FSFM minimum principle (which is in general only a necessary condition) was investigated. By introducing the notion of a signaling strategy as defined in the literature on games, conditions under which the FSFM minimum principle is sufficient were determined. This result explicitly interconnects the information structure of the FSFM problem with its optimality conditions. The min-H algorithm for the FSFM problem was studied. It is demonstrated that a version of the algorithm always converges to a particular type of local minimum termed a person - by - person extremal.
Gekeler, Simon
2016-01-01
The book provides suggestions on how to start using bionic optimization methods, including pseudo-code examples of each of the important approaches and outlines of how to improve them. The most efficient methods for accelerating the studies are discussed. These include the selection of size and generations of a study’s parameters, modification of these driving parameters, switching to gradient methods when approaching local maxima, and the use of parallel working hardware. Bionic Optimization means finding the best solution to a problem using methods found in nature. As Evolutionary Strategies and Particle Swarm Optimization seem to be the most important methods for structural optimization, we primarily focus on them. Other methods such as neural nets or ant colonies are more suited to control or process studies, so their basic ideas are outlined in order to motivate readers to start using them. A set of sample applications shows how Bionic Optimization works in practice. From academic studies on simple fra...
Real-Time Optimal Flood Control Decision Making and Risk Propagation Under Multiple Uncertainties
Zhu, Feilin; Zhong, Ping-An; Sun, Yimeng; Yeh, William W.-G.
2017-12-01
Multiple uncertainties exist in the optimal flood control decision-making process, presenting risks involving flood control decisions. This paper defines the main steps in optimal flood control decision making that constitute the Forecast-Optimization-Decision Making (FODM) chain. We propose a framework for supporting optimal flood control decision making under multiple uncertainties and evaluate risk propagation along the FODM chain from a holistic perspective. To deal with uncertainties, we employ stochastic models at each link of the FODM chain. We generate synthetic ensemble flood forecasts via the martingale model of forecast evolution. We then establish a multiobjective stochastic programming with recourse model for optimal flood control operation. The Pareto front under uncertainty is derived via the constraint method coupled with a two-step process. We propose a novel SMAA-TOPSIS model for stochastic multicriteria decision making. Then we propose the risk assessment model, the risk of decision-making errors and rank uncertainty degree to quantify the risk propagation process along the FODM chain. We conduct numerical experiments to investigate the effects of flood forecast uncertainty on optimal flood control decision making and risk propagation. We apply the proposed methodology to a flood control system in the Daduhe River basin in China. The results indicate that the proposed method can provide valuable risk information in each link of the FODM chain and enable risk-informed decisions with higher reliability.
Risk Management of Interest Rate Derivative Portfolios: A Stochastic Control Approach
Directory of Open Access Journals (Sweden)
Konstantinos Kiriakopoulos
2014-10-01
Full Text Available In this paper we formulate the Risk Management Control problem in the interest rate area as a constrained stochastic portfolio optimization problem. The utility that we use can be any continuous function and based on the viscosity theory, the unique solution of the problem is guaranteed. The numerical approximation scheme is presented and applied using a single factor interest rate model. It is shown how the whole methodology works in practice, with the implementation of the algorithm for a specific interest rate portfolio. The recent financial crisis showed that risk management of derivatives portfolios especially in the interest rate market is crucial for the stability of the financial system. Modern Value at Risk (VAR and Conditional Value at Risk (CVAR techniques, although very useful and easy to understand, fail to grasp the need for on-line controlling and monitoring of derivatives portfolio. The portfolios should be designed in a way that risk and return be quantified and controlled in every possible state of the world. We hope that this methodology contributes towards this direction.
International Nuclear Information System (INIS)
Holmberg, J.
1997-04-01
The thesis models risk management as an optimal control problem for a stochastic process. The approach classes the decisions made by management into three categories according to the control methods of a point process: (1) planned process lifetime, (2) modification of the design, and (3) operational decisions. The approach is used for optimization of plant shutdown criteria and surveillance test strategies of a hypothetical nuclear power plant
Energy Technology Data Exchange (ETDEWEB)
Holmberg, J [VTT Automation, Espoo (Finland)
1997-04-01
The thesis models risk management as an optimal control problem for a stochastic process. The approach classes the decisions made by management into three categories according to the control methods of a point process: (1) planned process lifetime, (2) modification of the design, and (3) operational decisions. The approach is used for optimization of plant shutdown criteria and surveillance test strategies of a hypothetical nuclear power plant. 62 refs. The thesis includes also five previous publications by author.
HCCI Engine Optimization and Control
Energy Technology Data Exchange (ETDEWEB)
Rolf D. Reitz
2005-09-30
The goal of this project was to develop methods to optimize and control Homogeneous-Charge Compression Ignition (HCCI) engines, with emphasis on diesel-fueled engines. HCCI offers the potential of nearly eliminating IC engine NOx and particulate emissions at reduced cost over Compression Ignition Direct Injection engines (CIDI) by controlling pollutant emissions in-cylinder. The project was initiated in January, 2002, and the present report is the final report for work conducted on the project through December 31, 2004. Periodic progress has also been reported at bi-annual working group meetings held at USCAR, Detroit, MI, and at the Sandia National Laboratories. Copies of these presentation materials are available on CD-ROM, as distributed by the Sandia National Labs. In addition, progress has been documented in DOE Advanced Combustion Engine R&D Annual Progress Reports for FY 2002, 2003 and 2004. These reports are included as the Appendices in this Final report.
Lyapunov-Based Controller for a Class of Stochastic Chaotic Systems
Directory of Open Access Journals (Sweden)
Hossein Shokouhi-Nejad
2014-01-01
Full Text Available This study presents a general control law based on Lyapunov’s direct method for a group of well-known stochastic chaotic systems. Since real chaotic systems have undesired random-like behaviors which have also been deteriorated by environmental noise, chaotic systems are modeled by exciting a deterministic chaotic system with a white noise obtained from derivative of Wiener process which eventually generates an Ito differential equation. Proposed controller not only can asymptotically stabilize these systems in mean-square sense against their undesired intrinsic properties, but also exhibits good transient response. Simulation results highlight effectiveness and feasibility of proposed controller in outperforming stochastic chaotic systems.
International Nuclear Information System (INIS)
Fakir, Hatim; Hlatky, Lynn; Li, Huamin; Sachs, Rainer
2013-01-01
Purpose: Optimal treatment planning for fractionated external beam radiation therapy requires inputs from radiobiology based on recent thinking about the “five Rs” (repopulation, radiosensitivity, reoxygenation, redistribution, and repair). The need is especially acute for the newer, often individualized, protocols made feasible by progress in image guided radiation therapy and dose conformity. Current stochastic tumor control probability (TCP) models incorporating tumor repopulation effects consider “stem-like cancer cells” (SLCC) to be independent, but the authors here propose that SLCC-SLCC interactions may be significant. The authors present a new stochastic TCP model for repopulating SLCC interacting within microenvironmental niches. Our approach is meant mainly for comparing similar protocols. It aims at practical generalizations of previous mathematical models. Methods: The authors consider protocols with complete sublethal damage repair between fractions. The authors use customized open-source software and recent mathematical approaches from stochastic process theory for calculating the time-dependent SLCC number and thereby estimating SLCC eradication probabilities. As specific numerical examples, the authors consider predicted TCP results for a 2 Gy per fraction, 60 Gy protocol compared to 64 Gy protocols involving early or late boosts in a limited volume to some fractions. Results: In sample calculations with linear quadratic parameters α = 0.3 per Gy, α/β = 10 Gy, boosting is predicted to raise TCP from a dismal 14.5% observed in some older protocols for advanced NSCLC to above 70%. This prediction is robust as regards: (a) the assumed values of parameters other than α and (b) the choice of models for intraniche SLCC-SLCC interactions. However, α = 0.03 per Gy leads to a prediction of almost no improvement when boosting. Conclusions: The predicted efficacy of moderate boosts depends sensitively on α. Presumably, the larger values of α are
Fakir, Hatim; Hlatky, Lynn; Li, Huamin; Sachs, Rainer
2013-12-01
Optimal treatment planning for fractionated external beam radiation therapy requires inputs from radiobiology based on recent thinking about the "five Rs" (repopulation, radiosensitivity, reoxygenation, redistribution, and repair). The need is especially acute for the newer, often individualized, protocols made feasible by progress in image guided radiation therapy and dose conformity. Current stochastic tumor control probability (TCP) models incorporating tumor repopulation effects consider "stem-like cancer cells" (SLCC) to be independent, but the authors here propose that SLCC-SLCC interactions may be significant. The authors present a new stochastic TCP model for repopulating SLCC interacting within microenvironmental niches. Our approach is meant mainly for comparing similar protocols. It aims at practical generalizations of previous mathematical models. The authors consider protocols with complete sublethal damage repair between fractions. The authors use customized open-source software and recent mathematical approaches from stochastic process theory for calculating the time-dependent SLCC number and thereby estimating SLCC eradication probabilities. As specific numerical examples, the authors consider predicted TCP results for a 2 Gy per fraction, 60 Gy protocol compared to 64 Gy protocols involving early or late boosts in a limited volume to some fractions. In sample calculations with linear quadratic parameters α = 0.3 per Gy, α∕β = 10 Gy, boosting is predicted to raise TCP from a dismal 14.5% observed in some older protocols for advanced NSCLC to above 70%. This prediction is robust as regards: (a) the assumed values of parameters other than α and (b) the choice of models for intraniche SLCC-SLCC interactions. However, α = 0.03 per Gy leads to a prediction of almost no improvement when boosting. The predicted efficacy of moderate boosts depends sensitively on α. Presumably, the larger values of α are the ones appropriate for individualized
Towards Quantum Cybernetics:. Optimal Feedback Control in Quantum Bio Informatics
Belavkin, V. P.
2009-02-01
A brief account of the quantum information dynamics and dynamical programming methods for the purpose of optimal control in quantum cybernetics with convex constraints and cońcave cost and bequest functions of the quantum state is given. Consideration is given to both open loop and feedback control schemes corresponding respectively to deterministic and stochastic semi-Markov dynamics of stable or unstable systems. For the quantum feedback control scheme with continuous observations we exploit the separation theorem of filtering and control aspects for quantum stochastic micro-dynamics of the total system. This allows to start with the Belavkin quantum filtering equation and derive the generalized Hamilton-Jacobi-Bellman equation using standard arguments of classical control theory. This is equivalent to a Hamilton-Jacobi equation with an extra linear dissipative term if the control is restricted to only Hamiltonian terms in the filtering equation. A controlled qubit is considered as an example throughout the development of the formalism. Finally, we discuss optimum observation strategies to obtain a pure quantum qubit state from a mixed one.
Directory of Open Access Journals (Sweden)
Jing Cai
2016-01-01
Full Text Available Considering the wide application of condition-based maintenance in aeroengine maintenance practice, it becomes possible for aeroengines to carry out their preventive maintenance in just-in-time (JIT manner by reasonably planning their shop visits (SVs. In this study, an approach is proposed to make aeroengine SV decisions following the concept of JIT. Firstly, a state space model (SSM for aeroengine based on exhaust gas temperature margin is developed to predict the remaining useful life (RUL of aeroengine. Secondly, the effect of SV decisions on risk and service level (SL is analyzed, and an optimization of the aeroengine SV decisions based on RUL and stochastic repair time is performed to carry out JIT manner with the requirement of safety and SL. Finally, a case study considering two CFM-56 aeroengines is presented to demonstrate the proposed approach. The results show that predictive accuracy of RUL with SSM is higher than with linear regression, and the process of SV decisions is simple and feasible for airlines to improve the inventory management level of their aeroengines.
Optimal routing of hazardous substances in time-varying, stochastic transportation networks
International Nuclear Information System (INIS)
Woods, A.L.; Miller-Hooks, E.; Mahmassani, H.S.
1998-07-01
This report is concerned with the selection of routes in a network along which to transport hazardous substances, taking into consideration several key factors pertaining to the cost of transport and the risk of population exposure in the event of an accident. Furthermore, the fact that travel time and the risk measures are not constant over time is explicitly recognized in the routing decisions. Existing approaches typically assume static conditions, possibly resulting in inefficient route selection and unnecessary risk exposure. The report described the application of recent advances in network analysis methodologies to the problem of routing hazardous substances. Several specific problem formulations are presented, reflecting different degrees of risk aversion on the part of the decision-maker, as well as different possible operational scenarios. All procedures explicitly consider travel times and travel costs (including risk measures) to be stochastic time-varying quantities. The procedures include both exact algorithms, which may require extensive computational effort in some situations, as well as more efficient heuristics that may not guarantee a Pareto-optimal solution. All procedures are systematically illustrated for an example application using the Texas highway network, for both normal and incident condition scenarios. The application illustrates the trade-offs between the information obtained in the solution and computational efficiency, and highlights the benefits of incorporating these procedures in a decision-support system for hazardous substance shipment routing decisions
Directory of Open Access Journals (Sweden)
Fatemeh Rastegaripour
2010-09-01
Full Text Available The present study investigates water allocation of Kardeh Reservoir to domestic and agricultural users using an Interval Parameter, Multi-stage, Stochastic Programming (IMSLP under uncertainty. The advantages of the method include its dynamics nature, use of a pre-defined policy in its optimization process, and the use of interval parameter and probability under uncertainty conditions. Additionally, it offers different decision-making alternatives for different scenarios of water shortage. The required data were collected from Khorasan Razavi Regional Water Organization and from the Water and Wastewater Co. for the period 1988-2007. Results showed that, under the worst conditions, the water deficits expected to occur for each of the next 3 years will be 1.9, 2.55, and 3.11 million cubic meters for the domestic use and 0.22, 0.32, 0.75 million cubic meters for irrigation. Approximate reductions of 0.5, 0.7, and 1 million cubic meters in the monthly consumption of the urban community and enhanced irrigation efficiencies of about 6, 11, and 20% in the agricultural sector are recommended as approaches for combating the water shortage over the next 3 years.
Stochastic dynamics of resistive switching: fluctuations lead to optimal particle number
International Nuclear Information System (INIS)
Radtke, Paul K; Schimansky-Geier, Lutz; Hazel, Andrew L; Straube, Arthur V
2017-01-01
Resistive switching (RS) is one of the foremost candidates for building novel types of non-volatile random access memories. Any practical implementation of such a memory cell calls for a strong miniaturization, at which point fluctuations start playing a role that cannot be neglected. A detailed understanding of switching mechanisms and reliability is essential. For this reason, we formulate a particle model based on the stochastic motion of oxygen vacancies. It allows us to investigate fluctuations in the resistance states of a switch with two active zones. The vacancies’ dynamics are governed by a master equation. Upon the application of a voltage pulse, the vacancies travel collectively through the switch. By deriving a generalized Burgers equation we can interpret this collective motion as nonlinear traveling waves, and numerically verify this result. Further, we define binary logical states by means of the underlying vacancy distributions, and establish a framework of writing and reading such memory element with voltage pulses. Considerations about the discriminability of these operations under fluctuations together with the markedness of the RS effect itself lead to the conclusion, that an intermediate vacancy number is optimal for performance. (paper)
Stochastic dynamics of resistive switching: fluctuations lead to optimal particle number
Radtke, Paul K.; Hazel, Andrew L.; Straube, Arthur V.; Schimansky-Geier, Lutz
2017-09-01
Resistive switching (RS) is one of the foremost candidates for building novel types of non-volatile random access memories. Any practical implementation of such a memory cell calls for a strong miniaturization, at which point fluctuations start playing a role that cannot be neglected. A detailed understanding of switching mechanisms and reliability is essential. For this reason, we formulate a particle model based on the stochastic motion of oxygen vacancies. It allows us to investigate fluctuations in the resistance states of a switch with two active zones. The vacancies’ dynamics are governed by a master equation. Upon the application of a voltage pulse, the vacancies travel collectively through the switch. By deriving a generalized Burgers equation we can interpret this collective motion as nonlinear traveling waves, and numerically verify this result. Further, we define binary logical states by means of the underlying vacancy distributions, and establish a framework of writing and reading such memory element with voltage pulses. Considerations about the discriminability of these operations under fluctuations together with the markedness of the RS effect itself lead to the conclusion, that an intermediate vacancy number is optimal for performance.
Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems
Antown, Fadi; Dragičević, Davor; Froyland, Gary
2018-03-01
The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous, sequential, or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.
International Nuclear Information System (INIS)
Yuan Yuan; Yi Hongliang; Shuai Yong; Wang Fuqiang; Tan Heping
2010-01-01
As a part of resolving optical properties in atmosphere radiative transfer calculations, this paper focuses on obtaining aerosol optical thicknesses (AOTs) in the visible and near infrared wave band through indirect method by gleaning the values of aerosol particle size distribution parameters. Although various inverse techniques have been applied to obtain values for these parameters, we choose a stochastic particle swarm optimization (SPSO) algorithm to perform an inverse calculation. Computational performances of different inverse methods are investigated and the influence of swarm size on the inverse problem of computation particles is examined. Next, computational efficiencies of various particle size distributions and the influences of the measured errors on computational accuracy are compared. Finally, we recover particle size distributions for atmospheric aerosols over Beijing using the measured AOT data (at wavelengths λ=0.400, 0.690, 0.870, and 1.020 μm) obtained from AERONET at different times and then calculate other AOT values for this band based on the inverse results. With calculations agreeing with measured data, the SPSO algorithm shows good practicability.
Adaptive and Optimal Control of Stochastic Dynamical Systems
2015-09-14
Advances in Statistics, Probability and Actuarial Sciences , Vol. 1, World Scientific, 2012, 451- 463. [4] T. E. Duncan and B. Pasik-Duncan, A...S. N. Cohen, T. K. Siu and H. Yang) Advances in Statistics, Probability and Actuarial Sciences , Vol. 1, World Scientific, 2012, 451-463. 4. T. E...games with gen- eral noise processes, Models and Methods in Economics and Management Science : Essays in Honor of Charles S. Tapiero, (eds. F. El
International Nuclear Information System (INIS)
Medeiros, Jose Antonio Carlos Canedo; Machado, Marcelo Dornellas; Lima, Alan Miranda M. de; Schirru, Roberto
2007-01-01
Predictive control systems are control systems that use a model of the controlled system (plant), used to predict the future behavior of the plant allowing the establishment of an anticipative control based on a future condition of the plant, and an optimizer that, considering a future time horizon of the plant output and a recent horizon of the control action, determines the controller's outputs to optimize a performance index of the controlled plant. The predictive control system does not require analytical models of the plant; the model of predictor of the plant can be learned from historical data of operation of the plant. The optimizer of the predictive controller establishes the strategy of the control: the minimization of a performance index (objective function) is done so that the present and future control actions are computed in such a way to minimize the objective function. The control strategy, implemented by the optimizer, induces the formation of an optimal control mechanism whose effect is to reduce the stabilization time, the 'overshoot' and 'undershoot', minimize the control actuation so that a compromise among those objectives is attained. The optimizer of the predictive controller is usually implemented using gradient-based algorithms. In this work we use the Particle Swarm Optimization algorithm (PSO) in the optimizer component of a predictive controller applied in the control of the xenon oscillation of a pressurized water reactor (PWR). The PSO is a stochastic optimization technique applied in several disciplines, simple and capable of providing a global optimal for high complexity problems and difficult to be optimized, providing in many cases better results than those obtained by other conventional and/or other artificial optimization techniques. (author)
Feng, Yen-Yi; Wu, I-Chin; Chen, Tzu-Li
2017-03-01
The number of emergency cases or emergency room visits rapidly increases annually, thus leading to an imbalance in supply and demand and to the long-term overcrowding of hospital emergency departments (EDs). However, current solutions to increase medical resources and improve the handling of patient needs are either impractical or infeasible in the Taiwanese environment. Therefore, EDs must optimize resource allocation given limited medical resources to minimize the average length of stay of patients and medical resource waste costs. This study constructs a multi-objective mathematical model for medical resource allocation in EDs in accordance with emergency flow or procedure. The proposed mathematical model is complex and difficult to solve because its performance value is stochastic; furthermore, the model considers both objectives simultaneously. Thus, this study develops a multi-objective simulation optimization algorithm by integrating a non-dominated sorting genetic algorithm II (NSGA II) with multi-objective computing budget allocation (MOCBA) to address the challenges of multi-objective medical resource allocation. NSGA II is used to investigate plausible solutions for medical resource allocation, and MOCBA identifies effective sets of feasible Pareto (non-dominated) medical resource allocation solutions in addition to effectively allocating simulation or computation budgets. The discrete event simulation model of ED flow is inspired by a Taiwan hospital case and is constructed to estimate the expected performance values of each medical allocation solution as obtained through NSGA II. Finally, computational experiments are performed to verify the effectiveness and performance of the integrated NSGA II and MOCBA method, as well as to derive non-dominated medical resource allocation solutions from the algorithms.
Huang, Si-Da; Shang, Cheng; Zhang, Xiao-Jie; Liu, Zhi-Pan
2017-09-01
While the underlying potential energy surface (PES) determines the structure and other properties of a material, it has been frustrating to predict new materials from theory even with the advent of supercomputing facilities. The accuracy of the PES and the efficiency of PES sampling are two major bottlenecks, not least because of the great complexity of the material PES. This work introduces a "Global-to-Global" approach for material discovery by combining for the first time a global optimization method with neural network (NN) techniques. The novel global optimization method, named the stochastic surface walking (SSW) method, is carried out massively in parallel for generating a global training data set, the fitting of which by the atom-centered NN produces a multi-dimensional global PES; the subsequent SSW exploration of large systems with the analytical NN PES can provide key information on the thermodynamics and kinetics stability of unknown phases identified from global PESs. We describe in detail the current implementation of the SSW-NN method with particular focuses on the size of the global data set and the simultaneous energy/force/stress NN training procedure. An important functional material, TiO 2 , is utilized as an example to demonstrate the automated global data set generation, the improved NN training procedure and the application in material discovery. Two new TiO 2 porous crystal structures are identified, which have similar thermodynamics stability to the common TiO 2 rutile phase and the kinetics stability for one of them is further proved from SSW pathway sampling. As a general tool for material simulation, the SSW-NN method provides an efficient and predictive platform for large-scale computational material screening.
Directory of Open Access Journals (Sweden)
Charles I Nkeki
2014-11-01
Full Text Available This paper aim at studying a mean-variance portfolio selection problem with stochastic salary, proportional administrative costs and taxation in the accumulation phase of a defined contribution (DC pension scheme. The fund process is subjected to taxation while the contribution of the pension plan member (PPM is tax exempt. It is assumed that the flow of contributions of a PPM are invested into a market that is characterized by a cash account and a stock. The optimal portfolio processes and expected wealth for the PPM are established. The efficient and parabolic frontiers of a PPM portfolios in mean-variance are obtained. It was found that capital market line can be attained when initial fund and the contribution rate are zero. It was also found that the optimal portfolio process involved an inter-temporal hedging term that will offset any shocks to the stochastic salary of the PPM.
Near optimal decentralized H_inf control
DEFF Research Database (Denmark)
Stoustrup, J.; Niemann, Hans Henrik
It is shown that foir a class of decentralized control problems there does not exist a sequence of controllers of bounded order which obtains near optimal control. Neither does there exist an infinity dimentional optimal controller. Using the insight of the line of proof of these results, a heuri......It is shown that foir a class of decentralized control problems there does not exist a sequence of controllers of bounded order which obtains near optimal control. Neither does there exist an infinity dimentional optimal controller. Using the insight of the line of proof of these results...
Directory of Open Access Journals (Sweden)
Meili Li
2015-01-01
Full Text Available The approximate controllability of semilinear neutral stochastic integrodifferential inclusions with infinite delay in an abstract space is studied. Sufficient conditions are established for the approximate controllability. The results are obtained by using the theory of analytic resolvent operator, the fractional power theory, and the theorem of nonlinear alternative for Kakutani maps. Finally, an example is provided to illustrate the theory.
Directory of Open Access Journals (Sweden)
C. Parthasarathy
2013-03-01
Full Text Available In this paper, we study the controllability results of first order impulsive stochastic differential and neutral differential systems with state-dependent delay by using semigroup theory. The controllability results are derived by the means of Leray-SchauderAlternative fixed point theorem. An example is provided to illustrate the theory.
Eichhorn, Ralf; Aurell, Erik
2014-04-01
theory for small deviations from equilibrium, in which a general framework is constructed from the analysis of non-equilibrium states close to equilibrium. In a next step, Prigogine and others developed linear irreversible thermodynamics, which establishes relations between transport coefficients and entropy production on a phenomenological level in terms of thermodynamic forces and fluxes. However, beyond the realm of linear response no general theoretical results were available for quite a long time. This situation has changed drastically over the last 20 years with the development of stochastic thermodynamics, revealing that the range of validity of thermodynamic statements can indeed be extended deep into the non-equilibrium regime. Early developments in that direction trace back to the observations of symmetry relations between the probabilities for entropy production and entropy annihilation in non-equilibrium steady states [5-8] (nowadays categorized in the class of so-called detailed fluctuation theorems), and the derivations of the Bochkov-Kuzovlev [9, 10] and Jarzynski relations [11] (which are now classified as so-called integral fluctuation theorems). Apart from its fundamental theoretical interest, the developments in stochastic thermodynamics have experienced an additional boost from the recent experimental progress in fabricating, manipulating, controlling and observing systems on the micro- and nano-scale. These advances are not only of formidable use for probing and monitoring biological processes on the cellular, sub-cellular and molecular level, but even include the realization of a microscopic thermodynamic heat engine [12] or the experimental verification of Landauer's principle in a colloidal system [13]. The scientific program Stochastic Thermodynamics held between 4 and 15 March 2013, and hosted by The Nordic Institute for Theoretical Physics (Nordita), was attended by more than 50 scientists from the Nordic countries and elsewhere, amongst them
Macian-Sorribes, Hector; Pulido-Velazquez, Manuel; Tilmant, Amaury
2015-04-01
Stochastic programming methods are better suited to deal with the inherent uncertainty of inflow time series in water resource management. However, one of the most important hurdles in their use in practical implementations is the lack of generalized Decision Support System (DSS) shells, usually based on a deterministic approach. The purpose of this contribution is to present a general-purpose DSS shell, named Explicit Stochastic Programming Advanced Tool (ESPAT), able to build and solve stochastic programming problems for most water resource systems. It implements a hydro-economic approach, optimizing the total system benefits as the sum of the benefits obtained by each user. It has been coded using GAMS, and implements a Microsoft Excel interface with a GAMS-Excel link that allows the user to introduce the required data and recover the results. Therefore, no GAMS skills are required to run the program. The tool is divided into four modules according to its capabilities: 1) the ESPATR module, which performs stochastic optimization procedures in surface water systems using a Stochastic Dual Dynamic Programming (SDDP) approach; 2) the ESPAT_RA module, which optimizes coupled surface-groundwater systems using a modified SDDP approach; 3) the ESPAT_SDP module, capable of performing stochastic optimization procedures in small-size surface systems using a standard SDP approach; and 4) the ESPAT_DET module, which implements a deterministic programming procedure using non-linear programming, able to solve deterministic optimization problems in complex surface-groundwater river basins. The case study of the Mijares river basin (Spain) is used to illustrate the method. It consists in two reservoirs in series, one aquifer and four agricultural demand sites currently managed using historical (XIV century) rights, which give priority to the most traditional irrigation district over the XX century agricultural developments. Its size makes it possible to use either the SDP or
Adaptive control of chaotic systems with stochastic time varying unknown parameters
Energy Technology Data Exchange (ETDEWEB)
Salarieh, Hassan [Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Azadi Avenue, Tehran (Iran, Islamic Republic of)], E-mail: salarieh@mech.sharif.edu; Alasty, Aria [Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Azadi Avenue, Tehran (Iran, Islamic Republic of)], E-mail: aalasti@sharif.edu
2008-10-15
In this paper based on the Lyapunov stability theorem, an adaptive control scheme is proposed for stabilizing the unstable periodic orbits (UPO) of chaotic systems. It is assumed that the chaotic system has some linearly dependent unknown parameters which are stochastically time varying. The stochastic parameters are modeled through the Weiner process derivative. To demonstrate the effectiveness of the proposed technique it has been applied to the Lorenz, Chen and Rossler dynamical systems, as some case studies. Simulation results indicate that the proposed adaptive controller has a high performance in stabilizing the UPO of chaotic systems in noisy environment.
International Nuclear Information System (INIS)
Moura, Scott J.; Fathy, Hosam K.; Stein, Jeffrey L.; Callaway, Duncan S.
2010-01-01
Recent results in plug-in hybrid electric vehicle (PHEV) power management research suggest that battery energy capacity requirements may be reduced through proper power management algorithm design. Specifically, algorithms which blend fuel and electricity during the charge depletion phase using smaller batteries may perform equally to algorithms that apply electric-only operation during charge depletion using larger batteries. The implication of this result is that ''blended'' power management algorithms may reduce battery energy capacity requirements, thereby lowering the acquisition costs of PHEVs. This article seeks to quantify the tradeoffs between power management algorithm design and battery energy capacity, in a systematic and rigorous manner. Namely, we (1) construct dynamic PHEV models with scalable battery energy capacities, (2) optimize power management using stochastic control theory, and (3) develop simulation methods to statistically quantify the performance tradeoffs. The degree to which blending enables smaller battery energy capacities is evaluated as a function of both daily driving distance and energy (fuel and electricity) pricing. (author)
Optimal harvesting of a stochastic delay tri-trophic food-chain model with Lévy jumps
Qiu, Hong; Deng, Wenmin
2018-02-01
In this paper, the optimal harvesting of a stochastic delay tri-trophic food-chain model with Lévy jumps is considered. We introduce two kinds of environmental perturbations in this model. One is called white noise which is continuous and is described by a stochastic integral with respect to the standard Brownian motion. And the other one is jumping noise which is modeled by a Lévy process. Under some mild assumptions, the critical values between extinction and persistent in the mean of each species are established. The sufficient and necessary criteria for the existence of optimal harvesting policy are established and the optimal harvesting effort and the maximum of sustainable yield are also obtained. We utilize the ergodic method to discuss the optimal harvesting problem. The results show that white noises and Lévy noises significantly affect the optimal harvesting policy while time delays is harmless for the optimal harvesting strategy in some cases. At last, some numerical examples are introduced to show the validity of our results.
Elfering, Achim; Schade, Volker; Stoecklin, Lukas; Baur, Simone; Burger, Christian; Radlinger, Lorenz
2014-05-01
Slip, trip, and fall injuries are frequent among health care workers. Stochastic resonance whole-body vibration training was tested to improve postural control. Participants included 124 employees of a Swiss university hospital. The randomized controlled trial included an experimental group given 8 weeks of training and a control group with no intervention. In both groups, postural control was assessed as mediolateral sway on a force plate before and after the 8-week trial. Mediolateral sway was significantly decreased by stochastic resonance whole-body vibration training in the experimental group but not in the control group that received no training (p < .05). Stochastic resonance whole-body vibration training is an option in the primary prevention of balance-related injury at work. Copyright 2014, SLACK Incorporated.
International Nuclear Information System (INIS)
Kitapbayev, Yerkin; Moriarty, John; Mancarella, Pierluigi
2015-01-01
Highlights: • We calculate the real option value of flexibility from CHP-thermal storage. • Stochastic optimal feedback control problem is solved under uncertain market prices. • Efficient real-time numerical solutions combine simulation, regression and recursion. • Clear, interpretable feedback control maps are produced for each hour of the day. • We give a realistic UK case study using projected market gas and electricity prices. - Abstract: In district energy systems powered by Combined Heat and Power (CHP) plants, thermal storage can significantly increase CHP flexibility to respond to real time market signals and therefore improve the business case of such demand response schemes in a Smart Grid environment. However, main challenges remain as to what is the optimal way to control inter-temporal storage operation in the presence of uncertain market prices, and then how to value the investment into storage as flexibility enabler. In this outlook, the aim of this paper is to propose a model for optimal and dynamic control and long term valuation of CHP-thermal storage in the presence of uncertain market prices. The proposed model is formulated as a stochastic control problem and numerically solved through Least Squares Monte Carlo regression analysis, with integrated investment and operational timescale analysis equivalent to real options valuation models encountered in finance. Outputs are represented by clear and interpretable feedback control strategy maps for each hour of the day, thus suitable for real time demand response under uncertainty. Numerical applications to a realistic UK case study with projected market gas and electricity prices exemplify the proposed approach and quantify the robustness of the selected storage solutions
Simulation-optimization framework for multi-site multi-season hybrid stochastic streamflow modeling
Srivastav, Roshan; Srinivasan, K.; Sudheer, K. P.
2016-11-01
A simulation-optimization (S-O) framework is developed for the hybrid stochastic modeling of multi-site multi-season streamflows. The multi-objective optimization model formulated is the driver and the multi-site, multi-season hybrid matched block bootstrap model (MHMABB) is the simulation engine within this framework. The multi-site multi-season simulation model is the extension of the existing single-site multi-season simulation model. A robust and efficient evolutionary search based technique, namely, non-dominated sorting based genetic algorithm (NSGA - II) is employed as the solution technique for the multi-objective optimization within the S-O framework. The objective functions employed are related to the preservation of the multi-site critical deficit run sum and the constraints introduced are concerned with the hybrid model parameter space, and the preservation of certain statistics (such as inter-annual dependence and/or skewness of aggregated annual flows). The efficacy of the proposed S-O framework is brought out through a case example from the Colorado River basin. The proposed multi-site multi-season model AMHMABB (whose parameters are obtained from the proposed S-O framework) preserves the temporal as well as the spatial statistics of the historical flows. Also, the other multi-site deficit run characteristics namely, the number of runs, the maximum run length, the mean run sum and the mean run length are well preserved by the AMHMABB model. Overall, the proposed AMHMABB model is able to show better streamflow modeling performance when compared with the simulation based SMHMABB model, plausibly due to the significant role played by: (i) the objective functions related to the preservation of multi-site critical deficit run sum; (ii) the huge hybrid model parameter space available for the evolutionary search and (iii) the constraint on the preservation of the inter-annual dependence. Split-sample validation results indicate that the AMHMABB model is
Nonlinear control of fixed-wing UAVs in presence of stochastic winds
Rubio Hervas, Jaime; Reyhanoglu, Mahmut; Tang, Hui; Kayacan, Erdal
2016-04-01
This paper studies the control of fixed-wing unmanned aerial vehicles (UAVs) in the presence of stochastic winds. A nonlinear controller is designed based on a full nonlinear mathematical model that includes the stochastic wind effects. The air velocity is controlled exclusively using the position of the throttle, and the rest of the dynamics are controlled with the aileron, elevator, and rudder deflections. The nonlinear control design is based on a smooth approximation of a sliding mode controller. An extended Kalman filter (EKF) is proposed for the state estimation and filtering. A case study is presented: landing control of a UAV on a ship deck in the presence of wind based exclusively on LADAR measurements. The effectiveness of the nonlinear control algorithm is illustrated through a simulation example.
Constrained Optimization and Optimal Control for Partial Differential Equations
Leugering, Günter; Griewank, Andreas
2012-01-01
This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The cont
Susceptibility of optimal train schedules to stochastic disturbances of process times
DEFF Research Database (Denmark)
Larsen, Rune; Pranzo, Marco; D’Ariano, Andrea
2013-01-01
study, an advanced branch and bound algorithm, on average, outperforms a First In First Out scheduling rule both in deterministic and stochastic traffic scenarios. However, the characteristic of the stochastic processes and the way a stochastic instance is handled turn out to have a serious impact...... and dwell times). In fact, the objective of railway traffic management is to reduce delay propagation and to increase disturbance robustness of train schedules at a network scale. We present a quantitative study of traffic disturbances and their effects on the schedules computed by simple and advanced...
International Nuclear Information System (INIS)
Luo, B.; Li, J.B.; Huang, G.H.; Li, H.L.
2006-01-01
This study presents a simulation-based interval two-stage stochastic programming (SITSP) model for agricultural nonpoint source (NPS) pollution control through land retirement under uncertain conditions. The modeling framework was established by the development of an interval two-stage stochastic program, with its random parameters being provided by the statistical analysis of the simulation outcomes of a distributed water quality approach. The developed model can deal with the tradeoff between agricultural revenue and 'off-site' water quality concern under random effluent discharge for a land retirement scheme through minimizing the expected value of long-term total economic and environmental cost. In addition, the uncertainties presented as interval numbers in the agriculture-water system can be effectively quantified with the interval programming. By subdividing the whole agricultural watershed into different zones, the most pollution-related sensitive cropland can be identified and an optimal land retirement scheme can be obtained through the modeling approach. The developed method was applied to the Swift Current Creek watershed in Canada for soil erosion control through land retirement. The Hydrological Simulation Program-FORTRAN (HSPF) was used to simulate the sediment information for this case study. Obtained results indicate that the total economic and environmental cost of the entire agriculture-water system can be limited within an interval value for the optimal land retirement schemes. Meanwhile, a best and worst land retirement scheme was obtained for the study watershed under various uncertainties
Fuzzy logic control and optimization system
Lou, Xinsheng [West Hartford, CT
2012-04-17
A control system (300) for optimizing a power plant includes a chemical loop having an input for receiving an input signal (369) and an output for outputting an output signal (367), and a hierarchical fuzzy control system (400) operably connected to the chemical loop. The hierarchical fuzzy control system (400) includes a plurality of fuzzy controllers (330). The hierarchical fuzzy control system (400) receives the output signal (367), optimizes the input signal (369) based on the received output signal (367), and outputs an optimized input signal (369) to the input of the chemical loop to control a process of the chemical loop in an optimized manner.
Age Replacement and Service Rate Control of Stochastically Degrading Queues
National Research Council Canada - National Science Library
Chapin, Patrick
2004-01-01
This thesis considers the problem of optimally selecting a periodic replacement time for a multiserver queueing system in which each server is subject to degradation as a function of the mean service...
The two-regime method for optimizing stochastic reaction-diffusion simulations
Flegg, M. B.; Chapman, S. J.; Erban, R.
2011-01-01
Spatial organization and noise play an important role in molecular systems biology. In recent years, a number of software packages have been developed for stochastic spatio-temporal simulation, ranging from detailed molecular-based approaches
International Nuclear Information System (INIS)
Najibi, Fatemeh; Niknam, Taher; Kavousi-Fard, Abdollah
2016-01-01
This paper aims to report the results of the research conducted to one thermal and electrical model for photovoltaic. Moreover, one probabilistic framework is introduced for considering all uncertainties in the optimal energy management of Micro-Grid problem. It should be noted that one typical Micro-Grid is being studied as a case, including different renewable energy sources, such as Photovoltaic, Micro Turbine, Wind Turbine, and one battery as a storage device for storing energy. The uncertainties of market price variation, photovoltaic and wind turbine output power change and load demand error are covered by the suggested probabilistic framework. The Micro-Grid problem is of nonlinear nature because of the stochastic behavior of the renewable energy sources such as Photovoltaic and Wind Turbine units, and hence there is need for a powerful tool to solve the problem. Therefore, in addition to the simulated thermal model and suggested probabilistic framework, a new algorithm is also introduced. The Backtracking Search Optimization Algorithm is described as a useful method to optimize the MG (micro-grids) problem. This algorithm has the benefit of escaping from the local optima while converging fast, too. The proposed algorithm is also tested on the typical Micro-Grid. - Highlights: • Proposing an electro-thermal model for PV. • Proposing a new stochastic formulation for optimal operation of renewable MGs. • Introduction of a new optimization method based on BSO to explore the problem search space.
Directory of Open Access Journals (Sweden)
Diem Dang Huan
2015-12-01
Full Text Available The current paper is concerned with the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a new set of sufficient conditions for the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps. Finally, an application to the stochastic nonlinear wave equation with infinite delay and Poisson jumps is given.
Czech Academy of Sciences Publication Activity Database
Kaňková, Vlasta
2017-01-01
Roč. 53, č. 6 (2017), s. 1026-1046 ISSN 0023-5954 R&D Projects: GA ČR GA15-10331S Institutional support: RVO:67985556 Keywords : stochastic programming * stochastic dominance * empirical estimates * financial applications Subject RIV: BB - Applied Statistics, Operational Research OBOR OECD: Statistics and probability Impact factor: 0.379, year: 2016 http://library.utia.cas.cz/separaty/2017/E/kankova-0485151.pdf
Optimal Inventory Control with Advance Supply Information
Directory of Open Access Journals (Sweden)
Marko Jaksic
2016-09-01
Full Text Available It has been shown in numerous situations that sharing information between the companies leads to improved performance of the supply chain. We study a positive lead time periodic-review inventory system of a retailer facing stochastic demand from his customer and stochastic limited supply capacity of the manufacturer supplying the products to him. The consequence of stochastic supply capacity is that the orders might not be delivered in full, and the exact size of the replenishment might not be known to the retailer. The manufacturer is willing to share the so-called advance supply information (ASI about the actual replenishment of the retailer's pipeline order with the retailer. ASI is provided at a certain time after the orders have been placed and the retailer can now use this information to decrease the uncertainty of the supply, and thus improve its inventory policy. For this model, we develop a dynamic programming formulation, and characterize the optimal ordering policy as a state-dependent base-stock policy. In addition, we show some properties of the base-stock level. While the optimal policy is highly complex, we obtain some additional insights by comparing it to the state-dependent myopic inventory policy. We conduct the numerical analysis to estimate the in uence of the system parameters on the value of ASI. While we show that the interaction between the parameters is relatively complex, the general insight is that due to increasing marginal returns, the majority of the benets are gained only in the case of full, or close to full, ASI visibility.
International Nuclear Information System (INIS)
Shishkin, Alexander A.
2001-02-01
A new method of particle motion control in toroidal magnetic traps with rotational transform using the estafette of drift resonances and stochasticity of particle trajectories is proposed. The use of the word estafette' here means that the particle passes through a set of resonances in consecutive order from one to another during its motion. The overlapping of adjacent resonances can be moved radially from the center to the edge of the plasma by switching on the corresponding perturbations in accordance with a particular rule in time. In this way particles (e.g. cold alpha-particle) can be removed from the center of the confinement volume to the plasma periphery. For the analytical treatment of the stochastic behaviour of particle motion the stochastic diffusion coefficients D r, r, D r,θ , D θ,θ are introduced. The new approach is demonstrated by numerical computations of the test helium particle trajectories in the toroidal trap Large Helical Device. (author)
Stochastic Greybox Modeling for Control of an Alternating Activated Sludge Process
DEFF Research Database (Denmark)
Halvgaard, Rasmus Fogtmann; Vezzaro, Luca; Grum, M.
We present a stochastic greybox model of a BioDenitro WWTP that can be used for short time horizon Model Predictive Control. The model is based on a simpliﬁed ASM1 model and takes model uncertainty in to account. It estimates unmeasured state variables in the system, e.g. the inlet concentration...
Operational Strategies for Predictive Dispatch of Control Reserves in View of Stochastic Generation
DEFF Research Database (Denmark)
Delikaraoglou, Stefanos; Heussen, Kai; Pinson, Pierre
2014-01-01
In view of the predictability and stochasticity of wind power generation, transmission system operators (TSOs) can benefit from predictive dispatch of slow and manual control reserves in order to maintain reactive reserve levels for unpredictable events. While scenario-based approaches for stocha...
Optimal control of tokamak and stellarator plasma behaviour
International Nuclear Information System (INIS)
Rastovic, Danilo
2007-01-01
The control of plasma transport, laminar and turbulent, is investigated, using the methods of scaling, optimal control and adaptive Monte Carlo simulations. For this purpose, the asymptotic behaviour of kinetic equation is considered in order to obtain finite-dimensional invariant manifolds, and in this way the finite-dimensional theory of control can be applied. We imagine the labyrinth of open doors and after applying self-similarity, the motion moved through all the desired doors in repeatable ways as Brownian motions. We take local actions for each piece of contractive ergodic motion, and, after self-organization in adaptive invariant measures, the optimum movement of particles is obtained according to the principle of maximum entropy. This is true for deterministic and stochastic cases that serve as models for plasma dynamics
Elsawy, Hesham
2014-08-01
Using stochastic geometry, we develop a tractable uplink modeling paradigm for outage probability and spectral efficiency in both single and multi-tier cellular wireless networks. The analysis accounts for per user equipment (UE) power control as well as the maximum power limitations for UEs. More specifically, for interference mitigation and robust uplink communication, each UE is required to control its transmit power such that the average received signal power at its serving base station (BS) is equal to a certain threshold ρo. Due to the limited transmit power, the UEs employ a truncated channel inversion power control policy with a cutoff threshold of ρo. We show that there exists a transfer point in the uplink system performance that depends on the following tuple: BS intensity λ, maximum transmit power of UEs Pu, and ρo. That is, when Pu is a tight operational constraint with respect to (w.r.t.) λ and ρo, the uplink outage probability and spectral efficiency highly depend on the values of λ and ρo. In this case, there exists an optimal cutoff threshold ρ*o, which depends on the system parameters, that minimizes the outage probability. On the other hand, when Pu is not a binding operational constraint w.r.t. λ and ρo, the uplink outage probability and spectral efficiency become independent of λ and ρo. We obtain approximate yet accurate simple expressions for outage probability and spectral efficiency, which reduce to closed forms in some special cases. © 2002-2012 IEEE.
Optimal control of raw timber production processes
Ivan Kolenka
1978-01-01
This paper demonstrates the possibility of optimal planning and control of timber harvesting activ-ities with mathematical optimization models. The separate phases of timber harvesting are represented by coordinated models which can be used to select the optimal decision for the execution of any given phase. The models form a system whose components are connected and...
Chiavico, Mattia; Raso, Luciano; Dorchies, David; Malaterre, Pierre-Olivier
2015-04-01
Seine river region is an extremely important logistic and economic junction for France and Europe. The hydraulic protection of most part of the region relies on four controlled reservoirs, managed by EPTB Seine-Grands Lacs. Presently, reservoirs operation is not centrally coordinated, and release rules are based on empirical filling curves. In this study, we analyze how a centralized release policy can face flood and drought risks, optimizing water system efficiency. The optimal and centralized decisional problem is solved by Stochastic Dual Dynamic Programming (SDDP) method, minimizing an operational indicator for each planning objective. SDDP allows us to include into the system: 1) the hydrological discharge, specifically a stochastic semi-distributed auto-regressive model, 2) the hydraulic transfer model, represented by a linear lag and route model, and 3) reservoirs and diversions. The novelty of this study lies on the combination of reservoir and hydraulic models in SDDP for flood and drought protection problems. The study case covers the Seine basin until the confluence with Aube River: this system includes two reservoirs, the city of Troyes, and the Nuclear power plant of Nogent-Sur-Seine. The conflict between the interests of flood protection, drought protection, water use and ecology leads to analyze the environmental system in a Multi-Objective perspective.
Adaptive optimization and control using neural networks
Energy Technology Data Exchange (ETDEWEB)
Mead, W.C.; Brown, S.K.; Jones, R.D.; Bowling, P.S.; Barnes, C.W.
1993-10-22
Recent work has demonstrated the ability of neural-network-based controllers to optimize and control machines with complex, non-linear, relatively unknown control spaces. We present a brief overview of neural networks via a taxonomy illustrating some capabilities of different kinds of neural networks. We present some successful control examples, particularly the optimization and control of a small-angle negative ion source.
Velarde, P.; Valverde, L.; Maestre, J. M.; Ocampo-Martinez, C.; Bordons, C.
2017-03-01
In this paper, a performance comparison among three well-known stochastic model predictive control approaches, namely, multi-scenario, tree-based, and chance-constrained model predictive control is presented. To this end, three predictive controllers have been designed and implemented in a real renewable-hydrogen-based microgrid. The experimental set-up includes a PEM electrolyzer, lead-acid batteries, and a PEM fuel cell as main equipment. The real experimental results show significant differences from the plant components, mainly in terms of use of energy, for each implemented technique. Effectiveness, performance, advantages, and disadvantages of these techniques are extensively discussed and analyzed to give some valid criteria when selecting an appropriate stochastic predictive controller.
Cheng, Yu; Ye, Dong; Sun, Zhaowei; Zhang, Shijie
2018-03-01
This paper proposes a novel feedback control law for spacecraft to deal with attitude constraint, input saturation, and stochastic disturbance during the attitude reorientation maneuver process. Applying the parameter selection method to improving the existence conditions for the repulsive potential function, the universality of the potential-function-based algorithm is enhanced. Moreover, utilizing the auxiliary system driven by the difference between saturated torque and command torque, a backstepping control law, which satisfies the input saturation constraint and guarantees the spacecraft stability, is presented. Unlike some methods that passively rely on the inherent characteristic of the existing controller to stabilize the adverse effects of external stochastic disturbance, this paper puts forward a nonlinear disturbance observer to compensate the disturbance in real-time, which achieves a better performance of robustness. The simulation results validate the effectiveness, reliability, and universality of the proposed control law.
A stochastic chemical dynamic approach to correlate autoimmunity and optimal vitamin-D range.
Roy, Susmita; Shrinivas, Krishna; Bagchi, Biman
2014-01-01
Motivated by several recent experimental observations that vitamin-D could interact with antigen presenting cells (APCs) and T-lymphocyte cells (T-cells) to promote and to regulate different stages of immune response, we developed a coarse grained but general kinetic model in an attempt to capture the role of vitamin-D in immunomodulatory responses. Our kinetic model, developed using the ideas of chemical network theory, leads to a system of nine coupled equations that we solve both by direct and by stochastic (Gillespie) methods. Both the analyses consistently provide detail information on the dependence of immune response to the variation of critical rate parameters. We find that although vitamin-D plays a negligible role in the initial immune response, it exerts a profound influence in the long term, especially in helping the system to achieve a new, stable steady state. The study explores the role of vitamin-D in preserving an observed bistability in the phase diagram (spanned by system parameters) of immune regulation, thus allowing the response to tolerate a wide range of pathogenic stimulation which could help in resisting autoimmune diseases. We also study how vitamin-D affects the time dependent population of dendritic cells that connect between innate and adaptive immune responses. Variations in dose dependent response of anti-inflammatory and pro-inflammatory T-cell populations to vitamin-D correlate well with recent experimental results. Our kinetic model allows for an estimation of the range of optimum level of vitamin-D required for smooth functioning of the immune system and for control of both hyper-regulation and inflammation. Most importantly, the present study reveals that an overdose or toxic level of vitamin-D or any steroid analogue could give rise to too large a tolerant response, leading to an inefficacy in adaptive immune function.
A stochastic chemical dynamic approach to correlate autoimmunity and optimal vitamin-D range.
Directory of Open Access Journals (Sweden)
Susmita Roy
Full Text Available Motivated by several recent experimental observations that vitamin-D could interact with antigen presenting cells (APCs and T-lymphocyte cells (T-cells to promote and to regulate different stages of immune response, we developed a coarse grained but general kinetic model in an attempt to capture the role of vitamin-D in immunomodulatory responses. Our kinetic model, developed using the ideas of chemical network theory, leads to a system of nine coupled equations that we solve both by direct and by stochastic (Gillespie methods. Both the analyses consistently provide detail information on the dependence of immune response to the variation of critical rate parameters. We find that although vitamin-D plays a negligible role in the initial immune response, it exerts a profound influence in the long term, especially in helping the system to achieve a new, stable steady state. The study explores the role of vitamin-D in preserving an observed bistability in the phase diagram (spanned by system parameters of immune regulation, thus allowing the response to tolerate a wide range of pathogenic stimulation which could help in resisting autoimmune diseases. We also study how vitamin-D affects the time dependent population of dendritic cells that connect between innate and adaptive immune responses. Variations in dose dependent response of anti-inflammatory and pro-inflammatory T-cell populations to vitamin-D correlate well with recent experimental results. Our kinetic model allows for an estimation of the range of optimum level of vitamin-D required for smooth functioning of the immune system and for control of both hyper-regulation and inflammation. Most importantly, the present study reveals that an overdose or toxic level of vitamin-D or any steroid analogue could give rise to too large a tolerant response, leading to an inefficacy in adaptive immune function.
Stochastic Averaging and Stochastic Extremum Seeking
Liu, Shu-Jun
2012-01-01
Stochastic Averaging and Stochastic Extremum Seeking develops methods of mathematical analysis inspired by the interest in reverse engineering and analysis of bacterial convergence by chemotaxis and to apply similar stochastic optimization techniques in other environments. The first half of the text presents significant advances in stochastic averaging theory, necessitated by the fact that existing theorems are restricted to systems with linear growth, globally exponentially stable average models, vanishing stochastic perturbations, and prevent analysis over infinite time horizon. The second half of the text introduces stochastic extremum seeking algorithms for model-free optimization of systems in real time using stochastic perturbations for estimation of their gradients. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton). The design of algorithms...
Directory of Open Access Journals (Sweden)
Xuefei Wu
2014-01-01
Full Text Available The complex projective synchronization in drive-response stochastic coupled networks with complex-variable systems is considered. The impulsive pinning control scheme is adopted to achieve complex projective synchronization and several simple and practical sufficient conditions are obtained in a general drive-response network. In addition, the adaptive feedback algorithms are proposed to adjust the control strength. Several numerical simulations are provided to show the effectiveness and feasibility of the proposed methods.
Macian-Sorribes, Hector; Pulido-Velazquez, Manuel
2016-04-01
This contribution presents a methodology for defining optimal seasonal operating rules in multireservoir systems coupling expert criteria and stochastic optimization. Both sources of information are combined using fuzzy logic. The structure of the operating rules is defined based on expert criteria, via a joint expert-technician framework consisting in a series of meetings, workshops and surveys carried out between reservoir managers and modelers. As a result, the decision-making process used by managers can be assessed and expressed using fuzzy logic: fuzzy rule-based systems are employed to represent the operating rules and fuzzy regression procedures are used for forecasting future inflows. Once done that, a stochastic optimization algorithm can be used to define optimal decisions and transform them into fuzzy rules. Finally, the optimal fuzzy rules and the inflow prediction scheme are combined into a Decision Support System for making seasonal forecasts and simulate the effect of different alternatives in response to the initial system state and the foreseen inflows. The approach presented has been applied to the Jucar River Basin (Spain). Reservoir managers explained how the system is operated, taking into account the reservoirs' states at the beginning of the irrigation season and the inflows previewed during that season. According to the information given by them, the Jucar River Basin operating policies were expressed via two fuzzy rule-based (FRB) systems that estimate the amount of water to be allocated to the users and how the reservoir storages should be balanced to guarantee those deliveries. A stochastic optimization model using Stochastic Dual Dynamic Programming (SDDP) was developed to define optimal decisions, which are transformed into optimal operating rules embedding them into the two FRBs previously created. As a benchmark, historical records are used to develop alternative operating rules. A fuzzy linear regression procedure was employed to
Directory of Open Access Journals (Sweden)
Khurram Hammed
2016-01-01
Full Text Available This paper presents a stochastic global optimization technique known as Particle Swarm Optimization (PSO for joint estimation of amplitude and direction of arrival of the targets in RADAR communication system. The proposed scheme is an excellent optimization methodology and a promising approach for solving the DOA problems in communication systems. Moreover, PSO is quite suitable for real time scenario and easy to implement in hardware. In this study, uniform linear array is used and targets are supposed to be in far field of the arrays. Formulation of the fitness function is based on mean square error and this function requires a single snapshot to obtain the best possible solution. To check the accuracy of the algorithm, all of the results are taken by varying the number of antenna elements and targets. Finally, these results are compared with existing heuristic techniques to show the accuracy of PSO.
Optimization analysis of propulsion motor control efficiency
Directory of Open Access Journals (Sweden)
CAI Qingnan
2017-12-01
Full Text Available [Objectives] This paper aims to strengthen the control effect of propulsion motors and decrease the energy used during actual control procedures.[Methods] Based on the traditional propulsion motor equivalence circuit, we increase the iron loss current component, introduce the definition of power matching ratio, calculate the highest efficiency of a motor at a given speed and discuss the flux corresponding to the power matching ratio with the highest efficiency. In the original motor vector efficiency optimization control module, an efficiency optimization control module is added so as to achieve motor efficiency optimization and energy conservation.[Results] MATLAB/Simulink simulation data shows that the efficiency optimization control method is suitable for most conditions. The operation efficiency of the improved motor model is significantly higher than that of the original motor model, and its dynamic performance is good.[Conclusions] Our motor efficiency optimization control method can be applied in engineering to achieve energy conservation.
Glick, Meir; Rayan, Anwar; Goldblum, Amiram
2002-01-01
The problem of global optimization is pivotal in a variety of scientific fields. Here, we present a robust stochastic search method that is able to find the global minimum for a given cost function, as well as, in most cases, any number of best solutions for very large combinatorial “explosive” systems. The algorithm iteratively eliminates variable values that contribute consistently to the highest end of a cost function's spectrum of values for the full system. Values that have not been eliminated are retained for a full, exhaustive search, allowing the creation of an ordered population of best solutions, which includes the global minimum. We demonstrate the ability of the algorithm to explore the conformational space of side chains in eight proteins, with 54 to 263 residues, to reproduce a population of their low energy conformations. The 1,000 lowest energy solutions are identical in the stochastic (with two different seed numbers) and full, exhaustive searches for six of eight proteins. The others retain the lowest 141 and 213 (of 1,000) conformations, depending on the seed number, and the maximal difference between stochastic and exhaustive is only about 0.15 Kcal/mol. The energy gap between the lowest and highest of the 1,000 low-energy conformers in eight proteins is between 0.55 and 3.64 Kcal/mol. This algorithm offers real opportunities for solving problems of high complexity in structural biology and in other fields of science and technology. PMID:11792838
Time-optimal control with finite bandwidth
Hirose, M.; Cappellaro, P.
2018-04-01
Time-optimal control theory provides recipes to achieve quantum operations with high fidelity and speed, as required in quantum technologies such as quantum sensing and computation. While technical advances have achieved the ultrastrong driving regime in many physical systems, these capabilities have yet to be fully exploited for the precise control of quantum systems, as other limitations, such as the generation of higher harmonics or the finite response time of the control apparatus, prevent the implementation of theoretical time-optimal control. Here we present a method to achieve time-optimal control of qubit systems that can take advantage of fast driving beyond the rotating wave approximation. We exploit results from time-optimal control theory to design driving protocols that can be implemented with realistic, finite-bandwidth control fields, and we find a relationship between bandwidth limitations and achievable control fidelity.
Directory of Open Access Journals (Sweden)
Zhongwen Li
2016-06-01
Full Text Available Microgrids (MGs are presented as a cornerstone of smart grids. With the potential to integrate intermittent renewable energy sources (RES in a flexible and environmental way, the MG concept has gained even more attention. Due to the randomness of RES, load, and electricity price in MG, the forecast errors of MGs will affect the performance of the power scheduling and the operating cost of an MG. In this paper, a combined stochastic programming and receding horizon control (SPRHC strategy is proposed for microgrid energy management under uncertainty, which combines the advantages of two-stage stochastic programming (SP and receding horizon control (RHC strategy. With an SP strategy, a scheduling plan can be derived that minimizes the risk of uncertainty by involving the uncertainty of MG in the optimization model. With an RHC strategy, the uncertainty within the MG can be further compensated through a feedback mechanism with the lately updated forecast information. In our approach, a proper strategy is also proposed to maintain the SP model as a mixed integer linear constrained quadratic programming (MILCQP problem, which is solvable without resorting to any heuristics algorithms. The results of numerical experiments explicitly demonstrate the superiority of the proposed strategy for both island and grid-connected operating modes of an MG.
Optimization of boundary controls of string vibrations
Energy Technology Data Exchange (ETDEWEB)
Il' in, V A; Moiseev, E I [Department of Computing Mathematics and Cybernetics, M.V. Lomonosov Moscow State University, Moscow (Russian Federation)
2005-12-31
For a large time interval T boundary controls of string vibrations are optimized in the following seven boundary-control problems: displacement control at one end (with the other end fixed or free); displacement control at both ends; elastic force control at one end (with the other end fixed or free); elastic force control at both ends; combined control (displacement control at one end and elastic force control at the other). Optimal boundary controls in each of these seven problems are sought as functions minimizing the corresponding boundary-energy integral under the constraints following from the initial and terminal conditions for the string at t=0 and t=T, respectively. For all seven problems, the optimal boundary controls are written out in closed analytic form.
Optimal control of a wave energy converter
Hendrikx, R.W.M.; Leth, J.; Andersen, P; Heemels, W.P.M.H.
2017-01-01
The optimal control strategy for a wave energy converter (WEC) with constraints on the control torque is investigated. The goal is to optimize the total energy delivered to the electricity grid. Using Pontryagin's maximum principle, the solution is found to be singular-bang. Using higher order
Bifurcation Regulations Governed by Delay Self-Control Feedback in a Stochastic Birhythmic System
Ma, Zhidan; Ning, Lijuan
2017-12-01
We aim to investigate bifurcation behaviors in a stochastic birhythmic van der Pol (BVDP) system subjected to delay self-control feedback. First, the harmonic approximation is adopted to drive the delay self-control feedback to state variables without delay. Then, Fokker-Planck-Kolmogorov (FPK) equation and stationary probability density function (SPDF) for amplitude are obtained by applying stochastic averaging method. Finally, dynamical scenarios of the change of delay self-control feedback as well as noise that markedly influence bifurcation performance are observed. It is found that: the big feedback strength and delay will suppress the large amplitude limit cycle (LC) while the relatively big noise strength facilitates the large amplitude LC, which imply the proposed regulation strategies are feasible. Interestingly enough, the inner LC is never destroyed due to noise. Furthermore, the validity of analytical results was verified by Monte Carlo simulation of the dynamics.
Sliding mode control-based linear functional observers for discrete-time stochastic systems
Singh, Satnesh; Janardhanan, Sivaramakrishnan
2017-11-01
Sliding mode control (SMC) is one of the most popular techniques to stabilise linear discrete-time stochastic systems. However, application of SMC becomes difficult when the system states are not available for feedback. This paper presents a new approach to design a SMC-based functional observer for discrete-time stochastic systems. The functional observer is based on the Kronecker product approach. Existence conditions and stability analysis of the proposed observer are given. The control input is estimated by a novel linear functional observer. This approach leads to a non-switching type of control, thereby eliminating the fundamental cause of chatter. Furthermore, the functional observer is designed in such a way that the effect of process and measurement noise is minimised. Simulation example is given to illustrate and validate the proposed design method.
This study evaluated the impact of gas concentration and wind sensor locations on the accuracy of the backward Lagrangian stochastic inverse-dispersion technique (bLS) for measuring gas emission rates from a typical lagoon environment. Path-integrated concentrations (PICs) and 3-dimensional (3D) wi...
Neutral Backward Stochastic Functional Differential Equations and Their Application
Wei, Wenning
2013-01-01
In this paper we are concerned with a new type of backward equations with anticipation which we call neutral backward stochastic functional differential equations. We obtain the existence and uniqueness and prove a comparison theorem. As an application, we discuss the optimal control of neutral stochastic functional differential equations, establish a Pontryagin maximum principle, and give an explicit optimal value for the linear optimal control.
Neural Networks for Optimal Control
DEFF Research Database (Denmark)
Sørensen, O.
1995-01-01
Two neural networks are trained to act as an observer and a controller, respectively, to control a non-linear, multi-variable process.......Two neural networks are trained to act as an observer and a controller, respectively, to control a non-linear, multi-variable process....
Optimal switching using coherent control
DEFF Research Database (Denmark)
Kristensen, Philip Trøst; Heuck, Mikkel; Mørk, Jesper
2013-01-01
that the switching time, in general, is not limited by the cavity lifetime. Therefore, the total energy required for switching is a more relevant figure of merit than the switching speed, and for a particular two-pulse switching scheme we use calculus of variations to optimize the switching in terms of input energy....
Population control methods in stochastic extinction and outbreak scenarios.
Directory of Open Access Journals (Sweden)
Juan Segura
Full Text Available Adaptive limiter control (ALC and adaptive threshold harvesting (ATH are two related control methods that have been shown to stabilize fluctuating populations. Large variations in population abundance can threaten the constancy and the persistence stability of ecological populations, which may impede the success and efficiency of managing natural resources. Here, we consider population models that include biological mechanisms characteristic for causing extinctions on the one hand and pest outbreaks on the other hand. These models include Allee effects and the impact of natural enemies (as is typical of forest defoliating insects. We study the impacts of noise and different levels of biological parameters in three extinction and two outbreak scenarios. Our results show that ALC and ATH have an effect on extinction and outbreak risks only for sufficiently large control intensities. Moreover, there is a clear disparity between the two control methods: in the extinction scenarios, ALC can be effective and ATH can be counterproductive, whereas in the outbreak scenarios the situation is reversed, with ATH being effective and ALC being potentially counterproductive.
Population control methods in stochastic extinction and outbreak scenarios.
Segura, Juan; Hilker, Frank M; Franco, Daniel
2017-01-01
Adaptive limiter control (ALC) and adaptive threshold harvesting (ATH) are two related control methods that have been shown to stabilize fluctuating populations. Large variations in population abundance can threaten the constancy and the persistence stability of ecological populations, which may impede the success and efficiency of managing natural resources. Here, we consider population models that include biological mechanisms characteristic for causing extinctions on the one hand and pest outbreaks on the other hand. These models include Allee effects and the impact of natural enemies (as is typical of forest defoliating insects). We study the impacts of noise and different levels of biological parameters in three extinction and two outbreak scenarios. Our results show that ALC and ATH have an effect on extinction and outbreak risks only for sufficiently large control intensities. Moreover, there is a clear disparity between the two control methods: in the extinction scenarios, ALC can be effective and ATH can be counterproductive, whereas in the outbreak scenarios the situation is reversed, with ATH being effective and ALC being potentially counterproductive.
N-Player Stochastic Differential Games. [control theory
Varaiya, P.
1974-01-01
Conditions are described which guarantee that the control strategies adopted by N players constitute an efficient solution, an equilibrium, or a core solution. The system dynamics are described by an Ito equation, and all players have perfect information. It was found that when the set of instantaneous joint costs and velocity vectors is convex, the conditions are necessary.
Zhao, Yu; Yuan, Sanling
2017-07-01
As well known that the sudden environmental shocks and toxicant can affect the population dynamics of fish species, a mechanistic understanding of how sudden environmental change and toxicant influence the optimal harvesting policy requires development. This paper presents the optimal harvesting of a stochastic two-species competitive model with Lévy noise in a polluted environment, where the Lévy noise is used to describe the sudden climate change. Due to the discontinuity of the Lévy noise, the classical optimal harvesting methods based on the explicit solution of the corresponding Fokker-Planck equation are invalid. The object of this paper is to fill up this gap and establish the optimal harvesting policy. By using of aggregation and ergodic methods, the approximation of the optimal harvesting effort and maximum expectation of sustainable yields are obtained. Numerical simulations are carried out to support these theoretical results. Our analysis shows that the Lévy noise and the mean stress measure of toxicant in organism may affect the optimal harvesting policy significantly.
Wang, Jianhui; Liu, Zhi; Chen, C L Philip; Zhang, Yun
2017-10-12
Hysteresis exists ubiquitously in physical actuators. Besides, actuator failures/faults may also occur in practice. Both effects would deteriorate the transient tracking performance, and even trigger instability. In this paper, we consider the problem of compensating for actuator failures and input hysteresis by proposing a fuzzy control scheme for stochastic nonlinear systems. Compared with the existing research on stochastic nonlinear uncertain systems, it is found that how to guarantee a prescribed transient tracking performance when taking into account actuator failures and hysteresis simultaneously also remains to be answered. Our proposed control scheme is designed on the basis of the fuzzy logic system and backstepping techniques for this purpose. It is proven that all the signals remain bounded and the tracking error is ensured to be within a preestablished bound with the failures of hysteretic actuator. Finally, simulations are provided to illustrate the effectiveness of the obtained theoretical results.
Existence theory in optimal control
International Nuclear Information System (INIS)
Olech, C.
1976-01-01
This paper treats the existence problem in two main cases. One case is that of linear systems when existence is based on closedness or compactness of the reachable set and the other, non-linear case refers to a situation where for the existence of optimal solutions closedness of the set of admissible solutions is needed. Some results from convex analysis are included in the paper. (author)
A stochastic six-degree-of-freedom flight simulator for passively controlled high power rockets
Box, Simon; Bishop, Christopher M.; Hunt, Hugh
2011-01-01
This paper presents a method for simulating the flight of a passively controlled rocket in six degrees of freedom, and the descent under parachute in three degrees of freedom, Also presented is a method for modelling the uncertainty in both the rocket dynamics and the atmospheric conditions using stochastic parameters and the Monte-Carlo method. Included within this we present a method for quantifying the uncertainty in the atmospheric conditions using historical atmospheric data. The core si...
Deterministic and stochastic control of chimera states in delayed feedback oscillator
Energy Technology Data Exchange (ETDEWEB)
Semenov, V. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Zakharova, A.; Schöll, E. [Institut für Theoretische Physik, TU Berlin, Hardenbergstraße 36, 10623 Berlin (Germany); Maistrenko, Y. [Institute of Mathematics and Center for Medical and Biotechnical Research, NAS of Ukraine, Tereschenkivska Str. 3, 01601 Kyiv (Ukraine)
2016-06-08
Chimera states, characterized by the coexistence of regular and chaotic dynamics, are found in a nonlinear oscillator model with negative time-delayed feedback. The control of these chimera states by external periodic forcing is demonstrated by numerical simulations. Both deterministic and stochastic external periodic forcing are considered. It is shown that multi-cluster chimeras can be achieved by adjusting the external forcing frequency to appropriate resonance conditions. The constructive role of noise in the formation of a chimera states is shown.
Directory of Open Access Journals (Sweden)
Wenlei Bai
2017-12-01
Full Text Available The deterministic methods generally used to solve DC optimal power flow (OPF do not fully capture the uncertainty information in wind power, and thus their solutions could be suboptimal. However, the stochastic dynamic AC OPF problem can be used to find an optimal solution by fully capturing the uncertainty information of wind power. That uncertainty information of future wind power can be well represented by the short-term future wind power scenarios that are forecasted using the generalized dynamic factor model (GDFM—a novel multivariate statistical wind power forecasting model. Furthermore, the GDFM can accurately represent the spatial and temporal correlations among wind farms through the multivariate stochastic process. Fully capturing the uncertainty information in the spatially and temporally correlated GDFM scenarios can lead to a better AC OPF solution under a high penetration level of wind power. Since the GDFM is a factor analysis based model, the computational time can also be reduced. In order to further reduce the computational time, a modified artificial bee colony (ABC algorithm is used to solve the AC OPF problem based on the GDFM forecasting scenarios. Using the modified ABC algorithm based on the GDFM forecasting scenarios has resulted in better AC OPF’ solutions on an IEEE 118-bus system at every hour for 24 h.
Optimal Control Development System for Electrical Drives
Directory of Open Access Journals (Sweden)
Marian GAICEANU
2008-08-01
Full Text Available In this paper the optimal electrical drive development system is presented. It consists of both electrical drive types: DC and AC. In order to implement the optimal control for AC drive system an Altivar 71 inverter, a Frato magnetic particle brake (as load, three-phase induction machine, and dSpace 1104 controller have been used. The on-line solution of the matrix Riccati differential equation (MRDE is computed by dSpace 1104 controller, based on the corresponding feedback signals, generating the optimal speed reference for the AC drive system. The optimal speed reference is tracked by Altivar 71 inverter, conducting to energy reduction in AC drive. The classical control (consisting of rotor field oriented control with PI controllers and the optimal one have been implemented by designing an adequate ControlDesk interface. The three-phase induction machine (IM is controlled at constant flux. Therefore, the linear dynamic mathematical model of the IM has been obtained. The optimal control law provides transient regimes with minimal energy consumption. The obtained solution by integration of the MRDE is orientated towards the numerical implementation-by using a zero order hold. The development system is very useful for researchers, doctoral students or experts training in electrical drive. The experimental results are shown.
Dynamic optimization and adaptive controller design
Inamdar, S. R.
2010-10-01
In this work I present a new type of controller which is an adaptive tracking controller which employs dynamic optimization for optimizing current value of controller action for the temperature control of nonisothermal continuously stirred tank reactor (CSTR). We begin with a two-state model of nonisothermal CSTR which are mass and heat balance equations and then add cooling system dynamics to eliminate input multiplicity. The initial design value is obtained using local stability of steady states where approach temperature for cooling action is specified as a steady state and a design specification. Later we make a correction in the dynamics where material balance is manipulated to use feed concentration as a system parameter as an adaptive control measure in order to avoid actuator saturation for the main control loop. The analysis leading to design of dynamic optimization based parameter adaptive controller is presented. The important component of this mathematical framework is reference trajectory generation to form an adaptive control measure.
Raso , L.; Malaterre , P.O.; Bader , J.C.
2017-01-01
International audience; This article presents an innovative streamflow process model for use in reservoir operational rule design in stochastic dual dynamic programming (SDDP). Model features, which can be applied independently, are (1) a multiplicative process model for the forward phase and its linearized version for the backward phase; and (2) a nonuniform time-step length that is inversely proportional to seasonal variability. The advantages are (1) guaranteeing positive streamflow values...
Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons
Guillermo Gallego; Garrett van Ryzin
1994-01-01
In many industries, managers face the problem of selling a given stock of items by a deadline. We investigate the problem of dynamically pricing such inventories when demand is price sensitive and stochastic and the firm's objective is to maximize expected revenues. Examples that fit this framework include retailers selling fashion and seasonal goods and the travel and leisure industry, which markets space such as seats on airline flights, cabins on vacation cruises, and rooms in hotels that ...
International Nuclear Information System (INIS)
Rougé, Charles; Mathias, Jean-Denis; Deffuant, Guillaume
2014-01-01
The goal of this paper is twofold: (1) to show that time-variant reliability and a branch of control theory called stochastic viability address similar problems with different points of view, and (2) to demonstrate the relevance of concepts and methods from stochastic viability in reliability problems. On the one hand, reliability aims at evaluating the probability of failure of a system subjected to uncertainty and stochasticity. On the other hand, viability aims at maintaining a controlled dynamical system within a survival set. When the dynamical system is stochastic, this work shows that a viability problem belongs to a specific class of design and maintenance problems in time-variant reliability. Dynamic programming, which is used for solving Markovian stochastic viability problems, then yields the set of design states for which there exists a maintenance strategy which guarantees reliability with a confidence level β for a given period of time T. Besides, it leads to a straightforward computation of the date of the first outcrossing, informing on when the system is most likely to fail. We illustrate this approach with a simple example of population dynamics, including a case where load increases with time. - Highlights: • Time-variant reliability tools cannot devise complex maintenance strategies. • Stochastic viability is a control theory that computes a probability of failure. • Some design and maintenance problems are stochastic viability problems. • Used in viability, dynamic programming can find reliable maintenance actions. • Confronting reliability and control theories such as viability is promising
Directory of Open Access Journals (Sweden)
Renaldas Vilkancas
2016-05-01
Full Text Available Purpose of the article: While using asymmetric risk-return measures an important role is played by selection of the investor‘s required or threshold rate of return. The scientific literature usually states that every investor should define this rate according to their degree of risk aversion. In this paper, it is attempted to look at the problem from a different perspective – empirical research is aimed at determining the influence of the threshold rate of return on the portfolio characteristics. Methodology/methods: In order to determine the threshold rate of return a stochastic dominance criterion was used. The results are verified using the commonly applied method of backtesting. Scientific aim: The aim of this paper is to propose a method allowing selecting the threshold rate of return reliably and objectively. Findings: Empirical research confirms that stochastic dominance criteria can be successfully applied to determine the rate of return preferred by the investor. Conclusions: A risk-free investment rate or simply a zero rate of return commonly used in practice is often justified neither by theoretical nor empirical studies. This work suggests determining the threshold rate of return by applying the stochastic dominance criterion
On the optimal polynomial approximation of stochastic PDEs by galerkin and collocation methods
Beck, Joakim; Tempone, Raul; Nobile, Fabio; Tamellini, Lorenzo
2012-01-01
In this work we focus on the numerical approximation of the solution u of a linear elliptic PDE with stochastic coefficients. The problem is rewritten as a parametric PDE and the functional dependence of the solution on the parameters is approximated by multivariate polynomials. We first consider the stochastic Galerkin method, and rely on sharp estimates for the decay of the Fourier coefficients of the spectral expansion of u on an orthogonal polynomial basis to build a sequence of polynomial subspaces that features better convergence properties, in terms of error versus number of degrees of freedom, than standard choices such as Total Degree or Tensor Product subspaces. We consider then the Stochastic Collocation method, and use the previous estimates to introduce a new class of Sparse Grids, based on the idea of selecting a priori the most profitable hierarchical surpluses, that, again, features better convergence properties compared to standard Smolyak or tensor product grids. Numerical results show the effectiveness of the newly introduced polynomial spaces and sparse grids. © 2012 World Scientific Publishing Company.
On the optimal polynomial approximation of stochastic PDEs by galerkin and collocation methods
Beck, Joakim
2012-09-01
In this work we focus on the numerical approximation of the solution u of a linear elliptic PDE with stochastic coefficients. The problem is rewritten as a parametric PDE and the functional dependence of the solution on the parameters is approximated by multivariate polynomials. We first consider the stochastic Galerkin method, and rely on sharp estimates for the decay of the Fourier coefficients of the spectral expansion of u on an orthogonal polynomial basis to build a sequence of polynomial subspaces that features better convergence properties, in terms of error versus number of degrees of freedom, than standard choices such as Total Degree or Tensor Product subspaces. We consider then the Stochastic Collocation method, and use the previous estimates to introduce a new class of Sparse Grids, based on the idea of selecting a priori the most profitable hierarchical surpluses, that, again, features better convergence properties compared to standard Smolyak or tensor product grids. Numerical results show the effectiveness of the newly introduced polynomial spaces and sparse grids. © 2012 World Scientific Publishing Company.
Optimal Control of Evolution Mixed Variational Inclusions
Energy Technology Data Exchange (ETDEWEB)
Alduncin, Gonzalo, E-mail: alduncin@geofisica.unam.mx [Universidad Nacional Autónoma de México, Departamento de Recursos Naturales, Instituto de Geofísica (Mexico)
2013-12-15
Optimal control problems of primal and dual evolution mixed variational inclusions, in reflexive Banach spaces, are studied. The solvability analysis of the mixed state systems is established via duality principles. The optimality analysis is performed in terms of perturbation conjugate duality methods, and proximation penalty-duality algorithms to mixed optimality conditions are further presented. Applications to nonlinear diffusion constrained problems as well as quasistatic elastoviscoplastic bilateral contact problems exemplify the theory.
Optimal Control of Evolution Mixed Variational Inclusions
International Nuclear Information System (INIS)
Alduncin, Gonzalo
2013-01-01
Optimal control problems of primal and dual evolution mixed variational inclusions, in reflexive Banach spaces, are studied. The solvability analysis of the mixed state systems is established via duality principles. The optimality analysis is performed in terms of perturbation conjugate duality methods, and proximation penalty-duality algorithms to mixed optimality conditions are further presented. Applications to nonlinear diffusion constrained problems as well as quasistatic elastoviscoplastic bilateral contact problems exemplify the theory
Role of controllability in optimizing quantum dynamics
International Nuclear Information System (INIS)
Wu Rebing; Hsieh, Michael A.; Rabitz, Herschel
2011-01-01
This paper reveals an important role that controllability plays in the complexity of optimizing quantum control dynamics. We show that the loss of controllability generally leads to multiple locally suboptimal controls when gate fidelity in a quantum control system is maximized, which does not happen if the system is controllable. Such local suboptimal controls may attract an optimization algorithm into a local trap when a global optimal solution is sought, even if the target gate can be perfectly realized. This conclusion results from an analysis of the critical topology of the corresponding quantum control landscape, which refers to the gate fidelity objective as a functional of the control fields. For uncontrollable systems, due to SU(2) and SU(3) dynamical symmetries, the control landscape corresponding to an implementable target gate is proven to possess multiple locally optimal critical points, and its ruggedness can be further increased if the target gate is not realizable. These results imply that the optimization of quantum dynamics can be seriously impeded when operating with local search algorithms under these conditions, and thus full controllability is demanded.
International Nuclear Information System (INIS)
Bornapour, Mosayeb; Hooshmand, Rahmat-Allah; Khodabakhshian, Amin; Parastegari, Moein
2017-01-01
Highlights: • Stochastic model is proposed for coordinated scheduling of renewable energy sources. • The effect of combined heat and power is considered. • Uncertainties of wind speed, solar radiation and electricity market price are considered. • Profit maximization, emission and AENS minimization are considered as objective functions. • Modified firefly algorithm is employed to solve the problem. - Abstract: Nowadays the operation of renewable energy sources and combined heat and power (CHP) units is increased in micro grids; therefore, to reach optimal performance, optimal scheduling of these units is required. In this regard, in this paper a micro grid consisting of proton exchange membrane fuel cell-combined heat and power (PEMFC-CHP), wind turbines (WT) and photovoltaic (PV) units, is modeled to determine the optimal scheduling state of these units by considering uncertain behavior of renewable energy resources. For this purpose, a scenario-based method is used for modeling the uncertainties of electrical market price, the wind speed, and solar irradiance. It should be noted that the hydrogen storage strategy is also applied in this study for PEMFC-CHP units. Market profit, total emission production, and average energy not supplied (AENS) are the objective functions considered in this paper simultaneously. Consideration of the above-mentioned objective functions converts the proposed problem to a mixed integer nonlinear programming. To solve this problem, a multi-objective firefly algorithm is used. The uncertainties of parameters convert the mixed integer nonlinear programming problem to a stochastic mixed integer nonlinear programming problem. Moreover, optimal coordinated scheduling of renewable energy resources and thermal units in micro-grids improve the value of the objective functions. Simulation results obtained from a modified 33-bus distributed network as a micro grid illustrates the effectiveness of the proposed method.
Optimal Speed Control for Cruising
DEFF Research Database (Denmark)
Blanke, M.
1994-01-01
With small profit margins in merchant shipping and more than eighty percent of sailing time being cross ocean voyages, speed control is crucial for vessel profitability......With small profit margins in merchant shipping and more than eighty percent of sailing time being cross ocean voyages, speed control is crucial for vessel profitability...
Energy Technology Data Exchange (ETDEWEB)
Liu, Yunlong; Wang, Aiping; Guo, Lei; Wang, Hong
2017-07-09
This paper presents an error-entropy minimization tracking control algorithm for a class of dynamic stochastic system. The system is represented by a set of time-varying discrete nonlinear equations with non-Gaussian stochastic input, where the statistical properties of stochastic input are unknown. By using Parzen windowing with Gaussian kernel to estimate the probability densities of errors, recursive algorithms are then proposed to design the controller such that the tracking error can be minimized. The performance of the error-entropy minimization criterion is compared with the mean-square-error minimization in the simulation results.
International Nuclear Information System (INIS)
Nagl, Stephan; Fuersch, Michaela; Lindenberger, Dietmar
2012-01-01
Renewable energies are meant to produce a large share of the future electricity demand. However, the availability of wind and solar power depends on local weather conditions and therefore weather characteristics must be considered when optimizing the future electricity mix. In this article we analyze the impact of the stochastic availability of wind and solar energy on the cost-minimal power plant mix and the related total system costs. To determine optimal conventional, renewable and storage capacities for different shares of renewables, we apply a stochastic investment and dispatch optimization model to the European electricity market. The model considers stochastic feed-in structures and full load hours of wind and solar technologies and different correlations between regions and technologies. Key findings include the overestimation of fluctuating renewables and underestimation of total system costs compared to deterministic investment and dispatch models. Furthermore, solar technologies are - relative to wind turbines - underestimated when neglecting negative correlations between wind speeds and solar radiation.
Directory of Open Access Journals (Sweden)
Rui Zhang
2013-01-01
Full Text Available We consider a parallel machine scheduling problem with random processing/setup times and adjustable production rates. The objective functions to be minimized consist of two parts; the first part is related with the due date performance (i.e., the tardiness of the jobs, while the second part is related with the setting of machine speeds. Therefore, the decision variables include both the production schedule (sequences of jobs and the production rate of each machine. The optimization process, however, is significantly complicated by the stochastic factors in the manufacturing system. To address the difficulty, a simulation-based three-stage optimization framework is presented in this paper for high-quality robust solutions to the integrated scheduling problem. The first stage (crude optimization is featured by the ordinal optimization theory, the second stage (finer optimization is implemented with a metaheuristic called differential evolution, and the third stage (fine-tuning is characterized by a perturbation-based local search. Finally, computational experiments are conducted to verify the effectiveness of the proposed approach. Sensitivity analysis and practical implications are also discussed.
Parameters control in GAs for dynamic optimization
Directory of Open Access Journals (Sweden)
Khalid Jebari
2013-02-01
Full Text Available The Control of Genetic Algorithms parameters allows to optimize the search process and improves the performance of the algorithm. Moreover it releases the user to dive into a game process of trial and failure to find the optimal parameters.
Optimal Control Design for a Solar Greenhouse
Ooteghem, van R.J.C.
2010-01-01
Abstract: An optimal climate control has been designed for a solar greenhouse to achieve optimal crop production with sustainable instead of fossil energy. The solar greenhouse extends a conventional greenhouse with an improved roof cover, ventilation with heat recovery, a heat pump, a heat
Optimization and control of metal forming processes
Havinga, Gosse Tjipke
2016-01-01
Inevitable variations in process and material properties limit the accuracy of metal forming processes. Robust optimization methods or control systems can be used to improve the production accuracy. Robust optimization methods are used to design production processes with low sensitivity to the
Optimal control and the calculus of variations
Pinch, Enid R
1993-01-01
This introduction to optimal control theory is intended for undergraduate mathematicians and for engineers and scientists with some knowledge of classical analysis. It includes sections on classical optimization and the calculus of variations. All the important theorems are carefully proved. There are many worked examples and exercises for the reader to attempt.
Direct Optimal Control of Duffing Dynamics
Oz, Hayrani; Ramsey, John K.
2002-01-01
The "direct control method" is a novel concept that is an attractive alternative and competitor to the differential-equation-based methods. The direct method is equally well applicable to nonlinear, linear, time-varying, and time-invariant systems. For all such systems, the method yields explicit closed-form control laws based on minimization of a quadratic control performance measure. We present an application of the direct method to the dynamics and optimal control of the Duffing system where the control performance measure is not restricted to a quadratic form and hence may include a quartic energy term. The results we present in this report also constitute further generalizations of our earlier work in "direct optimal control methodology." The approach is demonstrated for the optimal control of the Duffing equation with a softening nonlinear stiffness.
A Feedback Optimal Control Algorithm with Optimal Measurement Time Points
Directory of Open Access Journals (Sweden)
Felix Jost
2017-02-01
Full Text Available Nonlinear model predictive control has been established as a powerful methodology to provide feedback for dynamic processes over the last decades. In practice it is usually combined with parameter and state estimation techniques, which allows to cope with uncertainty on many levels. To reduce the uncertainty it has also been suggested to include optimal experimental design into the sequential process of estimation and control calculation. Most of the focus so far was on dual control approaches, i.e., on using the controls to simultaneously excite the system dynamics (learning as well as minimizing a given objective (performing. We propose a new algorithm, which sequentially solves robust optimal control, optimal experimental design, state and parameter estimation problems. Thus, we decouple the control and the experimental design problems. This has the advantages that we can analyze the impact of measurement timing (sampling independently, and is practically relevant for applications with either an ethical limitation on system excitation (e.g., chemotherapy treatment or the need for fast feedback. The algorithm shows promising results with a 36% reduction of parameter uncertainties for the Lotka-Volterra fishing benchmark example.