A multi-objective dynamic programming approach to constrained discrete-time optimal control
Energy Technology Data Exchange (ETDEWEB)
Driessen, B.J.; Kwok, K.S.
1997-09-01
This work presents a multi-objective differential dynamic programming approach to constrained discrete-time optimal control. In the backward sweep of the dynamic programming in the quadratic sub problem, the sub problem input at a stage or time step is solved for in terms of the sub problem state entering that stage so as to minimize the summed immediate and future cost subject to minimizing the summed immediate and future constraint violations, for all such entering states. The method differs from previous dynamic programming methods, which used penalty methods, in that the constraints of the sub problem, which may include terminal constraints and path constraints, are solved exactly if they are solvable; otherwise, their total violation is minimized. Again, the resulting solution of the sub problem is an input history that minimizes the quadratic cost function subject to being a minimizer of the total constraint violation. The expected quadratic convergence of the proposed algorithm is demonstrated on a numerical example.
Discrete-time optimal control and games on large intervals
Zaslavski, Alexander J
2017-01-01
Devoted to the structure of approximate solutions of discrete-time optimal control problems and approximate solutions of dynamic discrete-time two-player zero-sum games, this book presents results on properties of approximate solutions in an interval that is independent lengthwise, for all sufficiently large intervals. Results concerning the so-called turnpike property of optimal control problems and zero-sum games in the regions close to the endpoints of the time intervals are the main focus of this book. The description of the structure of approximate solutions on sufficiently large intervals and its stability will interest graduate students and mathematicians in optimal control and game theory, engineering, and economics. This book begins with a brief overview and moves on to analyze the structure of approximate solutions of autonomous nonconcave discrete-time optimal control Lagrange problems.Next the structures of approximate solutions of autonomous discrete-time optimal control problems that are discret...
Discrete-time inverse optimal control for nonlinear systems
Sanchez, Edgar N
2013-01-01
Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). Th
Engineering applications of discrete-time optimal control
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui; Ravn, Hans V.
1990-01-01
of some well-known and new results in discrete time optimal control methods applicable to practical problem solving within engineering. Emphasis is placed on dynamic programming, the classical maximum principle and generalized versions of the maximum principle for optimal control of discrete time systems......Many problems of design and operation of engineering systems can be formulated as optimal control problems where time has been discretisized. This is also true even if 'time' is not involved in the formulation of the problem, but rather another one-dimensional parameter. This paper gives a review...
Engineering applications of discrete-time optimal control
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui; Ravn, Hans V.
1990-01-01
Many problems of design and operation of engineering systems can be formulated as optimal control problems where time has been discretisized. This is also true even if 'time' is not involved in the formulation of the problem, but rather another one-dimensional parameter. This paper gives a review...... of some well-known and new results in discrete time optimal control methods applicable to practical problem solving within engineering. Emphasis is placed on dynamic programming, the classical maximum principle and generalized versions of the maximum principle for optimal control of discrete time systems...
Optimal Robust Fault Detection for Linear Discrete Time Systems
Directory of Open Access Journals (Sweden)
Nike Liu
2008-01-01
Full Text Available This paper considers robust fault-detection problems for linear discrete time systems. It is shown that the optimal robust detection filters for several well-recognized robust fault-detection problems, such as ℋ−/ℋ∞, ℋ2/ℋ∞, and ℋ∞/ℋ∞ problems, are the same and can be obtained by solving a standard algebraic Riccati equation. Optimal filters are also derived for many other optimization criteria and it is shown that some well-studied and seeming-sensible optimization criteria for fault-detection filter design could lead to (optimal but useless fault-detection filters.
A discrete-time Lagrangian network for solving constrained quadratic programs.
Tang, W S; Wang, J
2000-08-01
A discrete-time recurrent neural network which is called the discrete-time Lagrangian network is proposed in this letter for solving convex quadratic programs. It is developed based on the classical Lagrange optimization method and solves quadratic programs without using any penalty parameter. The condition for the neural network to globally converge to the optimal solution of the quadratic program is given. Simulation results are presented to illustrate its performance.
Nguyen, Hoai-Nam
2014-01-01
A comprehensive development of interpolating control, this monograph demonstrates the reduced computational complexity of a ground-breaking technique compared with the established model predictive control. The text deals with the regulation problem for linear, time-invariant, discrete-time uncertain dynamical systems having polyhedral state and control constraints, with and without disturbances, and under state or output feedback. For output feedback a non-minimal state-space representation is used with old inputs and outputs as state variables. Constrained Control of Uncertain, Time-Varying, Discrete-time Systems details interpolating control in both its implicit and explicit forms. In the former at most two linear-programming or one quadratic-programming problem are solved on-line at each sampling instant to yield the value of the control variable. In the latter the control law is shown to be piecewise affine in the state, and so the state space is partitioned into polyhedral cells so that at each sampling ...
Discrete Time Optimal Adaptive Control for Linear Stochastic Systems
Institute of Scientific and Technical Information of China (English)
JIANG Rui; LUO Guiming
2007-01-01
The least-squares(LS)algorithm has been used for system modeling for a long time. Without any excitation conditions, only the convergence rate of the common LS algorithm can be obtained. This paper analyzed the weighted least-squares(WLS)algorithm and described the good properties of the WLS algorithm. The WLS algorithm was then used for daptive control of linear stochastic systems to show that the linear closed-loop system was globally stable and that the system identification was consistent. Compared to the past optimal adaptive controller,this controller does not impose restricted conditions on the coefficients of the system, such as knowing the first coefficient before the controller. Without any persistent excitation conditions, the analysis shows that, with the regulation of the adaptive control, the closed-loop system was globally stable and the adaptive controller converged to the one-step-ahead optimal controller in some sense.
U-D factorisation of the strengthened discrete-time optimal projection equations
Van Willigenburg, L. Gerard; De Koning, Willem L.
2016-04-01
Algorithms for optimal reduced-order dynamic output feedback control of linear discrete-time systems with white stochastic parameters are U-D factored in this paper. U-D factorisation enhances computational accuracy, stability and possibly efficiency. Since U-D factorisation of algorithms for optimal full-order output feedback controller design was recently published by us, this paper focusses on the U-D factorisation of the optimal oblique projection matrix that becomes part of the solution as a result of order-reduction. The equations producing the solution are known as the optimal projection equations which for discrete-time systems have been strengthened in the past. The U-D factored strengthened discrete-time optimal projection equations are presented in this paper by means of a transformation that has to be applied recursively until convergence. The U-D factored and conventional algorithms are compared through a series of examples.
Tenreiro Machado, J. A.; Galhano, Alexandra M.; Oliveira, Anabela M.; Tar, József K.
2010-03-01
This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.
Sampled-data and discrete-time H2 optimal control
Trentelman, Harry L.; Stoorvogel, Anton A.
1993-01-01
This paper deals with the sampled-data H2 optimal control problem. Given a linear time-invariant continuous-time system, the problem of minimizing the H2 performance over all sampled-data controllers with a fixed sampling period can be reduced to a pure discrete-time H2 optimal control problem. This
Sampled-Data and Discrete-Time H2 Optimal Control
Trentelman, H.L.; Stoorvogel, A.A.
1995-01-01
This paper deals with the sampled-data H2 optimal control problem. Given a linear time-invariant continuous-time system, the problem of minimizing the H2 performance over all sampled-data controllers with a fixed sampling period can be reduced to a pure discrete-time H2 optimal control problem. This
Ruiz-Cruz, Riemann; Sanchez, Edgar N; Ornelas-Tellez, Fernando; Loukianov, Alexander G; Harley, Ronald G
2013-12-01
In this paper, the authors propose a particle swarm optimization (PSO) for a discrete-time inverse optimal control scheme of a doubly fed induction generator (DFIG). For the inverse optimal scheme, a control Lyapunov function (CLF) is proposed to obtain an inverse optimal control law in order to achieve trajectory tracking. A posteriori, it is established that this control law minimizes a meaningful cost function. The CLFs depend on matrix selection in order to achieve the control objectives; this matrix is determined by two mechanisms: initially, fixed parameters are proposed for this matrix by a trial-and-error method and then by using the PSO algorithm. The inverse optimal control scheme is illustrated via simulations for the DFIG, including the comparison between both mechanisms.
Lee, C.-H.; Herget, C. J.
1976-01-01
This short paper considers the parameter-identification problem of general discrete-time, nonlinear, multiple input-multiple output dynamic systems with Gaussian white distributed measurement errors. Knowledge of the system parameterization is assumed to be available. Regions of constrained maximum likelihood (CML) parameter identifiability are established. A computation procedure employing interval arithmetic is proposed for finding explicit regions of parameter identifiability for the case of linear systems.
Carpentier, Pierre; Cohen, Guy; De Lara, Michel
2015-01-01
The focus of the present volume is stochastic optimization of dynamical systems in discrete time where - by concentrating on the role of information regarding optimization problems - it discusses the related discretization issues. There is a growing need to tackle uncertainty in applications of optimization. For example the massive introduction of renewable energies in power systems challenges traditional ways to manage them. This book lays out basic and advanced tools to handle and numerically solve such problems and thereby is building a bridge between Stochastic Programming and Stochastic Control. It is intended for graduates readers and scholars in optimization or stochastic control, as well as engineers with a background in applied mathematics.
On invariant ellipsoids for discrete-time systems by saturated optimal controls
Institute of Scientific and Technical Information of China (English)
Bin ZHOU; Guangren DUAN
2008-01-01
Analytical approximation of the maximal invariant ellipsoid for discrete-time linear systems with saturated optimal control is established, which is less conservative than existing computationally un-intensive results. Simultaneously, necessary and sufficient conditions for such approximation being equal to the real maximal invariant ellipsoid is presented.All results are given analytically and can easily be implemented in practice.An illustrative example is given to show the effectiveness of the proposed approach.
Minimal and non-minimal optimal fixed-order compensators for time-varying discrete-time systems
Willigenburg, van L.G.; Koning, de W.L.
2002-01-01
The finite horizon optimal fixed-order LQG compensation problem for time-varying discrete-time systems is considered. Using the minimality property of finite horizon time-varying compensators, established in this paper, strengthened discrete-time optimal projection equations and associated boundary
On Optimal Fault Detection for Discrete-time Markovian Jump Linear Systems
Institute of Scientific and Technical Information of China (English)
LI Yue-Yang; ZHONG Mai-Ying
2013-01-01
This paper deals with the problem of fault detection for discrete-time Markovian jump linear systems (MJLS).Using an observer-based fault detection filter (FDF) as a residual generator,the design of the FDF is formulated as an optimization problem for maximizing stochastic H_/H∞ or H∞/H∞ performance index.With the aid of an operator optimization method,it is shown that a unified optimal solution can be derived by solving a coupled Riccati equation.Numerical examples are given to show the effectiveness of the proposed method.
Gibson, J. S.; Rosen, I. G.
1988-01-01
An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.
Approximate optimal control for a class of nonlinear discrete-time systems with saturating actuators
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper, we solve the approximate optimal control problem for a class of nonlinear discrete-time systems with saturating actu- ators via greedy iterative Heuristic Dynamic Programming (GI-HDP) algorithm. In order to deal with the saturating problem of actu- ators, a novel nonquadratic functional is developed. Based on the nonquadratic functional, the GI-HDP algorithm is introduced to obtain the optimal saturated controller with a rigorous convergence analysis. For facilitating the implementation of the iterative algo- rithm, three neural networks are used to approximate the value function, compute the optimal control policy and model the unknown plant, respectively. An example is given to demonstrate the validity of the proposed optimal control scheme.
Approximation methods of mixed l 1/H2 optimization problems for MIMO discrete-time systems
Institute of Scientific and Technical Information of China (English)
李昇平
2004-01-01
The mixed l1/H2 optimization problem for MIMO (multiple input-multiple output) discrete-time systems is eonsidered. This problem is formulated as minimizing the l1-norm of a dosed-loop transfer matrix while maintaining the H2-norm of another closed-loop transfer matrix at prescribed level. The continuity property of the optimal value in respect to changes in the H2-norm constraint is studied. The existence of the optimal solutions of mixed l1/H2 problem is proved. Becatse the solution of the mixed l1/H2 problem is based on the scaled-Q method, it avoids the zero interpolation difficulties. The convergent upper and lower bounds can be obtained by solving a sequence of finite dimensional nonlinear programming for which many efficient numerical optimization algorithms exist.
Zhong, Xiangnan; He, Haibo; Zhang, Huaguang; Wang, Zhanshan
2014-12-01
In this paper, we develop and analyze an optimal control method for a class of discrete-time nonlinear Markov jump systems (MJSs) with unknown system dynamics. Specifically, an identifier is established for the unknown systems to approximate system states, and an optimal control approach for nonlinear MJSs is developed to solve the Hamilton-Jacobi-Bellman equation based on the adaptive dynamic programming technique. We also develop detailed stability analysis of the control approach, including the convergence of the performance index function for nonlinear MJSs and the existence of the corresponding admissible control. Neural network techniques are used to approximate the proposed performance index function and the control law. To demonstrate the effectiveness of our approach, three simulation studies, one linear case, one nonlinear case, and one single link robot arm case, are used to validate the performance of the proposed optimal control method.
Infinite horizon self-learning optimal control of nonaffine discrete-time nonlinear systems.
Wei, Qinglai; Liu, Derong; Yang, Xiong
2015-04-01
In this paper, a novel iterative adaptive dynamic programming (ADP)-based infinite horizon self-learning optimal control algorithm, called generalized policy iteration algorithm, is developed for nonaffine discrete-time (DT) nonlinear systems. Generalized policy iteration algorithm is a general idea of interacting policy and value iteration algorithms of ADP. The developed generalized policy iteration algorithm permits an arbitrary positive semidefinite function to initialize the algorithm, where two iteration indices are used for policy improvement and policy evaluation, respectively. It is the first time that the convergence, admissibility, and optimality properties of the generalized policy iteration algorithm for DT nonlinear systems are analyzed. Neural networks are used to implement the developed algorithm. Finally, numerical examples are presented to illustrate the performance of the developed algorithm.
LQR-Based Optimal Distributed Cooperative Design for Linear Discrete-Time Multiagent Systems.
Zhang, Huaguang; Feng, Tao; Liang, Hongjing; Luo, Yanhong
2017-03-01
In this paper, a novel linear quadratic regulator (LQR)-based optimal distributed cooperative design method is developed for synchronization control of general linear discrete-time multiagent systems on a fixed, directed graph. Sufficient conditions are derived for synchronization, which restrict the graph eigenvalues into a bounded circular region in the complex plane. The synchronizing speed issue is also considered, and it turns out that the synchronizing region reduces as the synchronizing speed becomes faster. To obtain more desirable synchronizing capacity, the weighting matrices are selected by sufficiently utilizing the guaranteed gain margin of the optimal regulators. Based on the developed LQR-based cooperative design framework, an approximate dynamic programming technique is successfully introduced to overcome the (partially or completely) model-free cooperative design for linear multiagent systems. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design methods.
Evolutionary constrained optimization
Deb, Kalyanmoy
2015-01-01
This book makes available a self-contained collection of modern research addressing the general constrained optimization problems using evolutionary algorithms. Broadly the topics covered include constraint handling for single and multi-objective optimizations; penalty function based methodology; multi-objective based methodology; new constraint handling mechanism; hybrid methodology; scaling issues in constrained optimization; design of scalable test problems; parameter adaptation in constrained optimization; handling of integer, discrete and mix variables in addition to continuous variables; application of constraint handling techniques to real-world problems; and constrained optimization in dynamic environment. There is also a separate chapter on hybrid optimization, which is gaining lots of popularity nowadays due to its capability of bridging the gap between evolutionary and classical optimization. The material in the book is useful to researchers, novice, and experts alike. The book will also be useful...
Approximately optimal tracking control for discrete time-delay systems with disturbances
Institute of Scientific and Technical Information of China (English)
Gongyou Tang; Huiying Sun; Haiping Pang
2008-01-01
Optimal tracking control (OTC) for discrete time-delay systems affected by persistent disturbances with quadratic performance index is considered. By introducing a sensitivity parameter, the original OTC problem is transformed into a series of two-point boundary value (TPBV) problems without time-advance or time-delay terms. The obtained OTC law consists of analytic feedforward and feedback terms and a compensation term which is the sum of an infinite series of adjoint vectors. The analytic feedforward and feedback terms can be found by solving a Riccati matrix equation and two Stein matrix equations. The compensation term can be obtained by using an iteration formula of the adjoint vectors. Observers are constructed to make the approximate OTC law physically realizable. A simulation example shows that the approximate approach is effective in tracking the reference input and robust with respect to exogenous persistent disturbances.
Sahoo, Avimanyu; Xu, Hao; Jagannathan, Sarangapani
2016-09-01
This paper presents an event-triggered near optimal control of uncertain nonlinear discrete-time systems. Event-driven neurodynamic programming (NDP) is utilized to design the control policy. A neural network (NN)-based identifier, with event-based state and input vectors, is utilized to learn the system dynamics. An actor-critic framework is used to learn the cost function and the optimal control input. The NN weights of the identifier, the critic, and the actor NNs are tuned aperiodically once every triggered instant. An adaptive event-trigger condition to decide the trigger instants is derived. Thus, a suitable number of events are generated to ensure a desired accuracy of approximation. A near optimal performance is achieved without using value and/or policy iterations. A detailed analysis of nontrivial inter-event times with an explicit formula to show the reduction in computation is also derived. The Lyapunov technique is used in conjunction with the event-trigger condition to guarantee the ultimate boundedness of the closed-loop system. The simulation results are included to verify the performance of the controller. The net result is the development of event-driven NDP.
Directory of Open Access Journals (Sweden)
Yujian Guo
2016-01-01
Full Text Available A design strategy of optimal output regulators for dual-rate discrete-time systems, whose output sampling period is an integer multiple of the input updating period, is proposed. At first, by using the discrete lifting technique, the dual-rate discrete-time system is converted to a single-rate augmented system in form and the lifted state-space model is constructed. Correspondingly, the performance index of the original system is modified to the performance index of the single-rate augmented system. And the original problem is transformed into an output regulation problem for the augmented system. Then, according to the optimal regulator theory, an optimal output regulator for the dual-rate discrete-time system is derived. In the meantime, the existence conditions of the optimal output regulator are discussed. Finally, a numerical example is included to illustrate the effectiveness of the proposed method.
Value Iteration Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems.
Wei, Qinglai; Liu, Derong; Lin, Hanquan
2016-03-01
In this paper, a value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon undiscounted optimal control problems for discrete-time nonlinear systems. The present value iteration ADP algorithm permits an arbitrary positive semi-definite function to initialize the algorithm. A novel convergence analysis is developed to guarantee that the iterative value function converges to the optimal performance index function. Initialized by different initial functions, it is proven that the iterative value function will be monotonically nonincreasing, monotonically nondecreasing, or nonmonotonic and will converge to the optimum. In this paper, for the first time, the admissibility properties of the iterative control laws are developed for value iteration algorithms. It is emphasized that new termination criteria are established to guarantee the effectiveness of the iterative control laws. Neural networks are used to approximate the iterative value function and compute the iterative control law, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.
Directory of Open Access Journals (Sweden)
Zhenhua Zhou
2015-01-01
Full Text Available This paper is concerned with the problem of designing robust H-infinity output feedback controller and resilient filtering for a class of discrete-time singular piecewise-affine systems with input saturation and state constraints. Based on a singular piecewise Lyapunov function combined with S-procedure and some matrix inequality convexifying techniques, the H-infinity stabilization condition is established and the resilient H-infinity filtering error dynamic system is investigated, and, meanwhile, the domain of attraction is well estimated. Under energy bounded disturbance, the input saturation disturbance tolerance condition is proposed; then, the resilient H-infinity filter is designed in some restricted region. It is shown that the controller gains and filter design parameters can be obtained by solving a family of LMIs parameterized by one or two scalar variables. Meanwhile, by using the corresponding optimization methods, the domain of attraction and the disturbance tolerance level is maximized, and the H-infinity performance γ is minimized. Numerical examples are given to illustrate the effectiveness of the proposed design methods.
Optimal Tracking Control of Unknown Discrete-Time Linear Systems Using Input-Output Measured Data.
Kiumarsi, Bahare; Lewis, Frank L; Naghibi-Sistani, Mohammad-Bagher; Karimpour, Ali
2015-12-01
In this paper, an output-feedback solution to the infinite-horizon linear quadratic tracking (LQT) problem for unknown discrete-time systems is proposed. An augmented system composed of the system dynamics and the reference trajectory dynamics is constructed. The state of the augmented system is constructed from a limited number of measurements of the past input, output, and reference trajectory in the history of the augmented system. A novel Bellman equation is developed that evaluates the value function related to a fixed policy by using only the input, output, and reference trajectory data from the augmented system. By using approximate dynamic programming, a class of reinforcement learning methods, the LQT problem is solved online without requiring knowledge of the augmented system dynamics only by measuring the input, output, and reference trajectory from the augmented system. We develop both policy iteration (PI) and value iteration (VI) algorithms that converge to an optimal controller that require only measuring the input, output, and reference trajectory data. The convergence of the proposed PI and VI algorithms is shown. A simulation example is used to verify the effectiveness of the proposed control scheme.
Optimizing the morphological design of discrete-time cellular neural networks
terBrugge, MH; Spaanenburg, L; Jansen, WJ; Nijhuis, JAG
1996-01-01
The morphological design of Discrete-Time Cellular Neural Networks (DTCNNs) has been presented in a companion paper [1]. DTCNN templates have been given for the elemental morphological operators. One way to obtain realizations for more complex operators is cascading the DTCNN equivalences of the
Constrained optimization using CODEQ
Energy Technology Data Exchange (ETDEWEB)
Omran, Mahamed G.H. [Department of Computer Science, Gulf University for Science and Technology, P.O. Box 7207, Hawally 32093 (Kuwait)], E-mail: omran.m@gust.edu.kw; Salman, Ayed [Computer Engineering Department, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)], E-mail: ayed@eng.kuniv.edu.kw
2009-10-30
Many real-world optimization problems are constrained problems that involve equality and inequality constraints. CODEQ is a new, parameter-free meta-heuristic algorithm that is a hybrid of concepts from chaotic search, opposition-based learning, differential evolution and quantum mechanics. The performance of the proposed approach when applied to five constrained benchmark problems is investigated and compared with other approaches proposed in the literature. The experiments conducted show that CODEQ provides excellent results with the added advantage of no parameter tuning.
Zhang, Huaguang; Song, Ruizhuo; Wei, Qinglai; Zhang, Tieyan
2011-12-01
In this paper, a novel heuristic dynamic programming (HDP) iteration algorithm is proposed to solve the optimal tracking control problem for a class of nonlinear discrete-time systems with time delays. The novel algorithm contains state updating, control policy iteration, and performance index iteration. To get the optimal states, the states are also updated. Furthermore, the "backward iteration" is applied to state updating. Two neural networks are used to approximate the performance index function and compute the optimal control policy for facilitating the implementation of HDP iteration algorithm. At last, we present two examples to demonstrate the effectiveness of the proposed HDP iteration algorithm.
Wang, Fei-Yue; Jin, Ning; Liu, Derong; Wei, Qinglai
2011-01-01
In this paper, we study the finite-horizon optimal control problem for discrete-time nonlinear systems using the adaptive dynamic programming (ADP) approach. The idea is to use an iterative ADP algorithm to obtain the optimal control law which makes the performance index function close to the greatest lower bound of all performance indices within an ε-error bound. The optimal number of control steps can also be obtained by the proposed ADP algorithms. A convergence analysis of the proposed ADP algorithms in terms of performance index function and control policy is made. In order to facilitate the implementation of the iterative ADP algorithms, neural networks are used for approximating the performance index function, computing the optimal control policy, and modeling the nonlinear system. Finally, two simulation examples are employed to illustrate the applicability of the proposed method.
Directory of Open Access Journals (Sweden)
Norman Josephy
2011-01-01
Full Text Available We present a method of optimal hedging and pricing of equity-linked life insurance products in an incomplete discrete-time financial market. A pure endowment life insurance contract with guarantee is used as an example. The financial market incompleteness is caused by the assumption that the underlying risky asset price ratios are distributed in a compact interval, generalizing the assumptions of multinomial incomplete market models. For a range of initial hedging capitals for the embedded financial option, we numerically solve an optimal hedging problem and determine a risk-return profile of each optimal non-self-financing hedging strategy. The fair price of the insurance contract is determined according to the insurer's risk-return preferences. Illustrative numerical results of testing our algorithm on hypothetical insurance contracts are documented. A discussion and a test of a hedging strategy recalibration technique for long-term contracts are presented.
Energy Technology Data Exchange (ETDEWEB)
Vanderbei, Robert J., E-mail: rvdb@princeton.edu [Princeton University, Department of Operations Research and Financial Engineering (United States); P Latin-Small-Letter-Dotless-I nar, Mustafa C., E-mail: mustafap@bilkent.edu.tr [Bilkent University, Department of Industrial Engineering (Turkey); Bozkaya, Efe B. [Sabanc Latin-Small-Letter-Dotless-I University, Faculty of Administrative Sciences (Turkey)
2013-02-15
An American option (or, warrant) is the right, but not the obligation, to purchase or sell an underlying equity at any time up to a predetermined expiration date for a predetermined amount. A perpetual American option differs from a plain American option in that it does not expire. In this study, we solve the optimal stopping problem of a perpetual American option (both call and put) in discrete time using linear programming duality. Under the assumption that the underlying stock price follows a discrete time and discrete state Markov process, namely a geometric random walk, we formulate the pricing problem as an infinite dimensional linear programming (LP) problem using the excessive-majorant property of the value function. This formulation allows us to solve complementary slackness conditions in closed-form, revealing an optimal stopping strategy which highlights the set of stock-prices where the option should be exercised. The analysis for the call option reveals that such a critical value exists only in some cases, depending on a combination of state-transition probabilities and the economic discount factor (i.e., the prevailing interest rate) whereas it ceases to be an issue for the put.
Directory of Open Access Journals (Sweden)
Jian Ding
2013-11-01
Full Text Available This paper is concerned with the linear unbiased minimum variance estimation problem for discrete-time stochastic linear control systems with one-step random delay and inconsecutive packet dropout. A new model is developed to describe the phenomena of the one-step delay and inconsecutive packet dropout by employing a Bernoulli distributed stochastic variable. Based on the model, a recursive linear unbiased optimal filter in the linear minimum variance sense is designed by the method of completing the square. The solution to the linear filter is given by three equations including a Riccati equation, a Lyapunov equation and a simple difference equation. A sufficient condition for the existence of the steady-state filter is given. A simulation shows the effectiveness of the proposed algorithm.
Optimal State Estimation for Discrete-Time Markov Jump Systems with Missing Observations
Directory of Open Access Journals (Sweden)
Qing Sun
2014-01-01
Full Text Available This paper is concerned with the optimal linear estimation for a class of direct-time Markov jump systems with missing observations. An observer-based approach of fault detection and isolation (FDI is investigated as a detection mechanic of fault case. For systems with known information, a conditional prediction of observations is applied and fault observations are replaced and isolated; then, an FDI linear minimum mean square error estimation (LMMSE can be developed by comprehensive utilizing of the correct information offered by systems. A recursive equation of filtering based on the geometric arguments can be obtained. Meanwhile, a stability of the state estimator will be guaranteed under appropriate assumption.
Linearly constrained minimax optimization
DEFF Research Database (Denmark)
Madsen, Kaj; Schjær-Jacobsen, Hans
1978-01-01
We present an algorithm for nonlinear minimax optimization subject to linear equality and inequality constraints which requires first order partial derivatives. The algorithm is based on successive linear approximations to the functions defining the problem. The resulting linear subproblems...
Constrained Optimization of Discontinuous Systems
Y.M. Ermoliev; V.I. Norkin
1996-01-01
In this paper we extend the results of Ermoliev, Norkin and Wets [8] and Ermoliev and Norkin [7] to the case of constrained discontinuous optimization problems. In contrast to [7] the attention is concentrated on the proof of general optimality conditions for problems with nonconvex feasible sets. Easily implementable random search technique is proposed.
Alfa, Attahiru S
2016-01-01
This book introduces the theoretical fundamentals for modeling queues in discrete-time, and the basic procedures for developing queuing models in discrete-time. There is a focus on applications in modern telecommunication systems. It presents how most queueing models in discrete-time can be set up as discrete-time Markov chains. Techniques such as matrix-analytic methods (MAM) that can used to analyze the resulting Markov chains are included. This book covers single node systems, tandem system and queueing networks. It shows how queues with time-varying parameters can be analyzed, and illustrates numerical issues associated with computations for the discrete-time queueing systems. Optimal control of queues is also covered. Applied Discrete-Time Queues targets researchers, advanced-level students and analysts in the field of telecommunication networks. It is suitable as a reference book and can also be used as a secondary text book in computer engineering and computer science. Examples and exercises are includ...
Trends in PDE constrained optimization
Benner, Peter; Engell, Sebastian; Griewank, Andreas; Harbrecht, Helmut; Hinze, Michael; Rannacher, Rolf; Ulbrich, Stefan
2014-01-01
Optimization problems subject to constraints governed by partial differential equations (PDEs) are among the most challenging problems in the context of industrial, economical and medical applications. Almost the entire range of problems in this field of research was studied and further explored as part of the Deutsche Forschungsgemeinschaft (DFG) priority program 1253 on “Optimization with Partial Differential Equations” from 2006 to 2013. The investigations were motivated by the fascinating potential applications and challenging mathematical problems that arise in the field of PDE constrained optimization. New analytic and algorithmic paradigms have been developed, implemented and validated in the context of real-world applications. In this special volume, contributions from more than fifteen German universities combine the results of this interdisciplinary program with a focus on applied mathematics. The book is divided into five sections on “Constrained Optimization, Identification and Control”...
Constrained Multiobjective Biogeography Optimization Algorithm
Directory of Open Access Journals (Sweden)
Hongwei Mo
2014-01-01
Full Text Available Multiobjective optimization involves minimizing or maximizing multiple objective functions subject to a set of constraints. In this study, a novel constrained multiobjective biogeography optimization algorithm (CMBOA is proposed. It is the first biogeography optimization algorithm for constrained multiobjective optimization. In CMBOA, a disturbance migration operator is designed to generate diverse feasible individuals in order to promote the diversity of individuals on Pareto front. Infeasible individuals nearby feasible region are evolved to feasibility by recombining with their nearest nondominated feasible individuals. The convergence of CMBOA is proved by using probability theory. The performance of CMBOA is evaluated on a set of 6 benchmark problems and experimental results show that the CMBOA performs better than or similar to the classical NSGA-II and IS-MOEA.
Constrained multiobjective biogeography optimization algorithm.
Mo, Hongwei; Xu, Zhidan; Xu, Lifang; Wu, Zhou; Ma, Haiping
2014-01-01
Multiobjective optimization involves minimizing or maximizing multiple objective functions subject to a set of constraints. In this study, a novel constrained multiobjective biogeography optimization algorithm (CMBOA) is proposed. It is the first biogeography optimization algorithm for constrained multiobjective optimization. In CMBOA, a disturbance migration operator is designed to generate diverse feasible individuals in order to promote the diversity of individuals on Pareto front. Infeasible individuals nearby feasible region are evolved to feasibility by recombining with their nearest nondominated feasible individuals. The convergence of CMBOA is proved by using probability theory. The performance of CMBOA is evaluated on a set of 6 benchmark problems and experimental results show that the CMBOA performs better than or similar to the classical NSGA-II and IS-MOEA.
Method of constrained global optimization
Energy Technology Data Exchange (ETDEWEB)
Altschuler, E.L.; Williams, T.J.; Ratner, E.R.; Dowla, F.; Wooten, F. (Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, California 94551 (United States) Department of Applied Physics, Stanford University, Stanford, California 94305 (United States) Department of Applied Science, University of California, Davis/Livermore, P.O. Box 808, Livermore, California 94551 (United States))
1994-04-25
We present a new method for optimization: constrained global optimization (CGO). CGO iteratively uses a Glauber spin flip probability and the Metropolis algorithm. The spin flip probability allows changing only the values of variables contributing excessively to the function to be minimized. We illustrate CGO with two problems---Thomson's problem of finding the minimum-energy configuration of unit charges on a spherical surface, and a problem of assigning offices---for which CGO finds better minima than other methods. We think CGO will apply to a wide class of optimization problems.
Zhang, Huaguang; Wei, Qinglai; Luo, Yanhong
2008-08-01
In this paper, we aim to solve the infinite-time optimal tracking control problem for a class of discrete-time nonlinear systems using the greedy heuristic dynamic programming (HDP) iteration algorithm. A new type of performance index is defined because the existing performance indexes are very difficult in solving this kind of tracking problem, if not impossible. Via system transformation, the optimal tracking problem is transformed into an optimal regulation problem, and then, the greedy HDP iteration algorithm is introduced to deal with the regulation problem with rigorous convergence analysis. Three neural networks are used to approximate the performance index, compute the optimal control policy, and model the nonlinear system for facilitating the implementation of the greedy HDP iteration algorithm. An example is given to demonstrate the validity of the proposed optimal tracking control scheme.
Bergstra, J.A.; Baeten, J.C.M.
1996-01-01
The axiom system ACP of [BeK84a] was extended with real time features in [BaB91]. Here we proceed to define a discrete time extension of ACP, along the lines of ATP [NiS94]. We present versions based on relative timing and on absolute timing. Both approaches are integrated using parametric timing. T
Directory of Open Access Journals (Sweden)
Luís F. P. Silva
2014-01-01
Full Text Available A convex condition in terms of linear matrix inequalities (LMIs is developed for the synthesis of stabilizing fuzzy state feedback controllers for nonlinear discrete-time systems with time-varying delays. A Takagi-Sugeno (T-S fuzzy model is used to represent exactly the nonlinear system in a restricted domain of the state space, called region of validity. The proposed stabilization condition is based on a Lyapunov-Krasovskii (L-K function and it takes into account the region of validity to determine a set of initial conditions for which the actual closed-loop system trajectories are asymptotically stable and do not evolve outside the region of validity. This set of allowable initial conditions is determined from the level set associated to a fuzzy L-K function as a Cartesian product of two subsets: one characterizing the set of states at the initial instant and another for the delayed state sequence necessary to characterize the initial conditions. Finally, we propose a convex programming problem to design a fuzzy controller that maximizes the set of initial conditions taking into account the shape of the region of validity of the T-S fuzzy model. Numerical simulations are given to illustrate this proposal.
Directory of Open Access Journals (Sweden)
Shi-Yuan Han
2015-01-01
Full Text Available The study is concerned with problem of optimal disturbance rejection for a class of discrete-time systems with multiple delayed inputs. In order to avoid the two-point boundary value (TPBV problem with items of time-delay and time-advance caused by multiple delayed inputs, the discrete-time system with multiple delayed inputs is transformed into a delay-free system by introducing a variable transformation, and the original performance index is reformulated as a corresponding form without the explicit appearance of time-delay items. Then, the approximate optimal disturbance rejection controller (AODRC is derived from Riccati equation and Stein equation based on the reduced system and reformulated performance index, which is combined with feedback item of system state, feedforward item of disturbances, and items of delayed inputs. Also, the existence and uniqueness of AODRC are proved, and the stability of the closed-loop system is analysed. Finally, numerical examples of disturbance rejection for jacket-type offshore structure and pure mathematical model are illustrated to validate the feasibility and effectiveness of the proposed approach.
Determination of optimal gains for constrained controllers
Energy Technology Data Exchange (ETDEWEB)
Kwan, C.M.; Mestha, L.K.
1993-08-01
In this report, we consider the determination of optimal gains, with respect to a certain performance index, for state feedback controllers where some elements in the gain matrix are constrained to be zero. Two iterative schemes for systematically finding the constrained gain matrix are presented. An example is included to demonstrate the procedures.
Han, Qing-Long; Liu, Yurong; Yang, Fuwen
2016-02-01
This paper is concerned with optimal communication network-based H∞ quantized control for a discrete-time neural network with distributed time delay. Control of the neural network (plant) is implemented via a communication network. Both quantization and communication network-induced data packet dropouts are considered simultaneously. It is assumed that the plant state signal is quantized by a logarithmic quantizer before transmission, and communication network-induced packet dropouts can be described by a Bernoulli distributed white sequence. A new approach is developed such that controller design can be reduced to the feasibility of linear matrix inequalities, and a desired optimal control gain can be derived in an explicit expression. It is worth pointing out that some new techniques based on a new sector-like expression of quantization errors, and the singular value decomposition of a matrix are developed and employed in the derivation of main results. An illustrative example is presented to show the effectiveness of the obtained results.
Optimal constrained layer damping with partial coverage
Marcelin, J.-L.; Trompette, Ph.; Smati, A.
1992-12-01
This paper deals with the optimal damping of beams constrained by viscoelastic layers when only one or several portions of the beam are covered. An efficient finite element model for dynamic analysis of such beams is used. The design variables are the dimensions and prescribed locations of the viscoelastic layers and the objective is the maximum viscoelastic damping factor. The method for nonlinear programming in structural optimization is the so-called method of moving asymptotes.
Neuroevolutionary Constrained Optimization for Content Creation
DEFF Research Database (Denmark)
Liapis, Antonios; Yannakakis, Georgios N.; Togelius, Julian
2011-01-01
and thruster types and topologies) independently of game physics and steering strategies. According to the proposed framework, the designer picks a set of requirements for the spaceship that a constrained optimizer attempts to satisfy. The constraint satisfaction approach followed is based on neuroevolution...
Principles of discrete time mechanics
Jaroszkiewicz, George
2014-01-01
Could time be discrete on some unimaginably small scale? Exploring the idea in depth, this unique introduction to discrete time mechanics systematically builds the theory up from scratch, beginning with the historical, physical and mathematical background to the chronon hypothesis. Covering classical and quantum discrete time mechanics, this book presents all the tools needed to formulate and develop applications of discrete time mechanics in a number of areas, including spreadsheet mechanics, classical and quantum register mechanics, and classical and quantum mechanics and field theories. A consistent emphasis on contextuality and the observer-system relationship is maintained throughout.
Constrained Graph Optimization: Interdiction and Preservation Problems
Energy Technology Data Exchange (ETDEWEB)
Schild, Aaron V [Los Alamos National Laboratory
2012-07-30
The maximum flow, shortest path, and maximum matching problems are a set of basic graph problems that are critical in theoretical computer science and applications. Constrained graph optimization, a variation of these basic graph problems involving modification of the underlying graph, is equally important but sometimes significantly harder. In particular, one can explore these optimization problems with additional cost constraints. In the preservation case, the optimizer has a budget to preserve vertices or edges of a graph, preventing them from being deleted. The optimizer wants to find the best set of preserved edges/vertices in which the cost constraints are satisfied and the basic graph problems are optimized. For example, in shortest path preservation, the optimizer wants to find a set of edges/vertices within which the shortest path between two predetermined points is smallest. In interdiction problems, one deletes vertices or edges from the graph with a particular cost in order to impede the basic graph problems as much as possible (for example, delete edges/vertices to maximize the shortest path between two predetermined vertices). Applications of preservation problems include optimal road maintenance, power grid maintenance, and job scheduling, while interdiction problems are related to drug trafficking prevention, network stability assessment, and counterterrorism. Computational hardness results are presented, along with heuristic methods for approximating solutions to the matching interdiction problem. Also, efficient algorithms are presented for special cases of graphs, including on planar graphs. The graphs in many of the listed applications are planar, so these algorithms have important practical implications.
Neuroevolutionary Constrained Optimization for Content Creation
DEFF Research Database (Denmark)
Liapis, Antonios; Yannakakis, Georgios N.; Togelius, Julian
2011-01-01
and thruster types and topologies) independently of game physics and steering strategies. According to the proposed framework, the designer picks a set of requirements for the spaceship that a constrained optimizer attempts to satisfy. The constraint satisfaction approach followed is based on neuroevolution......; Compositional Pattern-Producing Networks (CPPNs) which represent the spaceship’s design are trained via a constraint-based evolutionary algorithm. Results obtained in a number of evolutionary runs using a set of constraints and objectives show that the generated spaceships perform well in movement, combat...
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
Security constrained optimal power flow by modern optimization tools
African Journals Online (AJOL)
The fertilization is divided into self and Cross Pollination. The self ... Blossom steadiness can be considered as the generation l. 4. ..... discovered considering the base case is 801.8436, and this esteem is .... Gaing Z., and ChangR., 2006, Security-constrained optimal power flow by mixed-integer genetic algorithm with.
Optimal performance of constrained control systems
Harvey, P. Scott, Jr.; Gavin, Henri P.; Scruggs, Jeffrey T.
2012-08-01
This paper presents a method to compute optimal open-loop trajectories for systems subject to state and control inequality constraints in which the cost function is quadratic and the state dynamics are linear. For the case in which inequality constraints are decentralized with respect to the controls, optimal Lagrange multipliers enforcing the inequality constraints may be found at any time through Pontryagin’s minimum principle. In so doing, the set of differential algebraic Euler-Lagrange equations is transformed into a nonlinear two-point boundary-value problem for states and costates whose solution meets the necessary conditions for optimality. The optimal performance of inequality constrained control systems is calculable, allowing for comparison to previous, sub-optimal solutions. The method is applied to the control of damping forces in a vibration isolation system subjected to constraints imposed by the physical implementation of a particular controllable damper. An outcome of this study is the best performance achievable given a particular objective, isolation system, and semi-active damper constraints.
Institute of Scientific and Technical Information of China (English)
崔鹏; 张承慧
2007-01-01
The finite time horizon indefinite linear quadratic(LQ) optimal control problem for singular linear discrete time-varying systems is discussed. Indefinite LQ optimal control problem for singular systems can be transformed to that for standard state-space systems under a reasonable assumption. It is shown that the indefinite LQ optimal control problem is dual to that of projection for backward stochastic systems. Thus, the optimal LQ controller can be obtained by computing the gain matrices of Kalman filter.Necessary and sufficient conditions guaranteeing a unique solution for the indefinite LQ problem are given. An explicit solution for the problem is obtained in terms of the solution of Riccati difference equations.
Sundance: High-Level Software for PDE-Constrained Optimization
Directory of Open Access Journals (Sweden)
Kevin Long
2012-01-01
Full Text Available Sundance is a package in the Trilinos suite designed to provide high-level components for the development of high-performance PDE simulators with built-in capabilities for PDE-constrained optimization. We review the implications of PDE-constrained optimization on simulator design requirements, then survey the architecture of the Sundance problem specification components. These components allow immediate extension of a forward simulator for use in an optimization context. We show examples of the use of these components to develop full-space and reduced-space codes for linear and nonlinear PDE-constrained inverse problems.
Artificial bee colony algorithm variants on constrained optimization
National Research Council Canada - National Science Library
Bahriye Akay; Dervis Karaboga
2017-01-01
.... In this study, the performance analysis of artificial bee colony algorithm (ABC), one of the intelligent optimization techniques, is examined on constrained problems and the effect of some modifications on the performance of the algorithm is examined...
Remarks on a benchmark nonlinear constrained optimization problem
Institute of Scientific and Technical Information of China (English)
Luo Yazhong; Lei Yongjun; Tang Guojin
2006-01-01
Remarks on a benchmark nonlinear constrained optimization problem are made. Due to a citation error, two absolutely different results for the benchmark problem are obtained by independent researchers. Parallel simulated annealing using simplex method is employed in our study to solve the benchmark nonlinear constrained problem with mistaken formula and the best-known solution is obtained, whose optimality is testified by the Kuhn-Tucker conditions.
Robust Constrained Blackbox Optimization with Surrogates
2015-05-21
numbers assigned by the performing organization, e.g. BRL-1234; AFWL-TR-85-4017-Vol-21- PT -2. 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES...during reporting pe - riod: Published: 1. C. Audet, S. Le Digabel, and M. Peyrega. Linear equalities in blackbox optimization. Computational Optimization...A.E. Gheribi, S. Le Digabel, C. Audet, and P. Chartrand. Identifying optimal conditions for magnesium based alloy design using the mesh adaptive direct
Energetic Materials Optimization via Constrained Search
2015-06-01
space.18–20 LCAP and VP-DFT interpolate continuously between the Hamiltonians of various chemical species. Furthermore, recently an investigation into...Computational Chemistry Protocol All quantum- mechanical computations were performed using Gaussian 09.24 All geometries were preoptimized with B3LYP/3-21G under...via nonnegative Lagrange multipliers λ ∈ R3+ for the 3 constraints to the augmented Lagrangian function L(x, λ) := P (x) − λC(x) as a constrained min
Constrained Optimization of MIMO Training Sequences
Directory of Open Access Journals (Sweden)
Coon Justin P
2007-01-01
Full Text Available Multiple-input multiple-output (MIMO systems have shown a huge potential for increased spectral efficiency and throughput. With an increasing number of transmitting antennas comes the burden of providing training for channel estimation for coherent detection. In some special cases optimal, in the sense of mean-squared error (MSE, training sequences have been designed. However, in many practical systems it is not feasible to analytically find optimal solutions and numerical techniques must be used. In this paper, two systems (unique word (UW single carrier and OFDM with nulled subcarriers are considered and a method of designing near-optimal training sequences using nonlinear optimization techniques is proposed. In particular, interior-point (IP algorithms such as the barrier method are discussed. Although the two systems seem unrelated, the cost function, which is the MSE of the channel estimate, is shown to be effectively the same for each scenario. Also, additional constraints, such as peak-to-average power ratio (PAPR, are considered and shown to be easily included in the optimization process. Numerical examples illustrate the effectiveness of the designed training sequences, both in terms of MSE and bit-error rate (BER.
Finite-horizon control-constrained nonlinear optimal control using single network adaptive critics.
Heydari, Ali; Balakrishnan, Sivasubramanya N
2013-01-01
To synthesize fixed-final-time control-constrained optimal controllers for discrete-time nonlinear control-affine systems, a single neural network (NN)-based controller called the Finite-horizon Single Network Adaptive Critic is developed in this paper. Inputs to the NN are the current system states and the time-to-go, and the network outputs are the costates that are used to compute optimal feedback control. Control constraints are handled through a nonquadratic cost function. Convergence proofs of: 1) the reinforcement learning-based training method to the optimal solution; 2) the training error; and 3) the network weights are provided. The resulting controller is shown to solve the associated time-varying Hamilton-Jacobi-Bellman equation and provide the fixed-final-time optimal solution. Performance of the new synthesis technique is demonstrated through different examples including an attitude control problem wherein a rigid spacecraft performs a finite-time attitude maneuver subject to control bounds. The new formulation has great potential for implementation since it consists of only one NN with single set of weights and it provides comprehensive feedback solutions online, though it is trained offline.
Constrained optimization for image restoration using nonlinear programming
Yeh, C.-L.; Chin, R. T.
1985-01-01
The constrained optimization problem for image restoration, utilizing incomplete information and partial constraints, is formulated using nonlinear proramming techniques. This method restores a distorted image by optimizing a chosen object function subject to available constraints. The penalty function method of nonlinear programming is used. Both linear or nonlinear object function, and linear or nonlinear constraint functions can be incorporated in the formulation. This formulation provides a generalized approach to solve constrained optimization problems for image restoration. Experiments using this scheme have been performed. The results are compared with those obtained from other restoration methods and the comparative study is presented.
Insights into capacity-constrained optimal transport.
Korman, Jonathan; McCann, Robert J
2013-06-18
A variant of the classical optimal transportation problem is the following: among all joint measures with fixed marginals and that are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were established by Korman and McCann. In the present article, we expose an unexpected symmetry leading to explicit examples in two and more dimensions. These are inspired in part by simulations in one dimension that display singularities and topology and in part by two further developments: the identification of all extreme points in the feasible set and an approach to uniqueness based on constructing feasible perturbations.
Sequential unconstrained minimization algorithms for constrained optimization
Byrne, Charles
2008-02-01
The problem of minimizing a function f(x):RJ → R, subject to constraints on the vector variable x, occurs frequently in inverse problems. Even without constraints, finding a minimizer of f(x) may require iterative methods. We consider here a general class of iterative algorithms that find a solution to the constrained minimization problem as the limit of a sequence of vectors, each solving an unconstrained minimization problem. Our sequential unconstrained minimization algorithm (SUMMA) is an iterative procedure for constrained minimization. At the kth step we minimize the function G_k(x)=f(x)+g_k(x), to obtain xk. The auxiliary functions gk(x):D ⊆ RJ → R+ are nonnegative on the set D, each xk is assumed to lie within D, and the objective is to minimize the continuous function f:RJ → R over x in the set C=\\overline D , the closure of D. We assume that such minimizers exist, and denote one such by \\hat x . We assume that the functions gk(x) satisfy the inequalities 0\\leq g_k(x)\\leq G_{k-1}(x)-G_{k-1}(x^{k-1}), for k = 2, 3, .... Using this assumption, we show that the sequence {f(xk)} is decreasing and converges to f({\\hat x}) . If the restriction of f(x) to D has bounded level sets, which happens if \\hat x is unique and f(x) is closed, proper and convex, then the sequence {xk} is bounded, and f(x^*)=f({\\hat x}) , for any cluster point x*. Therefore, if \\hat x is unique, x^*={\\hat x} and \\{x^k\\}\\rightarrow {\\hat x} . When \\hat x is not unique, convergence can still be obtained, in particular cases. The SUMMA includes, as particular cases, the well-known barrier- and penalty-function methods, the simultaneous multiplicative algebraic reconstruction technique (SMART), the proximal minimization algorithm of Censor and Zenios, the entropic proximal methods of Teboulle, as well as certain cases of gradient descent and the Newton-Raphson method. The proof techniques used for SUMMA can be extended to obtain related results for the induced proximal
A CONSTRAINED OPTIMIZATION APPROACH FOR LCP
Institute of Scientific and Technical Information of China (English)
Ju-liang Zhang; Jian Chen; Xin-jian Zhuo
2004-01-01
In this paper, LCP is converted to an equivalent nonsmooth nonlinear equation system H(x, y) = 0 by using the famous NCP function-Fischer-Burmeister function. Note that some equations in H(x, y) = 0 are nonsmooth and nonlinear hence difficult to solve while the others are linear hence easy to solve. Then we further convert the nonlinear equation system H(x, y) = 0 to an optimization problem with linear equality constraints. After that we study the conditions under which the K T points of the optimization problem are the solutions of the original LCP and propose a method to solve the optimization problem.In this algorithm, the search direction is obtained by solving a strict convex programming at each iterative point. However, our algorithm is essentially different from traditional SQP method. The global convergence of the method is proved under mild conditions. In addition, we can prove that the algorithm is convergent superlinearly under the conditions:M is P0 matrix and the limit point is a strict complementarity solution of LCP. Preliminary numerical experiments are reported with this method.
Discrete-time nonlinear sliding mode controller
African Journals Online (AJOL)
user
: Discrete-time delay system, Sliding mode control, nonlinear sliding ... The concept of the sliding mode control in recent years has drawn the ...... His area of interest is dc-dc converters, electrical vehicle and distributed generation application.
Constrained regression models for optimization and forecasting
Directory of Open Access Journals (Sweden)
P.J.S. Bruwer
2003-12-01
Full Text Available Linear regression models and the interpretation of such models are investigated. In practice problems often arise with the interpretation and use of a given regression model in spite of the fact that researchers may be quite "satisfied" with the model. In this article methods are proposed which overcome these problems. This is achieved by constructing a model where the "area of experience" of the researcher is taken into account. This area of experience is represented as a convex hull of available data points. With the aid of a linear programming model it is shown how conclusions can be formed in a practical way regarding aspects such as optimal levels of decision variables and forecasting.
Asynchronous Parallel Evolutionary Algorithms for Constrained Optimizations
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Recently Guo Tao proposed a stochastic search algorithm in his PhD thesis for solving function op-timization problems. He combined the subspace search method (a general multi-parent recombination strategy) with the population hill-climbing method. The former keeps a global search for overall situation,and the latter keeps the convergence of the algorithm. Guo's algorithm has many advantages ,such as the sim-plicity of its structure ,the higher accuracy of its results, the wide range of its applications ,and the robustness of its use. In this paper a preliminary theoretical analysis of the algorithm is given and some numerical experiments has been done by using Guo's algorithm for demonstrating the theoretical results. Three asynchronous paral-lel evolutionary algorithms with different granularities for MIMD machines are designed by parallelizing Guo's Algorithm.
A Riccati approach for constrained linear quadratic optimal control
Sideris, Athanasios; Rodriguez, Luis A.
2011-02-01
An active-set method is proposed for solving linear quadratic optimal control problems subject to general linear inequality path constraints including mixed state-control and state-only constraints. A Riccati-based approach is developed for efficiently solving the equality constrained optimal control subproblems generated during the procedure. The solution of each subproblem requires computations that scale linearly with the horizon length. The algorithm is illustrated with numerical examples.
Optimal Constrained Layer Damping of Beams: Experimental and Numerical Studies
Directory of Open Access Journals (Sweden)
J.-L. Marcelin
1995-01-01
Full Text Available This article deals with the optimal damping of beams constrained by viscoelastic layers when only one or several portions of the beam are covered. The design variables are the dimensions and locations of the viscoelastic layers and the objective function is the maximum damping factor. The discrete design variable optimization problem is solved using a genetic algorithm. Numerical results for minimum and maximum damping are compared to experimental results. This is done for a various number of materials and beams.
Steepest-Ascent Constrained Simultaneous Perturbation for Multiobjective Optimization
DEFF Research Database (Denmark)
McClary, Dan; Syrotiuk, Violet; Kulahci, Murat
2011-01-01
that leverages information about the known gradient to constrain the perturbations used to approximate the others. We apply SP(SA)(2) to the cross-layer optimization of throughput, packet loss, and end-to-end delay in a mobile ad hoc network (MANET), a self-organizing wireless network. The results show that SP...
Adaptive double chain quantum genetic algorithm for constrained optimization problems
Directory of Open Access Journals (Sweden)
Kong Haipeng
2015-02-01
Full Text Available Optimization problems are often highly constrained and evolutionary algorithms (EAs are effective methods to tackle this kind of problems. To further improve search efficiency and convergence rate of EAs, this paper presents an adaptive double chain quantum genetic algorithm (ADCQGA for solving constrained optimization problems. ADCQGA makes use of double-individuals to represent solutions that are classified as feasible and infeasible solutions. Fitness (or evaluation functions are defined for both types of solutions. Based on the fitness function, three types of step evolution (SE are defined and utilized for judging evolutionary individuals. An adaptive rotation is proposed and used to facilitate updating individuals in different solutions. To further improve the search capability and convergence rate, ADCQGA utilizes an adaptive evolution process (AEP, adaptive mutation and replacement techniques. ADCQGA was first tested on a widely used benchmark function to illustrate the relationship between initial parameter values and the convergence rate/search capability. Then the proposed ADCQGA is successfully applied to solve other twelve benchmark functions and five well-known constrained engineering design problems. Multi-aircraft cooperative target allocation problem is a typical constrained optimization problem and requires efficient methods to tackle. Finally, ADCQGA is successfully applied to solving the target allocation problem.
Adaptive double chain quantum genetic algorithm for constrained optimization problems
Institute of Scientific and Technical Information of China (English)
Kong Haipeng; Li Ni; Shen Yuzhong
2015-01-01
Optimization problems are often highly constrained and evolutionary algorithms (EAs) are effective methods to tackle this kind of problems. To further improve search efficiency and con-vergence rate of EAs, this paper presents an adaptive double chain quantum genetic algorithm (ADCQGA) for solving constrained optimization problems. ADCQGA makes use of double-individuals to represent solutions that are classified as feasible and infeasible solutions. Fitness (or evaluation) functions are defined for both types of solutions. Based on the fitness function, three types of step evolution (SE) are defined and utilized for judging evolutionary individuals. An adaptive rotation is proposed and used to facilitate updating individuals in different solutions. To further improve the search capability and convergence rate, ADCQGA utilizes an adaptive evolution process (AEP), adaptive mutation and replacement techniques. ADCQGA was first tested on a widely used benchmark function to illustrate the relationship between initial parameter values and the convergence rate/search capability. Then the proposed ADCQGA is successfully applied to solve other twelve benchmark functions and five well-known constrained engineering design problems. Multi-aircraft cooperative target allocation problem is a typical constrained optimization problem and requires efficient methods to tackle. Finally, ADCQGA is successfully applied to solving the target allocation problem.
A Projection Neural Network for Constrained Quadratic Minimax Optimization.
Liu, Qingshan; Wang, Jun
2015-11-01
This paper presents a projection neural network described by a dynamic system for solving constrained quadratic minimax programming problems. Sufficient conditions based on a linear matrix inequality are provided for global convergence of the proposed neural network. Compared with some of the existing neural networks for quadratic minimax optimization, the proposed neural network in this paper is capable of solving more general constrained quadratic minimax optimization problems, and the designed neural network does not include any parameter. Moreover, the neural network has lower model complexities, the number of state variables of which is equal to that of the dimension of the optimization problems. The simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network.
Discrete Time Crystals: Rigidity, Criticality, and Realizations
Yao, N. Y.; Potter, A. C.; Potirniche, I.-D.; Vishwanath, A.
2017-01-01
Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one-dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.
Discrete Time Crystals: Rigidity, Criticality, and Realizations.
Yao, N Y; Potter, A C; Potirniche, I-D; Vishwanath, A
2017-01-20
Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one-dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.
Constrained optimal steady-state control for isolated traffic intersections
Institute of Scientific and Technical Information of China (English)
Jack HADDAD; David MAHALEL; Ilya IOSLOVICH; Per-Olof GUTMAN
2014-01-01
The steady-state or cyclic control problem for a simplified isolated traffic intersection is considered. The optimization problem for the green-red switching sequence is formulated with the help of a discrete-event max-plus model. Two steady-state control problems are formulated: optimal steady-state with green duration constraints, and optimal steady-state control with lost time. In the case when the criterion is a strictly increasing, linear function of the queue lengths, the steady-state control problems can be solved analytically. The structure of constrained optimal steady-state traffic control is revealed, and the effect of the lost time on the optimal solution is illustrated.
On the optimal identification of tag sets in time-constrained RFID configurations.
Vales-Alonso, Javier; Bueno-Delgado, María Victoria; Egea-López, Esteban; Alcaraz, Juan José; Pérez-Mañogil, Juan Manuel
2011-01-01
In Radio Frequency Identification facilities the identification delay of a set of tags is mainly caused by the random access nature of the reading protocol, yielding a random identification time of the set of tags. In this paper, the cumulative distribution function of the identification time is evaluated using a discrete time Markov chain for single-set time-constrained passive RFID systems, namely those ones where a single group of tags is assumed to be in the reading area and only for a bounded time (sojourn time) before leaving. In these scenarios some tags in a set may leave the reader coverage area unidentified. The probability of this event is obtained from the cumulative distribution function of the identification time as a function of the sojourn time. This result provides a suitable criterion to minimize the probability of losing tags. Besides, an identification strategy based on splitting the set of tags in smaller subsets is also considered. Results demonstrate that there are optimal splitting configurations that reduce the overall identification time while keeping the same probability of losing tags.
Stability Criterion for Discrete-Time Systems
Directory of Open Access Journals (Sweden)
K. Ratchagit
2010-01-01
Full Text Available This paper is concerned with the problem of delay-dependent stability analysis for discrete-time systems with interval-like time-varying delays. The problem is solved by applying a novel Lyapunov functional, and an improved delay-dependent stability criterion is obtained in terms of a linear matrix inequality.
A Globally Convergent Parallel SSLE Algorithm for Inequality Constrained Optimization
Directory of Open Access Journals (Sweden)
Zhijun Luo
2014-01-01
Full Text Available A new parallel variable distribution algorithm based on interior point SSLE algorithm is proposed for solving inequality constrained optimization problems under the condition that the constraints are block-separable by the technology of sequential system of linear equation. Each iteration of this algorithm only needs to solve three systems of linear equations with the same coefficient matrix to obtain the descent direction. Furthermore, under certain conditions, the global convergence is achieved.
SCOR: Software-defined Constrained Optimal Routing Platform for SDN
Layeghy, Siamak; Pakzad, Farzaneh; Portmann, Marius
2016-01-01
A Software-defined Constrained Optimal Routing (SCOR) platform is introduced as a Northbound interface in SDN architecture. It is based on constraint programming techniques and is implemented in MiniZinc modelling language. Using constraint programming techniques in this Northbound interface has created an efficient tool for implementing complex Quality of Service routing applications in a few lines of code. The code includes only the problem statement and the solution is found by a general s...
Hybrid particle swarm optimization for solving resource-constrained FMS
Institute of Scientific and Technical Information of China (English)
Dongyun Wang; Liping Liu
2008-01-01
In this paper,an approach for resource-constrained flexible manufacturing system(FMS)scheduling was proposed,which is based on the particle swarm optimization(PSO)algorithm and simulated annealing(SA)algorithm.First,the formulation for resource-con-strained FMS scheduling problem was introduced and cost function for this problem was obtained.Then.a hybrid algorithm of PSO and SA was employed to obtain optimal solution.The simulated results show that the approach can dislodge a state from a local min-imum and guide it to the global minimum.
Stress-constrained topology optimization for compliant mechanism design
DEFF Research Database (Denmark)
de Leon, Daniel M.; Alexandersen, Joe; Jun, Jun S.;
2015-01-01
This article presents an application of stress-constrained topology optimization to compliant mechanism design. An output displacement maximization formulation is used, together with the SIMP approach and a projection method to ensure convergence to nearly discrete designs. The maximum stress...... is approximated using a normalized version of the commonly-used p-norm of the effective von Mises stresses. The usual problems associated with topology optimization for compliant mechanism design: one-node and/or intermediate density hinges are alleviated by the stress constraint. However, it is also shown...
Viability decision of linear discrete-time stochastic systems with probability criterion
Institute of Scientific and Technical Information of China (English)
Wansheng TANG; Jun ZHENG; Jianxiong ZHANG
2009-01-01
In this paper,the optimal viability decision problem of linear discrete-time stochastic systems with probability criterion is investigated.Under the condition of sequence-reachable discrete-time dynamic systems,the existence theorem of optimal viability strategy is given and the solving procedure of the optimal strategy is provided based on dynamic programming.A numerical example shows the effectiveness of the proposed methods.
Optimization of multi-constrained structures based on optimality criteria
Rizzi, P.
1976-01-01
A weight-reduction algorithm is developed for the optimal design of structures subject to several multibehavioral inequality constraints. The structural weight is considered to depend linearly on the design variables. The algorithm incorporates a simple recursion formula derived from the Kuhn-Tucker necessary conditions for optimality, associated with a procedure to delete nonactive constraints based on the Gauss-Seidel iterative method for linear systems. A number of example problems is studied, including typical truss structures and simplified wings subject to static loads and with constraints imposed on stresses and displacements. For one of the latter structures, constraints on the fundamental natural frequency and flutter speed are also imposed. The results obtained show that the method is fast, efficient, and general when compared to other competing techniques. Extensions to the generality of the method to include equality constraints and nonlinear merit functions is discussed.
Bidirectional Dynamic Diversity Evolutionary Algorithm for Constrained Optimization
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Weishang Gao
2013-01-01
Full Text Available Evolutionary algorithms (EAs were shown to be effective for complex constrained optimization problems. However, inflexible exploration-exploitation and improper penalty in EAs with penalty function would lead to losing the global optimum nearby or on the constrained boundary. To determine an appropriate penalty coefficient is also difficult in most studies. In this paper, we propose a bidirectional dynamic diversity evolutionary algorithm (Bi-DDEA with multiagents guiding exploration-exploitation through local extrema to the global optimum in suitable steps. In Bi-DDEA potential advantage is detected by three kinds of agents. The scale and the density of agents will change dynamically according to the emerging of potential optimal area, which play an important role of flexible exploration-exploitation. Meanwhile, a novel double optimum estimation strategy with objective fitness and penalty fitness is suggested to compute, respectively, the dominance trend of agents in feasible region and forbidden region. This bidirectional evolving with multiagents can not only effectively avoid the problem of determining penalty coefficient but also quickly converge to the global optimum nearby or on the constrained boundary. By examining the rapidity and veracity of Bi-DDEA across benchmark functions, the proposed method is shown to be effective.
AN ADAPTIVE TRUST REGION METHOD FOR EQUALITY CONSTRAINED OPTIMIZATION
Institute of Scientific and Technical Information of China (English)
ZHANG Juliang; ZHANG Xiangsun; ZHUO Xinjian
2003-01-01
In this paper, a trust region method for equality constrained optimization based on nondifferentiable exact penalty is proposed. In this algorithm, the trail step is characterized by computation of its normal component being separated from computation of its tangential component, i.e., only the tangential component of the trail step is constrained by trust radius while the normal component and trail step itself have no constraints. The other main characteristic of the algorithm is the decision of trust region radius. Here, the decision of trust region radius uses the information of the gradient of objective function and reduced Hessian. However, Maratos effect will occur when we use the nondifferentiable exact penalty function as the merit function. In order to obtain the superlinear convergence of the algorithm, we use the twice order correction technique. Because of the speciality of the adaptive trust region method, we use twice order correction when p = 0 (the definition is as in Section 2) and this is different from the traditional trust region methods for equality constrained optimization. So the computation of the algorithm in this paper is reduced. What is more, we can prove that the algorithm is globally and superlinearly convergent.
Observation of a Discrete Time Crystal
Zhang, J; Kyprianidis, A; Becker, P; Lee, A; Smith, J; Pagano, G; Potirniche, I -D; Potter, A C; Vishwanath, A; Yao, N Y; Monroe, C
2016-01-01
Spontaneous symmetry breaking is a fundamental concept in many areas of physics, ranging from cosmology and particle physics to condensed matter. A prime example is the breaking of spatial translation symmetry, which underlies the formation of crystals and the phase transition from liquid to solid. Analogous to crystals in space, the breaking of translation symmetry in time and the emergence of a "time crystal" was recently proposed, but later shown to be forbidden in thermal equilibrium. However, non-equilibrium Floquet systems subject to a periodic drive can exhibit persistent time-correlations at an emergent sub-harmonic frequency. This new phase of matter has been dubbed a "discrete time crystal" (DTC). Here, we present the first experimental observation of a discrete time crystal, in an interacting spin chain of trapped atomic ions. We apply a periodic Hamiltonian to the system under many-body localization (MBL) conditions, and observe a sub-harmonic temporal response that is robust to external perturbat...
Controlling hopf bifurcations: Discrete-time systems
Directory of Open Access Journals (Sweden)
Guanrong Chen
2000-01-01
Full Text Available Bifurcation control has attracted increasing attention in recent years. A simple and unified state-feedback methodology is developed in this paper for Hopf bifurcation control for discrete-time systems. The control task can be either shifting an existing Hopf bifurcation or creating a new Hopf bifurcation. Some computer simulations are included to illustrate the methodology and to verify the theoretical results.
Evolutionary pattern search algorithms for unconstrained and linearly constrained optimization
Energy Technology Data Exchange (ETDEWEB)
HART,WILLIAM E.
2000-06-01
The authors describe a convergence theory for evolutionary pattern search algorithms (EPSAs) on a broad class of unconstrained and linearly constrained problems. EPSAs adaptively modify the step size of the mutation operator in response to the success of previous optimization steps. The design of EPSAs is inspired by recent analyses of pattern search methods. The analysis significantly extends the previous convergence theory for EPSAs. The analysis applies to a broader class of EPSAs,and it applies to problems that are nonsmooth, have unbounded objective functions, and which are linearly constrained. Further, they describe a modest change to the algorithmic framework of EPSAs for which a non-probabilistic convergence theory applies. These analyses are also noteworthy because they are considerably simpler than previous analyses of EPSAs.
Optimal Constrained Resource Allocation Strategies under Low Risk Circumstances
Andreica, Mugurel Ionut; Visan, Costel
2009-01-01
In this paper we consider multiple constrained resource allocation problems, where the constraints can be specified by formulating activity dependency restrictions or by using game-theoretic models. All the problems are focused on generic resources, with a few exceptions which consider financial resources in particular. The problems consider low-risk circumstances and the values of the uncertain variables which are used by the algorithms are the expected values of the variables. For each of the considered problems we propose novel algorithmic solutions for computing optimal resource allocation strategies. The presented solutions are optimal or near-optimal from the perspective of their time complexity. The considered problems have applications in a broad range of domains, like workflow scheduling in industry (e.g. in the mining and metallurgical industry) or the financial sector, motion planning, facility location and data transfer or job scheduling and resource management in Grids, clouds or other distribute...
Discrete-time control system design with applications
Rabbath, C A
2014-01-01
This book presents practical techniques of discrete-time control system design. In general, the design techniques lead to low-order dynamic compensators that ensure satisfactory closed-loop performance for a wide range of sampling rates. The theory is given in the form of theorems, lemmas, and propositions. The design of the control systems is presented as step-by-step procedures and algorithms. The proposed feedback control schemes are applied to well-known dynamic system models. This book also discusses: Closed-loop performance of generic models of mobile robot and airborne pursuer dynamic systems under discrete-time feedback control with limited computing capabilities Concepts of discrete-time models and sampled-data models of continuous-time systems, for both single- and dual-rate operation Local versus global digital redesign Optimal, closed-loop digital redesign methods Plant input mapping design Generalized holds and samplers for use in feedback control loops, Numerical simulation of fixed-point arithm...
Adaptive Multi-Agent Systems for Constrained Optimization
Macready, William; Bieniawski, Stefan; Wolpert, David H.
2004-01-01
Product Distribution (PD) theory is a new framework for analyzing and controlling distributed systems. Here we demonstrate its use for distributed stochastic optimization. First we review one motivation of PD theory, as the information-theoretic extension of conventional full-rationality game theory to the case of bounded rational agents. In this extension the equilibrium of the game is the optimizer of a Lagrangian of the (probability distribution of) the joint state of the agents. When the game in question is a team game with constraints, that equilibrium optimizes the expected value of the team game utility, subject to those constraints. The updating of the Lagrange parameters in the Lagrangian can be viewed as a form of automated annealing, that focuses the MAS more and more on the optimal pure strategy. This provides a simple way to map the solution of any constrained optimization problem onto the equilibrium of a Multi-Agent System (MAS). We present computer experiments involving both the Queen s problem and K-SAT validating the predictions of PD theory and its use for off-the-shelf distributed adaptive optimization.
Asynchronous parallel generating set search for linearly-constrained optimization.
Energy Technology Data Exchange (ETDEWEB)
Kolda, Tamara G.; Griffin, Joshua; Lewis, Robert Michael
2007-04-01
We describe an asynchronous parallel derivative-free algorithm for linearly-constrained optimization. Generating set search (GSS) is the basis of ourmethod. At each iteration, a GSS algorithm computes a set of search directionsand corresponding trial points and then evaluates the objective function valueat each trial point. Asynchronous versions of the algorithm have been developedin the unconstrained and bound-constrained cases which allow the iterations tocontinue (and new trial points to be generated and evaluated) as soon as anyother trial point completes. This enables better utilization of parallel resourcesand a reduction in overall runtime, especially for problems where the objec-tive function takes minutes or hours to compute. For linearly-constrained GSS,the convergence theory requires that the set of search directions conform to the3 nearby boundary. The complexity of developing the asynchronous algorithm forthe linearly-constrained case has to do with maintaining a suitable set of searchdirections as the search progresses and is the focus of this research. We describeour implementation in detail, including how to avoid function evaluations bycaching function values and using approximate look-ups. We test our imple-mentation on every CUTEr test problem with general linear constraints and upto 1000 variables. Without tuning to individual problems, our implementationwas able to solve 95% of the test problems with 10 or fewer variables, 75%of the problems with 11-100 variables, and nearly half of the problems with100-1000 variables. To the best of our knowledge, these are the best resultsthat have ever been achieved with a derivative-free method. Our asynchronousparallel implementation is freely available as part of the APPSPACK software.4
Iterative Dynamic Diversity Evolutionary Algorithm for Constrained Optimization
Institute of Scientific and Technical Information of China (English)
GAO Wei-Shang; SHAO Cheng
2014-01-01
Evolutionary algorithms (EAs) were shown to be effective for complex constrained optimization problems. However, inflexible exploration in general EAs would lead to losing the global optimum nearby the ill-convergence regions. In this paper, we propose an iterative dynamic diversity evolutionary algorithm (IDDEA) with contractive subregions guiding exploitation through local extrema to the global optimum in suitable steps. In IDDEA, a novel optimum estimation strategy with multi-agents evolving diversely is suggested to eﬃciently compute dominance trend and establish a subregion. In addition, a subregion converging iteration is designed to redistrict a smaller subregion in current subregion for next iteration, which is based on a special dominance estimation scheme. Meanwhile, an infimum penalty function is embedded into IDDEA to judge agents and penalize adaptively the unfeasible agents with the lowest fitness of feasible agents. Furthermore, several engineering design optimization problems taken from the specialized literature are successfully solved by the present algorithm with high reliable solutions.
A dynamic hybrid framework for constrained evolutionary optimization.
Wang, Yong; Cai, Zixing
2012-02-01
Based on our previous work, this paper presents a dynamic hybrid framework, called DyHF, for solving constrained optimization problems. This framework consists of two major steps: global search model and local search model. In the global and local search models, differential evolution serves as the search engine, and Pareto dominance used in multiobjective optimization is employed to compare the individuals in the population. Unlike other existing methods, the above two steps are executed dynamically according to the feasibility proportion of the current population in this paper, with the purpose of reasonably distributing the computational resource for the global and local search during the evolution. The performance of DyHF is tested on 22 benchmark test functions. The experimental results clearly show that the overall performance of DyHF is highly competitive with that of a number of state-of-the-art approaches from the literature.
Total energy control system autopilot design with constrained parameter optimization
Ly, Uy-Loi; Voth, Christopher
1990-01-01
A description is given of the application of a multivariable control design method (SANDY) based on constrained parameter optimization to the design of a multiloop aircraft flight control system. Specifically, the design method is applied to the direct synthesis of a multiloop AFCS inner-loop feedback control system based on total energy control system (TECS) principles. The design procedure offers a structured approach for the determination of a set of stabilizing controller design gains that meet design specifications in closed-loop stability, command tracking performance, disturbance rejection, and limits on control activities. The approach can be extended to a broader class of multiloop flight control systems. Direct tradeoffs between many real design goals are rendered systematic by proper formulation of the design objectives and constraints. Satisfactory designs are usually obtained in few iterations. Performance characteristics of the optimized TECS design have been improved, particularly in the areas of closed-loop damping and control activity in the presence of turbulence.
Nonlinearly-constrained optimization using asynchronous parallel generating set search.
Energy Technology Data Exchange (ETDEWEB)
Griffin, Joshua D.; Kolda, Tamara Gibson
2007-05-01
Many optimization problems in computational science and engineering (CS&E) are characterized by expensive objective and/or constraint function evaluations paired with a lack of derivative information. Direct search methods such as generating set search (GSS) are well understood and efficient for derivative-free optimization of unconstrained and linearly-constrained problems. This paper addresses the more difficult problem of general nonlinear programming where derivatives for objective or constraint functions are unavailable, which is the case for many CS&E applications. We focus on penalty methods that use GSS to solve the linearly-constrained problems, comparing different penalty functions. A classical choice for penalizing constraint violations is {ell}{sub 2}{sup 2}, the squared {ell}{sub 2} norm, which has advantages for derivative-based optimization methods. In our numerical tests, however, we show that exact penalty functions based on the {ell}{sub 1}, {ell}{sub 2}, and {ell}{sub {infinity}} norms converge to good approximate solutions more quickly and thus are attractive alternatives. Unfortunately, exact penalty functions are discontinuous and consequently introduce theoretical problems that degrade the final solution accuracy, so we also consider smoothed variants. Smoothed-exact penalty functions are theoretically attractive because they retain the differentiability of the original problem. Numerically, they are a compromise between exact and {ell}{sub 2}{sup 2}, i.e., they converge to a good solution somewhat quickly without sacrificing much solution accuracy. Moreover, the smoothing is parameterized and can potentially be adjusted to balance the two considerations. Since many CS&E optimization problems are characterized by expensive function evaluations, reducing the number of function evaluations is paramount, and the results of this paper show that exact and smoothed-exact penalty functions are well-suited to this task.
Distributed LQR control for discrete-time homogeneous systems
Wang, Wei; Zhang, Fangfang; Han, Chunyan
2016-11-01
This paper investigates the distributed linear quadratic regulation (LQR) controller design method for discrete-time homogeneous scalar systems. Based on the optimal centralised control theory, the existence condition for distributed optimal controller is firstly proposed. It shows that the globally optimal distributed controller is dependent on the structure of the penalty matrix. Such results can be used in consensus problems and used to find under which communication topology (may not be an all-to-all form) the optimal distributed controller exists. When the proposed condition cannot hold, a suboptimal design method with the aid of the decomposition of discrete algebraic Riccati equations and robustness of local controllers is proposed. The computation complexity and communication load for each subsystem are only dependent on the number of its neighbours.
Constrained Multi-Level Algorithm for Trajectory Optimization
Adimurthy, V.; Tandon, S. R.; Jessy, Antony; Kumar, C. Ravi
The emphasis on low cost access to space inspired many recent developments in the methodology of trajectory optimization. Ref.1 uses a spectral patching method for optimization, where global orthogonal polynomials are used to describe the dynamical constraints. A two-tier approach of optimization is used in Ref.2 for a missile mid-course trajectory optimization. A hybrid analytical/numerical approach is described in Ref.3, where an initial analytical vacuum solution is taken and gradually atmospheric effects are introduced. Ref.4 emphasizes the fact that the nonlinear constraints which occur in the initial and middle portions of the trajectory behave very nonlinearly with respect the variables making the optimization very difficult to solve in the direct and indirect shooting methods. The problem is further made complex when different phases of the trajectory have different objectives of optimization and also have different path constraints. Such problems can be effectively addressed by multi-level optimization. In the multi-level methods reported so far, optimization is first done in identified sub-level problems, where some coordination variables are kept fixed for global iteration. After all the sub optimizations are completed, higher-level optimization iteration with all the coordination and main variables is done. This is followed by further sub system optimizations with new coordination variables. This process is continued until convergence. In this paper we use a multi-level constrained optimization algorithm which avoids the repeated local sub system optimizations and which also removes the problem of non-linear sensitivity inherent in the single step approaches. Fall-zone constraints, structural load constraints and thermal constraints are considered. In this algorithm, there is only a single multi-level sequence of state and multiplier updates in a framework of an augmented Lagrangian. Han Tapia multiplier updates are used in view of their special role in
Chance-constrained optimization of demand response to price signals
DEFF Research Database (Denmark)
Dorini, Gianluca Fabio; Pinson, Pierre; Madsen, Henrik
2013-01-01
Household-based demand response is expected to play an increasing role in supporting the large scale integration of renewable energy generation in existing power systems and electricity markets. While the direct control of the consumption level of households is envisaged as a possibility, a credi......Household-based demand response is expected to play an increasing role in supporting the large scale integration of renewable energy generation in existing power systems and electricity markets. While the direct control of the consumption level of households is envisaged as a possibility......, a credible alternative is that of indirect control based on price signals to be sent to these end-consumers. A methodology is described here allowing to estimate in advance the potential response of flexible end-consumers to price variations, subsequently embedded in an optimal price-signal generator...... within a recursive least squares (RLS) framework using data measurable at the grid level, in an adaptive fashion. Optimal price signals are generated by embedding the FIR models within a chance-constrained optimization framework. The objective is to keep the price signal as unchanged as possible from...
A New Interpolation Approach for Linearly Constrained Convex Optimization
Espinoza, Francisco
2012-08-01
In this thesis we propose a new class of Linearly Constrained Convex Optimization methods based on the use of a generalization of Shepard\\'s interpolation formula. We prove the properties of the surface such as the interpolation property at the boundary of the feasible region and the convergence of the gradient to the null space of the constraints at the boundary. We explore several descent techniques such as steepest descent, two quasi-Newton methods and the Newton\\'s method. Moreover, we implement in the Matlab language several versions of the method, particularly for the case of Quadratic Programming with bounded variables. Finally, we carry out performance tests against Matab Optimization Toolbox methods for convex optimization and implementations of the standard log-barrier and active-set methods. We conclude that the steepest descent technique seems to be the best choice so far for our method and that it is competitive with other standard methods both in performance and empirical growth order.
Distributed Stochastic Approximation for Constrained and Unconstrained Optimization
Bianchi, Pascal
2011-01-01
In this paper, we analyze the convergence of a distributed Robbins-Monro algorithm for both constrained and unconstrained optimization in multi-agent systems. The algorithm searches local minima of a (nonconvex) objective function which is supposed to coincide with a sum of local utility functions of the agents. The algorithm under study consists of two steps: a local stochastic gradient descent at each agent and a gossip step that drives the network of agents to a consensus. It is proved that i) an agreement is achieved between agents on the value of the estimate, ii) the algorithm converges to the set of Kuhn-Tucker points of the optimization problem. The proof relies on recent results about differential inclusions. In the context of unconstrained optimization, intelligible sufficient conditions are provided in order to ensure the stability of the algorithm. In the latter case, we also provide a central limit theorem which governs the asymptotic fluctuations of the estimate. We illustrate our results in the...
Security Constrained Distributed Optimal Power Flow of Interconnected Power Systems
Institute of Scientific and Technical Information of China (English)
BINKOU Alhabib; YU Yixin
2008-01-01
The security constrained distributed optimal power flow (DOPF) of interconnected power systems is presented. The centralized OPF problem of the multi-area power systems is decomposed into independent DOPF subproblems, one for each area. The dynamic security region (DSR) to guarantee the transient stability constraints and static voltage stability region (SVSR) constraints, and line current limits are included as constraints. The solutions to the DOPF subproblems of the different areas are coordinated through a pricing mechanism until they converge to the centralized OPF solution. The nonlinear DOPF subproblem is solved by predictor-corrector interior point method (PCIPM). The IEEE three-area RTS-96 system is worked out in order to demonstrate the effectiveness of the proposed method.
Parallel Variable Distribution Algorithm for Constrained Optimization with Nonmonotone Technique
Directory of Open Access Journals (Sweden)
Congying Han
2013-01-01
Full Text Available A modified parallel variable distribution (PVD algorithm for solving large-scale constrained optimization problems is developed, which modifies quadratic subproblem QPl at each iteration instead of the QPl0 of the SQP-type PVD algorithm proposed by C. A. Sagastizábal and M. V. Solodov in 2002. The algorithm can circumvent the difficulties associated with the possible inconsistency of QPl0 subproblem of the original SQP method. Moreover, we introduce a nonmonotone technique instead of the penalty function to carry out the line search procedure with more flexibly. Under appropriate conditions, the global convergence of the method is established. In the final part, parallel numerical experiments are implemented on CUDA based on GPU (Graphics Processing unit.
Block-triangular preconditioners for PDE-constrained optimization
Rees, Tyrone
2010-11-26
In this paper we investigate the possibility of using a block-triangular preconditioner for saddle point problems arising in PDE-constrained optimization. In particular, we focus on a conjugate gradient-type method introduced by Bramble and Pasciak that uses self-adjointness of the preconditioned system in a non-standard inner product. We show when the Chebyshev semi-iteration is used as a preconditioner for the relevant matrix blocks involving the finite element mass matrix that the main drawback of the Bramble-Pasciak method-the appropriate scaling of the preconditioners-is easily overcome. We present an eigenvalue analysis for the block-triangular preconditioners that gives convergence bounds in the non-standard inner product and illustrates their competitiveness on a number of computed examples. Copyright © 2010 John Wiley & Sons, Ltd.
Early Universes with Effective Discrete Time
Baulieu, Laurent
2016-01-01
The mechanism for triggering the universe inflation could be that at very early periods the time variable was discrete instead of smooth. Alternatively, and perhaps equivalently, it could be the consequence that the metrics of the early universe was a strongly concentrated gravitational coherent state with very high frequency oscillations, allowing local pair creations by a generalisation to gravity of the Schwinger mechanism, perhaps by creation of black holes of masses superior to the Planck scale. The lattice spacing between two clicks in the discrete time picture corresponds to the inverse frequency of the gravitational coherent state in the other picture. In both cases, a much lower time than the Planck time might represent a new fundamental scale, giving new type of physics. To make possible a concrete estimation of the pair production probability, we propose that the oscillating coherent state metrics that defines this very early geometry minimises the Einstein gravity action coupled to interacting 1-,...
Discrete time queues with phase dependent arrivals
Daigle, J. N.; Lee, Y.; Magalhaes, M. N.
1994-02-01
The queueing behavior of many communication systems is well modeled by a queueing system in which time is slotted, and the number of entities that arrive during a slot is dependent upon the state of a discrete time, discrete state Markov chain. Techniques for analyzing such systems have appeared in the literature from time to time, but distributions have been presented in only rare instances. In this paper, we present the probability generating function (PGF) for joint and marginal buffer occupancy distributions of statistical time division multiplexing systems in this class. We discuss inversion of the PGF using discrete Fourier transforms, and also discuss a simple technique for obtaining moments of the queue length distribution. Numerical results, including queue length distributions for some special cases, are presented.
Multiplicative noise removal using variable splitting and constrained optimization.
Bioucas-Dias, José M; Figueiredo, Mário A T
2010-07-01
Multiplicative noise (also known as speckle noise) models are central to the study of coherent imaging systems, such as synthetic aperture radar and sonar, and ultrasound and laser imaging. These models introduce two additional layers of difficulties with respect to the standard Gaussian additive noise scenario: (1) the noise is multiplied by (rather than added to) the original image; (2) the noise is not Gaussian, with Rayleigh and Gamma being commonly used densities. These two features of multiplicative noise models preclude the direct application of most state-of-the-art algorithms, which are designed for solving unconstrained optimization problems where the objective has two terms: a quadratic data term (log-likelihood), reflecting the additive and Gaussian nature of the noise, plus a convex (possibly nonsmooth) regularizer (e.g., a total variation or wavelet-based regularizer/prior). In this paper, we address these difficulties by: (1) converting the multiplicative model into an additive one by taking logarithms, as proposed by some other authors; (2) using variable splitting to obtain an equivalent constrained problem; and (3) dealing with this optimization problem using the augmented Lagrangian framework. A set of experiments shows that the proposed method, which we name MIDAL (multiplicative image denoising by augmented Lagrangian), yields state-of-the-art results both in terms of speed and denoising performance.
Application of constrained optimization to active control of aeroelastic response
Newsom, J. R.; Mukhopadhyay, V.
1981-01-01
Active control of aeroelastic response is a complex in which the designer usually tries to satisfy many criteria which are often conflicting. To further complicate the design problem, the state space equations describing this type of control problem are usually of high order, involving a large number of states to represent the flexible structure and unsteady aerodynamics. Control laws based on the standard Linear-Quadratic-Gaussian (LQG) method are of the same high order as the aeroelastic plant. To overcome this disadvantage of the LQG mode, an approach developed for designing low order optimal control laws which uses a nonlinear programming algorithm to search for the values of the control law variables that minimize a composite performance index, was extended to the constrained optimization problem. The method involves searching for the values of the control law variables that minimize a basic performance index while satisfying several inequality constraints that describe the design criteria. The method is applied to gust load alleviation of a drone aircraft.
Robust integrated autopilot/autothrottle design using constrained parameter optimization
Ly, Uy-Loi; Voth, Christopher; Sanjay, Swamy
1990-01-01
A multivariable control design method based on constrained parameter optimization was applied to the design of a multiloop aircraft flight control system. Specifically, the design method is applied to the following: (1) direct synthesis of a multivariable 'inner-loop' feedback control system based on total energy control principles; (2) synthesis of speed/altitude-hold designs as 'outer-loop' feedback/feedforward control systems around the above inner loop; and (3) direct synthesis of a combined 'inner-loop' and 'outer-loop' multivariable control system. The design procedure offers a direct and structured approach for the determination of a set of controller gains that meet design specifications in closed-loop stability, command tracking performance, disturbance rejection, and limits on control activities. The presented approach may be applied to a broader class of multiloop flight control systems. Direct tradeoffs between many real design goals are rendered systematic by this method following careful problem formulation of the design objectives and constraints. Performance characteristics of the optimization design were improved over the current autopilot design on the B737-100 Transport Research Vehicle (TSRV) at the landing approach and cruise flight conditions; particularly in the areas of closed-loop damping, command responses, and control activity in the presence of turbulence.
Universal Denoising of Discrete-time Continuous-Amplitude Signals
Sivaramakrishnan, Kamakshi
2008-01-01
We consider the problem of reconstructing a discrete-time signal (sequence) with continuous-valued components corrupted by a known memoryless channel. When performance is measured using a per-symbol loss function satisfying mild regularity conditions, we develop a sequence of denoisers that, although independent of the distribution of the underlying `clean' sequence, is universally optimal in the limit of large sequence length. This sequence of denoisers is universal in the sense of performing as well as any sliding window denoising scheme which may be optimized for the underlying clean signal. Our results are initially developed in a ``semi-stochastic'' setting, where the noiseless signal is an unknown individual sequence, and the only source of randomness is due to the channel noise. It is subsequently shown that in the fully stochastic setting, where the noiseless sequence is a stationary stochastic process, our schemes universally attain optimum performance. The proposed schemes draw from nonparametric de...
Dong, Lu; Zhong, Xiangnan; Sun, Changyin; He, Haibo
2016-04-08
This paper presents the design of a novel adaptive event-triggered control method based on the heuristic dynamic programming (HDP) technique for nonlinear discrete-time systems with unknown system dynamics. In the proposed method, the control law is only updated when the event-triggered condition is violated. Compared with the periodic updates in the traditional adaptive dynamic programming (ADP) control, the proposed method can reduce the computation and transmission cost. An actor-critic framework is used to learn the optimal event-triggered control law and the value function. Furthermore, a model network is designed to estimate the system state vector. The main contribution of this paper is to design a new trigger threshold for discrete-time systems. A detailed Lyapunov stability analysis shows that our proposed event-triggered controller can asymptotically stabilize the discrete-time systems. Finally, we test our method on two different discrete-time systems, and the simulation results are included.
Robust stability of discrete-time nonlinear system with time-delay
Institute of Scientific and Technical Information of China (English)
LIU Xin-ge; WU Min
2005-01-01
The robustly asymptotical stability problem for discrete-time nonlinear systems with time-delay was investigated. Positive definite matrix are constructed through Lyapunov functional. With the identity transform, property of matrix inverse and S-procedure, a new sufficient condition independent of the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is established. With Schur complement, another equivalent sufficient condition for robust stability of discrete-time nonlinear systems with time-delay is given. Finally, a sufficient condition dependent on the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is obtained. A unified approach is used to cast the robust stability problem into a convex optimization involving linear matrix inequalities.
A collective neurodynamic optimization approach to bound-constrained nonconvex optimization.
Yan, Zheng; Wang, Jun; Li, Guocheng
2014-07-01
This paper presents a novel collective neurodynamic optimization method for solving nonconvex optimization problems with bound constraints. First, it is proved that a one-layer projection neural network has a property that its equilibria are in one-to-one correspondence with the Karush-Kuhn-Tucker points of the constrained optimization problem. Next, a collective neurodynamic optimization approach is developed by utilizing a group of recurrent neural networks in framework of particle swarm optimization by emulating the paradigm of brainstorming. Each recurrent neural network carries out precise constrained local search according to its own neurodynamic equations. By iteratively improving the solution quality of each recurrent neural network using the information of locally best known solution and globally best known solution, the group can obtain the global optimal solution to a nonconvex optimization problem. The advantages of the proposed collective neurodynamic optimization approach over evolutionary approaches lie in its constraint handling ability and real-time computational efficiency. The effectiveness and characteristics of the proposed approach are illustrated by using many multimodal benchmark functions.
Institute of Scientific and Technical Information of China (English)
吴建辉; 章兢; 刘朝华
2013-01-01
Aiming at discrete-time chaotic systems, the neural network sliding mode equivalent control method based on a hybrid algorithm which combines the particle swarm optimization algorithm and the Powell search method(Powell-PSO algorithm) is proposed. When taking the output of BP neural network as the coefficient of the switch part of sliding mode equivalent control, the method effectively overcomes the chattering phenomenon of conventional sliding mode equivalent control. The Powell-PSO algorithm is applied to globally optimize the parameters of neural network sliding mode controller and then to control discrete-time chaotic systems more effectively. Simulation results show that the method requires no knowledge about the precise mathematical model of discrete-time chaotic systems with fast response speed, high control precision and strong anti-interference ability.% 针对离散混沌系统，提出一种基于融合Powell法的粒子群优化策略(Powell-PSO算法)的神经滑模等效控制方法。该方法通过将BP神经网络的输出作为滑模等效控制的切换部分的系数，有效地克服了传统滑模等效控制的抖振现象；利用Powell-PSO算法对神经滑模控制器的参数进行全局优化，提高了离散混沌系统的控制品质。仿真实验结果表明，所提出的方法无需了解离散混沌系统精确模型，具有响应速度快、控制精度高以及抗干扰能力强的优点。
Geometry parameterization and multidisciplinary constrained optimization of coronary stents.
Pant, Sanjay; Bressloff, Neil W; Limbert, Georges
2012-01-01
Coronary stents are tubular type scaffolds that are deployed, using an inflatable balloon on a catheter, most commonly to recover the lumen size of narrowed (diseased) arterial segments. A common differentiating factor between the numerous stents used in clinical practice today is their geometric design. An ideal stent should have high radial strength to provide good arterial support post-expansion, have high flexibility for easy manoeuvrability during deployment, cause minimal injury to the artery when being expanded and, for drug eluting stents, should provide adequate drug in the arterial tissue. Often, with any stent design, these objectives are in competition such that improvement in one objective is a result of trade-off in others. This study proposes a technique to parameterize stent geometry, by varying the shape of circumferential rings and the links, and assess performance by modelling the processes of balloon expansion and drug diffusion. Finite element analysis is used to expand each stent (through balloon inflation) into contact with a representative diseased coronary artery model, followed by a drug release simulation. Also, a separate model is constructed to measure stent flexibility. Since the computational simulation time for each design is very high (approximately 24 h), a Gaussian process modelling approach is used to analyse the design space corresponding to the proposed parameterization. Four objectives to assess recoil, stress distribution, drug distribution and flexibility are set up to perform optimization studies. In particular, single objective constrained optimization problems are set up to improve the design relative to the baseline geometry-i.e. to improve one objective without compromising the others. Improvements of 8, 6 and 15% are obtained individually for stress, drug and flexibility metrics, respectively. The relative influence of the design features on each objective is quantified in terms of main effects, thereby suggesting the
APPROXIMATION LAWS OF DISCRETE-TIME VARIABLE STRUCTURE CONTROL SYSTEMS
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Two new approximation laws of sliding mode for discrete-time variable structure control systems are proposed in this paper. By applying the proposed approximation laws of sliding mode to discrete-time variable structure control systems,the stability of origin can be guaranteed,and the chattering along the switching surface caused by discrete-time variable structure control can be restrained effectively. In designing of these approximation laws,the problem that the system control input is restricted is also ...
Depletion mapping and constrained optimization to support managing groundwater extraction
Fienen, Michael N.; Bradbury, Kenneth R.; Kniffin, Maribeth; Barlow, Paul M.
2017-01-01
Groundwater models often serve as management tools to evaluate competing water uses including ecosystems, irrigated agriculture, industry, municipal supply, and others. Depletion potential mapping—showing the model-calculated potential impacts that wells have on stream baseflow - can form the basis for multiple potential management approaches in an oversubscribed basin. Specific management approaches can include scenarios proposed by stakeholders, systematic changes in well pumping based on depletion potential, and formal constrained optimization, which can be used to quantify the tradeoff between water use and stream baseflow. Variables such as the maximum amount of reduction allowed in each well and various groupings of wells using, for example, K-means clustering considering spatial proximity and depletion potential are considered. These approaches provide a potential starting point and guidance for resource managers and stakeholders to make decisions about groundwater management in a basin, spreading responsibility in different ways. We illustrate these approaches in the Little Plover River basin in central Wisconsin, United States—home to a rich agricultural tradition, with farmland and urban areas both in close proximity to a groundwater-dependent trout stream. Groundwater withdrawals have reduced baseflow supplying the Little Plover River below a legally established minimum. The techniques in this work were developed in response to engaged stakeholders with various interests and goals for the basin. They sought to develop a collaborative management plan at a watershed scale that restores the flow rate in the river in a manner that incorporates principles of shared governance and results in effective and minimally disruptive changes in groundwater extraction practices.
Linear discrete-time Pareto-Nash-Stackelberg control problem and principles for its solving
Directory of Open Access Journals (Sweden)
Valeriu Ungureanu
2013-04-01
Full Text Available A direct-straightforward method for solving linear discrete-time optimal control problem is applied to solve control problem of a linear discrete-time system as a mixture of multi-criteria Stackelberg and Nash games. For simplicity, the exposure starts with the simplest case of linear discrete-time optimal control problem and, by sequential considering of more general cases, investigation finalizes with the highlighted Pareto-Nash-Stackelberg and set valued control problems. Different principles of solving are compared and their equivalence is proved. Mathematics Subject Classification 2010: 49K21, 49N05, 93C05, 93C55, 90C05, 90C29, 91A10, 91A20, 91A44, 91A50.
Wei, Qinglai; Liu, Derong; Lin, Qiao
2016-08-03
In this paper, a novel local value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon optimal control problems for discrete-time nonlinear systems. The focuses of this paper are to study admissibility properties and the termination criteria of discrete-time local value iteration ADP algorithms. In the discrete-time local value iteration ADP algorithm, the iterative value functions and the iterative control laws are both updated in a given subset of the state space in each iteration, instead of the whole state space. For the first time, admissibility properties of iterative control laws are analyzed for the local value iteration ADP algorithm. New termination criteria are established, which terminate the iterative local ADP algorithm with an admissible approximate optimal control law. Finally, simulation results are given to illustrate the performance of the developed algorithm.
Institute of Scientific and Technical Information of China (English)
池荣虎; 侯忠生
2007-01-01
On the basis of a new dynamic linearization technology along the iteration axis, a dual-stage optimal iterative learning control is presented for nonlinear and non-affine discrete-time systems. Dual-stage indicates that two optimal learning stages are designed respectively to improve control input sequence and the learning gain iteratively. The main feature is that the controller design and convergence analysis only depend on the I/O data of the dynamical system. In other words, we can easily select the control parameters without knowing any other knowledge of the system. Simulation study illustrates the geometrical convergence of the presented method along the iteration axis, in which an example of freeway traffic iterative learning control is noteworthy for its intrinsic engineering importance.
Kanagaraj, G.; Ponnambalam, S. G.; Jawahar, N.; Mukund Nilakantan, J.
2014-10-01
This article presents an effective hybrid cuckoo search and genetic algorithm (HCSGA) for solving engineering design optimization problems involving problem-specific constraints and mixed variables such as integer, discrete and continuous variables. The proposed algorithm, HCSGA, is first applied to 13 standard benchmark constrained optimization functions and subsequently used to solve three well-known design problems reported in the literature. The numerical results obtained by HCSGA show competitive performance with respect to recent algorithms for constrained design optimization problems.
Nguyen, Q. H.; Choi, S. B.
2012-01-01
This research focuses on optimal design of different types of magnetorheological brakes (MRBs), from which an optimal selection of MRB types is identified. In the optimization, common types of MRB such as disc-type, drum-type, hybrid-types, and T-shaped type are considered. The optimization problem is to find the optimal value of significant geometric dimensions of the MRB that can produce a maximum braking torque. The MRB is constrained in a cylindrical volume of a specific radius and length. After a brief description of the configuration of MRB types, the braking torques of the MRBs are derived based on the Herschel-Bulkley model of the MR fluid. The optimal design of MRBs constrained in a specific cylindrical volume is then analysed. The objective of the optimization is to maximize the braking torque while the torque ratio (the ratio of maximum braking torque and the zero-field friction torque) is constrained to be greater than a certain value. A finite element analysis integrated with an optimization tool is employed to obtain optimal solutions of the MRBs. Optimal solutions of MRBs constrained in different volumes are obtained based on the proposed optimization procedure. From the results, discussions on the optimal selection of MRB types depending on constrained volumes are given.
Absolute Stability of Discrete-Time Systems with Delay
Directory of Open Access Journals (Sweden)
Medina Rigoberto
2008-01-01
Full Text Available We investigate the stability of nonlinear nonautonomous discrete-time systems with delaying arguments, whose linear part has slowly varying coefficients, and the nonlinear part has linear majorants. Based on the "freezing" technique to discrete-time systems, we derive explicit conditions for the absolute stability of the zero solution of such systems.
Self-powered discrete time piezoelectric vibration damper
Konak, Michael J.; Powlesland, Ian G.; van der Velden, Stephen P.; Galea, Stephen C.
1997-11-01
Structural vibration suppression is of great interest to the aircraft industry as it can reduce the amplitude of excessive vibration in lightly damped panels caused by conditions in their operational environment. One technique of suppressing vibration is to use passive damping techniques such as constrained layered damping incorporating viscoelastic materials. However these techniques may not be acceptable because of weight concerns or extreme temperature variations. Over the past decade much work has been done by researchers on the use of piezoelectric ceramic devices, using passive and active techniques, for structural vibration suppression. The passive piezoelectric damping devices consist of a piezoelectric element and either a resistive or resonant shunt. The resonant circuit shunt, which is analogous to a mechanical vibration absorber, gives better vibration reduction compared to the resistor shunt. This device requires a large value of inductance in order to be tuned to a particular structural vibration mode. A large value inductor can be made by a using a gyrator type circuit however the circuit needs external power. A method of vibration control using a discrete time controller and piezoelectric devices is presented. That is, this paper describes the concept of a self-powered discrete time piezoelectric vibration damper which does not need tuning to the structural resonant frequency and is powered by piezoelectric elements, i.e. does not need an external power supply. This device is referred to as a strain amplitude minimization patch (STAMP) damper. A brief description of the theory used and of the scheme is presented. Also the operation of this device is compared with other 'passive' techniques, involving piezoelectric elements, such as the resistive passive damper and the parallel resonant passive damper cases. Experimental results presented, on a cantilevered beam, demonstrate the concept and show that the device, even in its current underdeveloped
Fast Energy Minimization of large Polymers Using Constrained Optimization
Energy Technology Data Exchange (ETDEWEB)
Todd D. Plantenga
1998-10-01
A new computational technique is described that uses distance constraints to calculate empirical potential energy minima of partially rigid molecules. A constrained minimuzation algorithm that works entirely in Cartesian coordinates is used. The algorithm does not obey the constraints until convergence, a feature that reduces ill-conditioning and allows constrained local minima to be computed more quickly than unconstrained minima. Computational speedup exceeds the 3-fold factor commonly obtained in constained molecular dynamics simulations, where the constraints must be strictly obeyed at all times.
Institute of Scientific and Technical Information of China (English)
林小峰; 曹怒云; 宋绍剑
2014-01-01
针对实际工业常见的定点跟踪控制问题，通过数学变换，将原系统最优跟踪控制问题转化为新系统最优调节问题，以跟踪误差作为新系统的状态量，引入ε-自适应动态规划算法(ε-ADP)求解HJB方程，并以两个BP神经网络分别用于近似性能指标函数和最优控制，从而得到ε-最优跟踪控制。仿真实验表明，所设计的控制器可以在有限时间内将状态跟踪到目标值，并使得性能指标函数近似最优。%In order to deal with the common fix-point tracking control problems in actual industrial systems, a mathematical transformation is developed to change the original system optimal tracking control problem to an optimal regulator problem of a new system. The state variables of the new sys-tem are the tracking error. ε-adaptive dynamic programming (ε-ADP) is used to solve HJB equation while two BP neural networks are used to approximate the performance index function and optimal control. Thus ε-optimal tracking control is obtained. Simulation results show that the controller de-signed can track a state to the target and make the performance index function converges to optimal.
Variable structure control with sliding mode prediction for discrete-time nonlinear systems
Institute of Scientific and Technical Information of China (English)
Lingfei XIAO; Hongye SU; Xiaoyu ZHANG; Jian CHU
2006-01-01
A new variable structure control algorithm based on sliding mode prediction for a class of discrete-time nonlinear systems is presented. By employing a special model to predict future sliding mode value, and combining feedback correction and receding horizon optimization methods which are extensively applied on predictive control strategy, a discrete-time variable structure control law is constructed. The closed-loop systems are proved to have robustness to uncertainties with unspecified boundaries. Numerical simulation and pendulum experiment results illustrate that the closed-loop systems possess desired performance, such as strong robustness, fast convergence and chattering elimination.
Somasundaram, P.; Muthuselvan, N. B.
This paper presents new computationally efficient improved Particle Swarm algorithms for solving Security Constrained Optimal Power Flow (SCOPF) in power systems with the inclusion of FACTS devices. The proposed algorithms are developed based on the combined application of Gaussian and Cauchy Probability distribution functions incorporated in Particle Swarm Optimization (PSO). The power flow algorithm with the presence of Static Var Compensator (SVC) Thyristor Controlled Series Capacitor (TCSC) and Unified Power Flow Controller (UPFC), has been formulated and solved. The proposed algorithms are tested on standard IEEE 30-bus system. The analysis using PSO and modified PSO reveals that the proposed algorithms are relatively simple, efficient, reliable and suitable for real-time applications. And these algorithms can provide accurate solution with fast convergence and have the potential to be applied to other power engineering problems.
A hybrid multi-swarm particle swarm optimization to solve constrained optimization problems
Institute of Scientific and Technical Information of China (English)
Yong WANG; Zixing CAI
2009-01-01
In the real-world applications, most optimization problems are subject to different types of constraints. These problems are known as constrained optimization problems (COPs). Solving COPs is a very important area in the optimization field. In this paper, a hybrid multi-swarm particle swarm optimization (HMPSO) is proposed to deal with COPs. This method adopts a parallel search operator in which the current swarm is partitioned into several subswarms and particle swarm optimization (PSO) is severed as the search engine for each sub-swarm. Moreover, in order to explore more promising regions of the search space, differential evolution (DE) is incorporated to improve the personal best of each particle. First, the method is tested on 13 benchmark test functions and compared with three stateof-the-art approaches. The simulation results indicate that the proposed HMPSO is highly competitive in solving the 13 benchmark test functions. Afterward, the effectiveness of some mechanisms proposed in this paper and the effect of the parameter setting were validated by various experiments. Finally, HMPSO is further applied to solve 24 benchmark test functions collected in the 2006 IEEE Congress on Evolutionary Computation (CEC2006) and the experimental results indicate that HMPSO is able to deal with 22 test functions.
The limitations of discrete-time approaches to continuous-time contagion dynamics
Fennell, Peter G; Gleeson, James P
2016-01-01
Continuous-time Markov process models of contagions are widely studied, not least because of their utility in predicting the evolution of real-world contagions and in formulating control measures. It is often the case, however, that discrete-time approaches are employed to analyze such models or to simulate them numerically. In such cases, time is discretized into uniform steps and transition rates between states are replaced by transition probabilities. In this paper, we illustrate potential limitations to this approach. We show how discretizing time leads to a restriction on the values of the model parameters that can accurately be studied. We examine numerical simulation schemes employed in the literature, showing how synchronous-type updating schemes can bias discrete-time formalisms when compared against continuous-time formalisms. Event-based simulations, such as the Gillespie algorithm, are proposed as optimal simulation schemes both in terms of replicating the continuous-time process and computational...
Large-Scale PDE-Constrained Optimization in Applications
Hazra, Subhendu Bikash
2010-01-01
Dealing with the simulation based optimization problems, this title presents the systematic development of the methods and algorithms. It covers the time dependent optimization problems with applications in environmental engineering, and also deals with steady state optimization problems, in which the PDEs are solved
A Composite Algorithm for Mixed Integer Constrained Nonlinear Optimization.
1980-01-01
algorithm (FLEX) developed by Paviani and Himmelblau [53] is a direct search algorithm for constrained, nonlinear problems. It uses a variation on the...given in an appendix to Himmelblau [32]. Two changes were made to the program as listed in the rcference. Between card number 1340 and 1350 the...1972, pp. 293-308 (32] Himmelblau , D. M., Applied Nonlinear Programming, McGraw-Hill, 1972 (33] Himmelblau , D. M., "A Uniform Evaluation of Unconstrained
Approximation law for discrete-time variable structure control systems
Institute of Scientific and Technical Information of China (English)
Yan ZHENG; Yuanwei JING
2006-01-01
Two approximation laws of sliding mode for discrete-time variable structure control systems are proposed to overcome the limitations of the exponential approximation law and the variable rate approximation law. By applying the proposed approximation laws of sliding mode to discrete-time variable structure control systems, the stability of origin can be guaranteed, and the chattering along the switching surface caused by discrete-time variable structure control can be restrained effectively. In designing of approximation laws, the problem that the system control input is restricted is also considered, which is very important in practical systems. Finally a simulation example shows the effectiveness of the two approximation laws proposed.
Losslessness of Nonlinear Stochastic Discrete-Time Systems
Directory of Open Access Journals (Sweden)
Xikui Liu
2015-01-01
Full Text Available This paper will study stochastic losslessness theory for nonlinear stochastic discrete-time systems, which are expressed by the Itô-type difference equations. A necessary and sufficient condition is developed for a nonlinear stochastic discrete-time system to be lossless. By the stochastic lossless theory, we show that a nonlinear stochastic discrete-time system can be lossless via state feedback if and only if it has relative degree 0,…,0 and lossless zero dynamics. The effectiveness of the proposed results is illustrated by a numerical example.
Neural network for constrained nonsmooth optimization using Tikhonov regularization.
Qin, Sitian; Fan, Dejun; Wu, Guangxi; Zhao, Lijun
2015-03-01
This paper presents a one-layer neural network to solve nonsmooth convex optimization problems based on the Tikhonov regularization method. Firstly, it is shown that the optimal solution of the original problem can be approximated by the optimal solution of a strongly convex optimization problems. Then, it is proved that for any initial point, the state of the proposed neural network enters the equality feasible region in finite time, and is globally convergent to the unique optimal solution of the related strongly convex optimization problems. Compared with the existing neural networks, the proposed neural network has lower model complexity and does not need penalty parameters. In the end, some numerical examples and application are given to illustrate the effectiveness and improvement of the proposed neural network. Copyright © 2014 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Mahdi Sohrabi-Haghighat
2014-06-01
Full Text Available In this paper, a new algorithm based on SQP method is presented to solve the nonlinear inequality constrained optimization problem. As compared with the other existing SQP methods, per single iteration, the basic feasible descent direction is computed by solving at most two equality constrained quadratic programming. Furthermore, there is no need for any auxiliary problem to obtain the coefficients and update the parameters. Under some suitable conditions, the global and superlinear convergence are shown. Keywords: Global convergence, Inequality constrained optimization, Nonlinear programming problem, SQP method, Superlinear convergence rate.
Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem
Chen, Wei
2015-07-01
In this paper, we discuss the portfolio optimization problem with real-world constraints under the assumption that the returns of risky assets are fuzzy numbers. A new possibilistic mean-semiabsolute deviation model is proposed, in which transaction costs, cardinality and quantity constraints are considered. Due to such constraints the proposed model becomes a mixed integer nonlinear programming problem and traditional optimization methods fail to find the optimal solution efficiently. Thus, a modified artificial bee colony (MABC) algorithm is developed to solve the corresponding optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed model and the corresponding algorithm.
Geometric Approach to Lie Symmetry of Discrete Time Toda Equation
Institute of Scientific and Technical Information of China (English)
JIA Xiao-Yu; WANG Na
2009-01-01
By using the extended Harrison and Estabrook geometric approach,we investigate the Lie symmetry of discrete time Toda equation from the geometric point of view.Its one-dimensional continuous symmetry group is presented.
On periodic orbits in discrete-time cascade systems
Directory of Open Access Journals (Sweden)
Huimin Li
2006-01-01
Full Text Available We present some results on existence, minimum period, number of periodic orbits, and stability of periodic orbits in discrete-time cascade systems. Some examples are presented to illustrate these results.
Efficient Genetic Algorithm sets for optimizing constrained building design problem
National Research Council Canada - National Science Library
Wright, Jonathan; Alajmi, Ali
2016-01-01
.... This requires trying large possible solutions which need heuristic optimization algorithms. A comparison between several heuristic optimization algorithms showed that Genetic Algorithm (GA) is robust on getting the optimum(s) simulation ( Wetter and Wright, 2004; Brownlee et al., 2011; Bichiou and Krarti, 2011; Sahu et al., 2012 ) while the building simulat...
W-Stability of Multistable Nonlinear Discrete-Time Systems
Directory of Open Access Journals (Sweden)
Zhishuai Ding
2012-01-01
Full Text Available Motivated by the importance and application of discrete dynamical systems, this paper presents a new Lyapunov characterization which is an extension of conventional Lyapunov characterization for multistable discrete-time nonlinear systems. Based on a new type stability notion of W-stability introduced by D. Efimov, the estimates of solution and the Lyapunov stability theorem and converse theorem are proposed for multi-stable discrete-time nonlinear systems.
Absolute Stability of Discrete-Time Systems with Delay
Directory of Open Access Journals (Sweden)
Rigoberto Medina
2008-02-01
Full Text Available We investigate the stability of nonlinear nonautonomous discrete-time systems with delaying arguments, whose linear part has slowly varying coefficients, and the nonlinear part has linear majorants. Based on the Ã¢Â€ÂœfreezingÃ¢Â€Â technique to discrete-time systems, we derive explicit conditions for the absolute stability of the zero solution of such systems.
Approximate Controllability of Abstract Discrete-Time Systems
Directory of Open Access Journals (Sweden)
Cuevas Claudio
2010-01-01
Full Text Available Approximate controllability for semilinear abstract discrete-time systems is considered. Specifically, we consider the semilinear discrete-time system , , where are bounded linear operators acting on a Hilbert space , are -valued bounded linear operators defined on a Hilbert space , and is a nonlinear function. Assuming appropriate conditions, we will show that the approximate controllability of the associated linear system implies the approximate controllability of the semilinear system.
Pfrommer, Julius
2015-01-01
The Max-Sum algorithm, an instance of the Generalized Distributive Law family, is known to solve Distributed Constraint Optimization Problems (DCOP) where the summed utility functions of interacting agents are maximized. However, Max-Sum relies on available communication channels between all agents that partake in a utility function. We present a generalization of Max-Sum that solves DCOP exactly in situations where the communication network layout does not match the agents' utility inter-dep...
Optimal charging profiles for mechanically constrained lithium-ion batteries
Energy Technology Data Exchange (ETDEWEB)
Suthar, B; Ramadesigan, V; De, S; Braatz, RD; Subramanian, VR
2014-01-01
The cost and safety related issues of lithium-ion batteries require intelligent charging profiles that can efficiently utilize the battery. This paper illustrates the application of dynamic optimization in obtaining the optimal current profile for charging a lithium-ion battery using a single-particle model while incorporating intercalation-induced stress generation. In this paper, we focus on the problem of maximizing the charge stored in a given time while restricting the development of stresses inside the particle. Conventional charging profiles for lithium-ion batteries (e.g., constant current followed by constant voltage) were not derived by considering capacity fade mechanisms. These charging profiles are not only inefficient in terms of lifetime usage of the batteries but are also slower since they do not exploit the changing dynamics of the system. Dynamic optimization based approaches have been used to derive optimal charging and discharging profiles with different objective functions. The progress made in understanding the capacity fade mechanisms has paved the way for inclusion of that knowledge in deriving optimal controls. While past efforts included thermal constraints, this paper for the first time presents strategies for optimally charging batteries by guaranteeing minimal mechanical damage to the electrode particles during intercalation. In addition, an executable form of the code has been developed and provided. This code can be used to identify optimal charging profiles for any material and design parameters.
A STABILITY THEOREM FOR CONSTRAINED OPTIMAL CONTROL PROBLEMS
Institute of Scientific and Technical Information of China (English)
M.H. Farag
2004-01-01
This paper presents the stability of difference approximations of an optimal control problem for a quasilinear parabolic equation with controls in the coefficients, boundary conditions and additional restrictions. The optimal control problem has been convered to one of the optimization problem using a penalty function technique. The difference approximations problem for the considered problem is obtained. The estimations of stability of the solution of difference approximations problem are proved. The stability estimation of the solution of difference approximations problem by the controls is obtained.
Stable MIMO Constrained Predictive Control with Steady state Objective Optimization
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A two-stage multi-objective optimization model-predictive control algorithms(MPC) strategy is pre sented. A domain MPC controller with input constraints is used to increase freedom for steady-state objective and enhance stabilization of the controller. A steady-state objective optimization algorithm oriented to transient process is adopted to realize optimization of objectives else than dynamic control. It is proved that .the stabilization for both dynamic control and steady-state objective optimization can be guaranteed. The theoretical results are demonstrated and discussed using a distillation tower as the model. Theoretical analysis and simulation results show that this control strategy is efficient and provides a good strategic solution to practical process control.
Modified constrained differential evolution for solving nonlinear global optimization problems
2013-01-01
Nonlinear optimization problems introduce the possibility of multiple local optima. The task of global optimization is to find a point where the objective function obtains its most extreme value while satisfying the constraints. Some methods try to make the solution feasible by using penalty function methods, but the performance is not always satisfactory since the selection of the penalty parameters for the problem at hand is not a straightforward issue. Differential evolut...
Energy-Constrained Optimal Quantization for Wireless Sensor Networks
Directory of Open Access Journals (Sweden)
Georgios B. Giannakis
2008-02-01
Full Text Available As low power, low cost, and longevity of transceivers are major requirements in wireless sensor networks, optimizing their design under energy constraints is of paramount importance. To this end, we develop quantizers under strict energy constraints to effect optimal reconstruction at the fusion center. Propagation, modulation, as well as transmitter and receiver structures are jointly accounted for using a binary symmetric channel model. We first optimize quantization for reconstructing a single sensor's measurement, and deriving the optimal number of quantization levels as well as the optimal energy allocation across bits. The constraints take into account not only the transmission energy but also the energy consumed by the transceiver's circuitry. Furthermore, we consider multiple sensors collaborating to estimate a deterministic parameter in noise. Similarly, optimum energy allocation and optimum number of quantization bits are derived and tested with simulated examples. Finally, we study the effect of channel coding on the reconstruction performance under strict energy constraints and jointly optimize the number of quantization levels as well as the number of channel uses.
Directory of Open Access Journals (Sweden)
Kaczorek Tadeusz
2016-06-01
Full Text Available The minimum energy control problem for the descriptor discrete-time linear systems by the use of Weierstrass-Kronecker decomposition is formulated and solved. Necessary and sufficient conditions for the reachability of descriptor discrete-time linear systems are given. A procedure for computation of optimal input and a minimal value of the performance index is proposed and illustrated by a numerical example.
On optimal solutions of the constrained ℓ 0 regularization and its penalty problem
Zhang, Na; Li, Qia
2017-02-01
The constrained {{\\ell}0} regularization plays an important role in sparse reconstruction. A widely used approach for solving this problem is the penalty method, of which the least square penalty problem is a special case. However, the connections between global minimizers of the constrained {{\\ell}0} problem and its penalty problem have never been studied in a systematic way. This work provides a comprehensive investigation on optimal solutions of these two problems and their connections. We give detailed descriptions of optimal solutions of the two problems, including existence, stability with respect to the parameter, cardinality and strictness. In particular, we find that the optimal solution set of the penalty problem is piecewise constant with respect to the penalty parameter. Then we analyze in-depth the relationship between optimal solutions of the two problems. It is shown that, in the noisy case the least square penalty problem probably has no common optimal solutions with the constrained {{\\ell}0} problem for any penalty parameter. Under a mild condition on the penalty function, we establish that the penalty problem has the same optimal solution set as the constrained {{\\ell}0} problem when the penalty parameter is sufficiently large. Based on the conditions, we further propose exact penalty problems for the constrained {{\\ell}0} problem. Finally, we present a numerical example to illustrate our main theoretical results.
Receding horizon H∞ control for constrained time-delay systems
Institute of Scientific and Technical Information of China (English)
Lu Mei; Jin Chengbo; Shao Huihe
2009-01-01
A receding horizon H∞ control algorithm is presented for linear discrete time-delay system in the presence of constrained input and disturbances. Disturbance attenuation level is optimized at each time instant, and the receding optimization problem includes several linear matrix inequality constraints. When the convex hull is applied to denote the saturating input, the algorithm has better performance. The numerical example can verify this result.
2013-08-01
dynamic pressure, time- rate of change of flight path angle, loads and a terminal phase target. Furthermore, the optimal control problem uses derived... rate of change of altitude. The optimal control variables are specified to be the guidance variable derivatives; this allows for constraining attitude
Iwan Solihin, Mahmud; Fauzi Zanil, Mohd
2016-11-01
Cuckoo Search (CS) and Differential Evolution (DE) algorithms are considerably robust meta-heuristic algorithms to solve constrained optimization problems. In this study, the performance of CS and DE are compared in solving the constrained optimization problem from selected benchmark functions. Selection of the benchmark functions are based on active or inactive constraints and dimensionality of variables (i.e. number of solution variable). In addition, a specific constraint handling and stopping criterion technique are adopted in the optimization algorithm. The results show, CS approach outperforms DE in term of repeatability and the quality of the optimum solutions.
Constrained simultaneous multi-state reconfigurable wing structure configuration optimization
Snyder, Matthew
A reconfigurable aircraft is capable of in-flight shape change to increase mission performance or provide multi-mission capability. Reconfigurability has always been a consideration in aircraft design, from the Wright Flyer, to the F-14, and most recently the Lockheed-Martin folding wing concept. The Wright Flyer used wing-warping for roll control, the F-14 had a variable-sweep wing to improve supersonic flight capabilities, and the Lockheed-Martin folding wing demonstrated radical in-flight shape change. This dissertation will examine two questions that aircraft reconfigurability raises, especially as reconfiguration increases in complexity. First, is there an efficient method to develop a light weight structure which supports all the loads generated by each configuration? Second, can this method include the capability to propose a sub-structure topology that weighs less than other considered designs? The first question requires a method that will design and optimize multiple configurations of a reconfigurable aerostructure. Three options exist, this dissertation will show one is better than the others. Simultaneous optimization considers all configurations and their respective load cases and constraints at the same time. Another method is sequential optimization which considers each configuration of the vehicle one after the other - with the optimum design variable values from the first configuration becoming the lower bounds for subsequent configurations. This process repeats for each considered configuration and the lower bounds update as necessary. The third approach is aggregate combination — this method keeps the thickness or area of each member for the most critical configuration, the configuration that requires the largest cross-section. This research will show that simultaneous optimization produces a lower weight and different topology for the considered structures when compared to the sequential and aggregate techniques. To answer the second question
Constrained Burn Optimization for the International Space Station
Brown, Aaron J.; Jones, Brandon A.
2017-01-01
In long-term trajectory planning for the International Space Station (ISS), translational burns are currently targeted sequentially to meet the immediate trajectory constraints, rather than simultaneously to meet all constraints, do not employ gradient-based search techniques, and are not optimized for a minimum total deltav (v) solution. An analytic formulation of the constraint gradients is developed and used in an optimization solver to overcome these obstacles. Two trajectory examples are explored, highlighting the advantage of the proposed method over the current approach, as well as the potential v and propellant savings in the event of propellant shortages.
Shape modification of Bézier curves by constrained optimization
Institute of Scientific and Technical Information of China (English)
WU Qing-biao; XIA Fei-hai
2005-01-01
The Bézier curve is one of the most commonly used parametric curves in CAGD and Computer Graphics and has many portant problem, and is also an important research issue in CAD/CAM and NC technology fields. This work investigates the curves to satisfy the given constraints and modify the shape of the curves optimally. Practical examples are also given.
Efficient relaxations for joint chance constrained AC optimal power flow
Energy Technology Data Exchange (ETDEWEB)
Baker, Kyri; Toomey, Bridget
2017-07-01
Evolving power systems with increasing levels of stochasticity call for a need to solve optimal power flow problems with large quantities of random variables. Weather forecasts, electricity prices, and shifting load patterns introduce higher levels of uncertainty and can yield optimization problems that are difficult to solve in an efficient manner. Solution methods for single chance constraints in optimal power flow problems have been considered in the literature, ensuring single constraints are satisfied with a prescribed probability; however, joint chance constraints, ensuring multiple constraints are simultaneously satisfied, have predominantly been solved via scenario-based approaches or by utilizing Boole's inequality as an upper bound. In this paper, joint chance constraints are used to solve an AC optimal power flow problem while preventing overvoltages in distribution grids under high penetrations of photovoltaic systems. A tighter version of Boole's inequality is derived and used to provide a new upper bound on the joint chance constraint, and simulation results are shown demonstrating the benefit of the proposed upper bound. The new framework allows for a less conservative and more computationally efficient solution to considering joint chance constraints, specifically regarding preventing overvoltages.
A constrained optimization framework for compliant underactuated grasping
Directory of Open Access Journals (Sweden)
M. Ciocarlie
2011-02-01
Full Text Available This study focuses on the design and analysis of underactuated robotic hands that use tendons and compliant joints to enable passive mechanical adaptation during grasping tasks. We use a quasistatic equilibrium formulation to predict the stability of a given grasp. This method is then used as the inner loop of an optimization algorithm that can find a set of actuation mechanism parameters that optimize the stability measure for an entire set of grasps. We discuss two possible approaches to design optimization using this framework, one using exhaustive search over the parameter space, and the other using a simplified gripper construction to cast the problem to a form that is directly solvable using well-established optimization methods. Computations are performed in 3-D, allow arbitrary geometry of the grasped objects and take into account frictional constraints.
This paper was presented at the IFToMM/ASME International Workshop on Underactuated Grasping (UG2010, 19 August 2010, Montréal, Canada.
CONIC TRUST REGION METHOD FOR LINEARLY CONSTRAINED OPTIMIZATION
Institute of Scientific and Technical Information of China (English)
Wen-yu Sun; Jin-yun Yuan; Ya-xiang Yuan
2003-01-01
In this paper we present a trust region method of conic model for linearly constrainedoptimization problems. We discuss trust region approaches with conic model subproblems.Some equivalent variation properties and optimality conditions are given. A trust regionalgorithm based on conic model is constructed. Global convergence of the method isestablished.
Improved Sensitivity Relations in State Constrained Optimal Control
Energy Technology Data Exchange (ETDEWEB)
Bettiol, Piernicola, E-mail: piernicola.bettiol@univ-brest.fr [Université de Bretagne Occidentale, Laboratoire de Mathematiques (France); Frankowska, Hélène, E-mail: frankowska@math.jussieu.fr [Université Pierre et Marie Curie (Paris 6), CNRS and Institut de Mathématiques de Jussieu (France); Vinter, Richard B., E-mail: r.vinter@imperial.ac.uk [Imperial College London, Department of Electrical and Electronic Engineering (United Kingdom)
2015-04-15
Sensitivity relations in optimal control provide an interpretation of the costate trajectory and the Hamiltonian, evaluated along an optimal trajectory, in terms of gradients of the value function. While sensitivity relations are a straightforward consequence of standard transversality conditions for state constraint free optimal control problems formulated in terms of control-dependent differential equations with smooth data, their verification for problems with either pathwise state constraints, nonsmooth data, or for problems where the dynamic constraint takes the form of a differential inclusion, requires careful analysis. In this paper we establish validity of both ‘full’ and ‘partial’ sensitivity relations for an adjoint state of the maximum principle, for optimal control problems with pathwise state constraints, where the underlying control system is described by a differential inclusion. The partial sensitivity relation interprets the costate in terms of partial Clarke subgradients of the value function with respect to the state variable, while the full sensitivity relation interprets the couple, comprising the costate and Hamiltonian, as the Clarke subgradient of the value function with respect to both time and state variables. These relations are distinct because, for nonsmooth data, the partial Clarke subdifferential does not coincide with the projection of the (full) Clarke subdifferential on the relevant coordinate space. We show for the first time (even for problems without state constraints) that a costate trajectory can be chosen to satisfy the partial and full sensitivity relations simultaneously. The partial sensitivity relation in this paper is new for state constraint problems, while the full sensitivity relation improves on earlier results in the literature (for optimal control problems formulated in terms of Lipschitz continuous multifunctions), because a less restrictive inward pointing hypothesis is invoked in the proof, and because
Optimal Constrained Stationary Intervention in Gene Regulatory Networks
Directory of Open Access Journals (Sweden)
Golnaz Vahedi
2008-05-01
Full Text Available A key objective of gene network modeling is to develop intervention strategies to alter regulatory dynamics in such a way as to reduce the likelihood of undesirable phenotypes. Optimal stationary intervention policies have been developed for gene regulation in the framework of probabilistic Boolean networks in a number of settings. To mitigate the possibility of detrimental side effects, for instance, in the treatment of cancer, it may be desirable to limit the expected number of treatments beneath some bound. This paper formulates a general constraint approach for optimal therapeutic intervention by suitably adapting the reward function and then applies this formulation to bound the expected number of treatments. A mutated mammalian cell cycle is considered as a case study.
Optimal Constrained Stationary Intervention in Gene Regulatory Networks
Directory of Open Access Journals (Sweden)
Faryabi Babak
2008-01-01
Full Text Available A key objective of gene network modeling is to develop intervention strategies to alter regulatory dynamics in such a way as to reduce the likelihood of undesirable phenotypes. Optimal stationary intervention policies have been developed for gene regulation in the framework of probabilistic Boolean networks in a number of settings. To mitigate the possibility of detrimental side effects, for instance, in the treatment of cancer, it may be desirable to limit the expected number of treatments beneath some bound. This paper formulates a general constraint approach for optimal therapeutic intervention by suitably adapting the reward function and then applies this formulation to bound the expected number of treatments. A mutated mammalian cell cycle is considered as a case study.
Smooth Constrained Heuristic Optimization of a Combinatorial Chemical Space
2015-05-01
CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7...Advances in computational protein design. Curr Opin Struct Biol. 2004;14(4):487–494. 4. Mang NG, Zeng C. Reference energy extremal optimization: A
A TRUST-REGION ALGORITHM FOR NONLINEAR INEQUALITY CONSTRAINED OPTIMIZATION
Institute of Scientific and Technical Information of China (English)
Xiaojiao Tong; Shuzi Zhou
2003-01-01
This paper presents a new trust-region algorithm for n-dimension nonlinear optimization subject to m nonlinear inequality constraints. Equivalent KKT conditions are derived,which is the basis for constructing the new algorithm. Global convergence of the algorithm to a first-order KKT point is established under mild conditions on the trial steps, local quadratic convergence theorem is proved for nondegenerate minimizer point. Numerical experiment is presented to show the effectiveness of our approach.
Kinetic Constrained Optimization of the Golf Swing Hub Path
Directory of Open Access Journals (Sweden)
Steven M. Nesbit
2014-12-01
Full Text Available This study details an optimization of the golf swing, where the hand path and club angular trajectories are manipulated. The optimization goal was to maximize club head velocity at impact within the interaction kinetic limitations (force, torque, work, and power of the golfer as determined through the analysis of a typical swing using a two-dimensional dynamic model. The study was applied to four subjects with diverse swing capabilities and styles. It was determined that it is possible for all subjects to increase their club head velocity at impact within their respective kinetic limitations through combined modifications to their respective hand path and club angular trajectories. The manner of the modifications, the degree of velocity improvement, the amount of kinetic reduction, and the associated kinetic limitation quantities were subject dependent. By artificially minimizing selected kinetic inputs within the optimization algorithm, it was possible to identify swing trajectory characteristics that indicated relative kinetic weaknesses of a subject. Practical implications are offered based upon the findings of the study.
Constrained Fuzzy Predictive Control Using Particle Swarm Optimization
Directory of Open Access Journals (Sweden)
Oussama Ait Sahed
2015-01-01
Full Text Available A fuzzy predictive controller using particle swarm optimization (PSO approach is proposed. The aim is to develop an efficient algorithm that is able to handle the relatively complex optimization problem with minimal computational time. This can be achieved using reduced population size and small number of iterations. In this algorithm, instead of using the uniform distribution as in the conventional PSO algorithm, the initial particles positions are distributed according to the normal distribution law, within the area around the best position. The radius limiting this area is adaptively changed according to the tracking error values. Moreover, the choice of the initial best position is based on prior knowledge about the search space landscape and the fact that in most practical applications the dynamic optimization problem changes are gradual. The efficiency of the proposed control algorithm is evaluated by considering the control of the model of a 4 × 4 Multi-Input Multi-Output industrial boiler. This model is characterized by being nonlinear with high interactions between its inputs and outputs, having a nonminimum phase behaviour, and containing instabilities and time delays. The obtained results are compared to those of the control algorithms based on the conventional PSO and the linear approach.
Preconditioning for partial differential equation constrained optimization with control constraints
Stoll, Martin
2011-10-18
Optimal control problems with partial differential equations play an important role in many applications. The inclusion of bound constraints for the control poses a significant additional challenge for optimization methods. In this paper, we propose preconditioners for the saddle point problems that arise when a primal-dual active set method is used. We also show for this method that the same saddle point system can be derived when the method is considered as a semismooth Newton method. In addition, the projected gradient method can be employed to solve optimization problems with simple bounds, and we discuss the efficient solution of the linear systems in question. In the case when an acceleration technique is employed for the projected gradient method, this again yields a semismooth Newton method that is equivalent to the primal-dual active set method. We also consider the Moreau-Yosida regularization method for control constraints and efficient preconditioners for this technique. Numerical results illustrate the competitiveness of these approaches. © 2011 John Wiley & Sons, Ltd.
Directory of Open Access Journals (Sweden)
Zheng Ling
2011-01-01
Full Text Available Damping treatments have been extensively used as a powerful means to damp out structural resonant vibrations. Usually, damping materials are fully covered on the surface of plates. The drawbacks of this conventional treatment are also obvious due to an added mass and excess material consumption. Therefore, it is not always economical and effective from an optimization design view. In this paper, a topology optimization approach is presented to maximize the modal damping ratio of the plate with constrained layer damping treatment. The governing equation of motion of the plate is derived on the basis of energy approach. A finite element model to describe dynamic performances of the plate is developed and used along with an optimization algorithm in order to determine the optimal topologies of constrained layer damping layout on the plate. The damping of visco-elastic layer is modeled by the complex modulus formula. Considering the vibration and energy dissipation mode of the plate with constrained layer damping treatment, damping material density and volume factor are considered as design variable and constraint respectively. Meantime, the modal damping ratio of the plate is assigned as the objective function in the topology optimization approach. The sensitivity of modal damping ratio to design variable is further derived and Method of Moving Asymptote (MMA is adopted to search the optimized topologies of constrained layer damping layout on the plate. Numerical examples are used to demonstrate the effectiveness of the proposed topology optimization approach. The results show that vibration energy dissipation of the plates can be enhanced by the optimal constrained layer damping layout. This optimal technology can be further extended to vibration attenuation of sandwich cylindrical shells which constitute the major building block of many critical structures such as cabins of aircrafts, hulls of submarines and bodies of rockets and missiles as an
Kinetic constrained optimization of the golf swing hub path.
Nesbit, Steven M; McGinnis, Ryan S
2014-12-01
This study details an optimization of the golf swing, where the hand path and club angular trajectories are manipulated. The optimization goal was to maximize club head velocity at impact within the interaction kinetic limitations (force, torque, work, and power) of the golfer as determined through the analysis of a typical swing using a two-dimensional dynamic model. The study was applied to four subjects with diverse swing capabilities and styles. It was determined that it is possible for all subjects to increase their club head velocity at impact within their respective kinetic limitations through combined modifications to their respective hand path and club angular trajectories. The manner of the modifications, the degree of velocity improvement, the amount of kinetic reduction, and the associated kinetic limitation quantities were subject dependent. By artificially minimizing selected kinetic inputs within the optimization algorithm, it was possible to identify swing trajectory characteristics that indicated relative kinetic weaknesses of a subject. Practical implications are offered based upon the findings of the study. Key PointsThe hand path trajectory is an important characteristic of the golf swing and greatly affects club head velocity and golfer/club energy transfer.It is possible to increase the energy transfer from the golfer to the club by modifying the hand path and swing trajectories without increasing the kinetic output demands on the golfer.It is possible to identify relative kinetic output strengths and weakness of a golfer through assessment of the hand path and swing trajectories.Increasing any one of the kinetic outputs of the golfer can potentially increase the club head velocity at impact.The hand path trajectory has important influences over the club swing trajectory.
Thermodynamics constrains allometric scaling of optimal development time in insects.
Directory of Open Access Journals (Sweden)
Michael E Dillon
Full Text Available Development time is a critical life-history trait that has profound effects on organism fitness and on population growth rates. For ectotherms, development time is strongly influenced by temperature and is predicted to scale with body mass to the quarter power based on 1 the ontogenetic growth model of the metabolic theory of ecology which describes a bioenergetic balance between tissue maintenance and growth given the scaling relationship between metabolism and body size, and 2 numerous studies, primarily of vertebrate endotherms, that largely support this prediction. However, few studies have investigated the allometry of development time among invertebrates, including insects. Abundant data on development of diverse insects provides an ideal opportunity to better understand the scaling of development time in this ecologically and economically important group. Insects develop more quickly at warmer temperatures until reaching a minimum development time at some optimal temperature, after which development slows. We evaluated the allometry of insect development time by compiling estimates of minimum development time and optimal developmental temperature for 361 insect species from 16 orders with body mass varying over nearly 6 orders of magnitude. Allometric scaling exponents varied with the statistical approach: standardized major axis regression supported the predicted quarter-power scaling relationship, but ordinary and phylogenetic generalized least squares did not. Regardless of the statistical approach, body size alone explained less than 28% of the variation in development time. Models that also included optimal temperature explained over 50% of the variation in development time. Warm-adapted insects developed more quickly, regardless of body size, supporting the "hotter is better" hypothesis that posits that ectotherms have a limited ability to evolutionarily compensate for the depressing effects of low temperatures on rates of
Optimized, budget-constrained monitoring well placement using DREAM
Energy Technology Data Exchange (ETDEWEB)
Yonkofski, Catherine MR; Davidson, Casie L.; Rodriguez, Luke R.; Porter, Ellen A.; Bender, Sadie R.; Brown, Christopher F.
2017-07-01
Defining the ideal suite of monitoring technologies to be deployed at a carbon capture and storage (CCS) site presents a challenge to project developers, financers, insurers, regulators and other stakeholders. The monitoring, verification, and accounting (MVA) toolkit offers a suite of technologies to monitor an extensive range of parameters across a wide span of spatial and temporal resolutions, each with their own degree of sensitivity to changes in the parameter being monitored. Understanding how best to optimize MVA budgets to minimize the time to leak detection could help to address issues around project risks, and in turn help support broad CCS deployment. This paper presents a case study demonstrating an application of the Designs for Risk Evaluation and Management (DREAM) tool using an ensemble of CO2 leakage scenarios taken from a previous study on leakage impacts to groundwater. Impacts were assessed and monitored as a function of pH, total dissolved solids (TDS), and trace metal concentrations of arsenic (As), cadmium (Cd), chromium (Cr), and lead (Pb). Using output from the previous study, DREAM was used to optimize monitoring system designs based on variable sampling locations and parameters. The algorithm requires the user to define a finite budget to limit the number of monitoring wells and technologies deployed, and then iterates well placement and sensor type and location until it converges on the configuration with the lowest time to first detection of the leak averaged across all scenarios. To facilitate an understanding of the optimal number of sampling wells, DREAM was used to assess the marginal utility of additional sampling locations. Based on assumptions about monitoring costs and replacement costs of degraded water, the incremental cost of each additional sampling well can be compared against its marginal value in terms of avoided aquifer degradation. Applying this method, DREAM identified the most cost-effective ensemble with 14
Optimal MPC for tracking of constrained linear systems
Ferramosca, A.; Limon, D.; Alvarado, I.; Alamo, T.; Castaño, F.; Camacho, E. F.
2011-08-01
Model predictive control (MPC) is one of the few techniques which is able to handle constraints on both state and input of the plant. The admissible evolution and asymptotic convergence of the closed-loop system is ensured by means of suitable choice of the terminal cost and terminal constraint. However, most of the existing results on MPC are designed for a regulation problem. If the desired steady-state changes, the MPC controller must be redesigned to guarantee the feasibility of the optimisation problem, the admissible evolution as well as the asymptotic stability. Recently, a novel MPC has been proposed to ensure the feasibility of the optimisation problem, constraints satisfaction and asymptotic evolution of the system to any admissible target steady-state. A drawback of this controller is the loss of a desirable property of the MPC controllers: the local optimality property. In this article, a novel formulation of the MPC for tracking is proposed aimed to recover the optimality property maintaining all the properties of the original formulation.
Multiplicative Noise Removal Using Variable Splitting and Constrained Optimization
Bioucas-Dias, José M
2009-01-01
Multiplicative noise (also known as speckle noise) models are central to the study of coherent imaging systems, such as synthetic aperture radar and sonar, and ultrasound and laser imaging. These models introduce two additional layers of difficulties with respect to the standard Gaussian additive noise scenario: (1) the noise is multiplied by (rather than added to) the original image; (2) the noise is not Gaussian, with Rayleigh and Gamma being commonly used densities. These two features of multiplicative noise models preclude the direct application of most state-of-the-art algorithms, which are designed for solving unconstrained optimization problems where the objective has two terms: a quadratic data term (log-likelihood), reflecting the additive and Gaussian nature of the noise, plus a convex (possibly nonsmooth) regularizer (e.g., a total variation or wavelet-based regularizer/prior). In this paper, we address these difficulties by: (1) converting the multiplicative model into an additive one by taking lo...
A new IPSO-SA approach for cardinality constrained portfolio optimization
Directory of Open Access Journals (Sweden)
Marzieh Mozafari
2011-04-01
Full Text Available The problem of portfolio optimization has always been a key concern for investors. This paper addresses a realistic portfolio optimization problem with floor, ceiling, and cardinality constraints. This problem is a mixed integer quadratic programming where traditional optimization methods fail to find the optimal solution, efficiently. The present paper develops a new hybrid approach based on an improved particle swarm optimization (PSO and a modified simulated annealing (SA methods to find the cardinality constrained efficient frontier. The proposed algorithm benefits simple and easy characteristics of PSO with an adaptation of inertia weights and constriction factor. In addition, incorporating an SA procedure into IPSO helps escaping from local optima and improves the precision of convergence. Computational results on benchmark problems with up to 225 assets signify that our proposed algorithm exceeds not only the standard PSO but also the other heuristic algorithms previously presented to solve the cardinality constrained portfolio problem.
A one-layer recurrent neural network for constrained nonsmooth invex optimization.
Li, Guocheng; Yan, Zheng; Wang, Jun
2014-02-01
Invexity is an important notion in nonconvex optimization. In this paper, a one-layer recurrent neural network is proposed for solving constrained nonsmooth invex optimization problems, designed based on an exact penalty function method. It is proved herein that any state of the proposed neural network is globally convergent to the optimal solution set of constrained invex optimization problems, with a sufficiently large penalty parameter. In addition, any neural state is globally convergent to the unique optimal solution, provided that the objective function and constraint functions are pseudoconvex. Moreover, any neural state is globally convergent to the feasible region in finite time and stays there thereafter. The lower bounds of the penalty parameter and convergence time are also estimated. Two numerical examples are provided to illustrate the performances of the proposed neural network.
Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach
Energy Technology Data Exchange (ETDEWEB)
Pham, Huyên, E-mail: pham@math.univ-paris-diderot.fr; Wei, Xiaoli, E-mail: tyswxl@gmail.com [Laboratoire de Probabilités et Modèles Aléatoires, CNRS, UMR 7599, Université Paris Diderot (France)
2016-12-15
We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.
Directory of Open Access Journals (Sweden)
Minggang Dong
2014-01-01
Full Text Available Motivated by recent advancements in differential evolution and constraints handling methods, this paper presents a novel modified oracle penalty function-based composite differential evolution (MOCoDE for constrained optimization problems (COPs. More specifically, the original oracle penalty function approach is modified so as to satisfy the optimization criterion of COPs; then the modified oracle penalty function is incorporated in composite DE. Furthermore, in order to solve more complex COPs with discrete, integer, or binary variables, a discrete variable handling technique is introduced into MOCoDE to solve complex COPs with mix variables. This method is assessed on eleven constrained optimization benchmark functions and seven well-studied engineering problems in real life. Experimental results demonstrate that MOCoDE achieves competitive performance with respect to some other state-of-the-art approaches in constrained optimization evolutionary algorithms. Moreover, the strengths of the proposed method include few parameters and its ease of implementation, rendering it applicable to real life. Therefore, MOCoDE can be an efficient alternative to solving constrained optimization problems.
Constrained optimization techniques for active control of aeroelastic response
Mukhopadhyay, Vivekananda
1987-01-01
Active control of aeroelastic response is a complex problem in which the designer usually tries to satisfy many design criteria which are often conflicting in nature. To further complicate the design problem, the state space equations describing this type of control problem are usually of high order, involving a large number of states to represent the flexible structure and unsteady aerodynamics. Control laws based on the standard Linear - Quadratic - Gaussian method are of the same high order as the aeroelastic plant and may be difficult to implement in the flight computer. To overcome this disadvantage a new approach was developed for designing low-order optimized robust control laws. In this approach, a nonlinear programming algorithm is used to search for the values of control law design variables that minimize a performance index while satisfying several inequality constraints that describe the design criteria on the stability robustness and responses. The method is applied to a gust load alleviation problem and a stability robustness improvement problem of a drone aircraft.
Bertram, John E A; Gutmann, Anne; Randev, Jabina; Hulliger, Manuel
2014-08-01
To evaluate how fundamental gait parameters used in walking (stride length, frequency, speed) are selected by cats we compared stride characteristics selected when walking on a solid surface to those selected when they were constrained to specific stride lengths using a pedestal walkway. Humans spontaneously select substantially different stride length-stride frequency-speed relationships in walking when each of these parameters is constrained, as in walking to a metronome beat (frequency constrained), evenly spaced floor markers (stride length constrained) or on a treadmill (speed constrained). In humans such adjustments largely provide energetic economy under the prescribed walking conditions. Cats show a similar shift in gait parameter selection between conditions as observed in humans. This suggests that cats (and by extension, quadrupedal mammals) also select gait parameters to optimize walking cost-effectiveness. Cats with a profound peripheral sensory deficit (from pyridoxine overdose) appeared to parallel the optimization seen in healthy cats, but without the same level of precision. Recent studies in humans suggest that gait optimization may proceed in two stages - a fast perception-based stage that provides the initial gait selection strategy which is then fine-tuned by feedback. The sensory deficit cats appeared unable to accomplish the feedback-dependent aspect of this process.
Mixed continuous/discrete time modelling with exact time adjustments
Rovers, K.C.; Kuper, Jan; van de Burgwal, M.D.; Kokkeler, Andre B.J.; Smit, Gerardus Johannes Maria
2011-01-01
Many systems interact with their physical environment. Design of such systems need a modelling and simulation tool which can deal with both the continuous and discrete aspects. However, most current tools are not adequately able to do so, as they implement both continuous and discrete time signals
Minimal Martingale Measures for Discrete-time Incomplete Financial Markets
Institute of Scientific and Technical Information of China (English)
Ping Li; Jian-ming Xia
2002-01-01
In this note, we give a characterization of the minimal martingale measure for a general discretetime incomplete financial market. Then we concretely work out the minimal martingale measure for a specific discrete-time market model in which the assets' returns in different times are independent.
Stability of Nonlinear Stochastic Discrete-Time Systems
2013-01-01
This paper studies the stability for nonlinear stochastic discrete-time systems. First of all, several definitions on stability are introduced, such as stability, asymptotical stability, and pth moment exponential stability. Moreover, using the method of the Lyapunov functionals, some efficient criteria for stochastic stability are obtained. Some examples are presented to illustrate the effectiveness of the proposed theoretical results.
Polynomial Transformations For Discrete-Time Linear Systems
Baram, Yoram
1991-01-01
Transformations based on polynomial matrices of finite degree developed for use in computing functions for compensation, inversion, and approximation of discrete-time, multivariable, linear systems. Method derived from z-transform transfer-function form of matrices. Applicable to cascade-compensation problems in design of control systems.
Local Parametric Analysis of Hedging in Discrete Time
Bossaerts, P.L.M.; Hillion, P.
1995-01-01
When continuous-time portfolio weights are applied to a discrete-time hedging problem, errors are likely to occur. This paper evaluates the overall importance of the discretization-induced tracking error. It does so by comparing the performance of Black-Scholes hedge ratios against those obtained
STABILITY CRITERIA FOR STOCHASTIC DISCRETE-TIME FRACTIONAL ORDER SYSTEMS
Directory of Open Access Journals (Sweden)
Carmen BARBACIORU
2016-05-01
Full Text Available In this paper are discussed stability problems for a class of discrete-time fractional systems (DTFSs with independent random perturbations. Two notions of mean square stability (MSS and mean square asymptotic stability (MSAS are introduced for the DTFSs by using an approximating linear stochastic system. Necessary and sufficient conditions for MSS and MSA are then derived.
A trust-region and affine scaling algorithm for linearly constrained optimization
Institute of Scientific and Technical Information of China (English)
陈中文; 章祥荪
2002-01-01
A new trust-region and affine scaling algorithm for linearly constrained optimization is presentedin this paper. Under no nondegenerate assumption, we prove that any limit point of the sequence generatedby the new algorithm satisfies the first order necessary condition and there exists at least one limit point ofthe sequence which satisfies the second order necessary condition. Some preliminary numerical experiments are reported.
Solution of Constrained Optimal Control Problems Using Multiple Shooting and ESDIRK Methods
DEFF Research Database (Denmark)
Capolei, Andrea; Jørgensen, John Bagterp
2012-01-01
In this paper, we describe a novel numerical algorithm for solution of constrained optimal control problems of the Bolza type for stiff and/or unstable systems. The numerical algorithm combines explicit singly diagonally implicit Runge-Kutta (ESDIRK) integration methods with a multiple shooting...
Stability Constrained Efficiency Optimization for Droop Controlled DC-DC Conversion System
DEFF Research Database (Denmark)
Meng, Lexuan; Dragicevic, Tomislav; Guerrero, Josep M.
2013-01-01
implementing tertiary regulation. Moreover, system dynamic is affected when shifting VRs. Therefore, the stability is considered in optimization by constraining the eigenvalues arising from dynamic state space model of the system. Genetic algorithm is used in searching for global efficiency optimum while...
Image denoising: Learning the noise model via nonsmooth PDE-constrained optimization
Reyes, Juan Carlos De los
2013-11-01
We propose a nonsmooth PDE-constrained optimization approach for the determination of the correct noise model in total variation (TV) image denoising. An optimization problem for the determination of the weights corresponding to different types of noise distributions is stated and existence of an optimal solution is proved. A tailored regularization approach for the approximation of the optimal parameter values is proposed thereafter and its consistency studied. Additionally, the differentiability of the solution operator is proved and an optimality system characterizing the optimal solutions of each regularized problem is derived. The optimal parameter values are numerically computed by using a quasi-Newton method, together with semismooth Newton type algorithms for the solution of the TV-subproblems. © 2013 American Institute of Mathematical Sciences.
Robust exponential stability analysis of a larger class of discrete-time recurrent neural networks
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The robust exponential stability of a larger class of discrete-time recurrent neural networks (RNNs) is explored in this paper. A novel neural network model, named standard neural network model (SNNM), is introduced to provide a general framework for stability analysis of RNNs. Most of the existing RNNs can be transformed into SNNMs to be analyzed in a unified way.Applying Lyapunov stability theory method and S-Procedure technique, two useful criteria of robust exponential stability for the discrete-time SNNMs are derived. The conditions presented are formulated as linear matrix inequalities (LMIs) to be easily solved using existing efficient convex optimization techniques. An example is presented to demonstrate the transformation procedure and the effectiveness of the results.
Directory of Open Access Journals (Sweden)
R. Venkata Rao
2014-01-01
Full Text Available The present work proposes a multi-objective improved teaching-learning based optimization (MO-ITLBO algorithm for unconstrained and constrained multi-objective function optimization. The MO-ITLBO algorithm is the improved version of basic teaching-learning based optimization (TLBO algorithm adapted for multi-objective problems. The basic TLBO algorithm is improved to enhance its exploration and exploitation capacities by introducing the concept of number of teachers, adaptive teaching factor, tutorial training and self-motivated learning. The MO-ITLBO algorithm uses a grid-based approach to adaptively assess the non-dominated solutions (i.e. Pareto front maintained in an external archive. The performance of the MO-ITLBO algorithm is assessed by implementing it on unconstrained and constrained test problems proposed for the Congress on Evolutionary Computation 2009 (CEC 2009 competition. The performance assessment is done by using the inverted generational distance (IGD measure. The IGD measures obtained by using the MO-ITLBO algorithm are compared with the IGD measures of the other state-of-the-art algorithms available in the literature. Finally, Lexicographic ordering is used to assess the overall performance of competitive algorithms. Results have shown that the proposed MO-ITLBO algorithm has obtained the 1st rank in the optimization of unconstrained test functions and the 3rd rank in the optimization of constrained test functions.
Zhang, Songchuan; Xia, Youshen; Wang, Jun
2015-12-01
In this paper, we present a complex-valued projection neural network for solving constrained convex optimization problems of real functions with complex variables, as an extension of real-valued projection neural networks. Theoretically, by developing results on complex-valued optimization techniques, we prove that the complex-valued projection neural network is globally stable and convergent to the optimal solution. Obtained results are completely established in the complex domain and thus significantly generalize existing results of the real-valued projection neural networks. Numerical simulations are presented to confirm the obtained results and effectiveness of the proposed complex-valued projection neural network.
Discrete-Time LPV Current Control of an Induction Motor
DEFF Research Database (Denmark)
Bendtsen, Jan Dimon; Trangbæk, Klaus
2003-01-01
further complications. The synthesis method is applied to the model, yielding an LPV discrete-time controller. Finally, the efficiency of the control scheme is validated via simulations as well as on the actual induction motor, both in open-loop current control and when an outer speed control loop......In this paper we apply a new method for gain-scheduled output feedback control of nonlinear systems to current control of an induction motor. The method relies on recently developed controller synthesis results for linear parameter-varying (LPV) systems, where the controller synthesis is formulated...... as a set of linear matrix inequalities with full-block multipliers. A standard nonlinear model of the motor is constructed and written on LPV form. We then show that, although originally developed in continuous time, the controller synthesis results can be applied to a discrete-time model as well without...
Discrete-Time Nonlinear Control of VSC-HVDC System
Directory of Open Access Journals (Sweden)
TianTian Qian
2015-01-01
Full Text Available Because VSC-HVDC is a kind of strong nonlinear, coupling, and multi-input multioutput (MIMO system, its control problem is always attracting much attention from scholars. And a lot of papers have done research on its control strategy in the continuous-time domain. But the control system is implemented through the computer discrete sampling in practical engineering. It is necessary to study the mathematical model and control algorithm in the discrete-time domain. The discrete mathematical model based on output feedback linearization and discrete sliding mode control algorithm is proposed in this paper. And to ensure the effectiveness of the control system in the quasi sliding mode state, the fast output sampling method is used in the output feedback. The results from simulation experiment in MATLAB/SIMULINK prove that the proposed discrete control algorithm can make the VSC-HVDC system have good static, dynamic, and robust characteristics in discrete-time domain.
Discrete-Time LPV Current Control of an Induction Motor
DEFF Research Database (Denmark)
Bendtsen, Jan Dimon; Trangbæk, Klaus
2003-01-01
In this paper we apply a new method for gain-scheduled output feedback control of nonlinear systems to current control of an induction motor. The method relies on recently developed controller synthesis results for linear parameter-varying (LPV) systems, where the controller synthesis is formulated...... as a set of linear matrix inequalities with full-block multipliers. A standard nonlinear model of the motor is constructed and written on LPV form. We then show that, although originally developed in continuous time, the controller synthesis results can be applied to a discrete-time model as well without...... further complications. The synthesis method is applied to the model, yielding an LPV discrete-time controller. Finally, the efficiency of the control scheme is validated via simulations as well as on the actual induction motor, both in open-loop current control and when an outer speed control loop...
Discrete-Time LPV Current Control of an Induction Motor
DEFF Research Database (Denmark)
Bendtsen, Jan Dimon; Trangbæk, Klaus
2001-01-01
In this paper we apply a new method for gain-scheduled output feedback control of nonlinear systems to current control of an induction motor. The method relies on recently developed controller synthesis results for linear parameter-varying (LPV) systems, where the controller synthesis is formulated...... as a set of linear matrix inequalities with full-block multipliers. A standard nonlinear model of the motor is then constructed and written on LPV form. We then show that, although originally developed in continuous time, the controller synthesis results can be applied to a discrete-time model as well...... without further complications. The synthesis method is applied to the model, yielding an LPV discrete-time controller. Finally, the efficiency of the control scheme is validated via simulations as well as experimentally on the actual induction motor, both in open-loop current control and when an outer...
ROBUST STABILITY WITH GUARANTEEING COST FOR DISCRETE TIME-DELAY SYSTEMS WITH NONLINEAR PERTURBATION
Institute of Scientific and Technical Information of China (English)
JIA Xinchun; ZHENG Nanning; LIU Yuehu
2005-01-01
The problems of robust stability and robust stability with a guaranteeing cost for discrete time-delay systems with nonlinear perturbation are discussed. A sufficient criterion for robust stability is established in an LMI framework and a linear convex optimization problem with LMI constraints for computing maximal perturbation bound is proposed. Meanwhile, a sufficient criterion for robust stability with a guaranteeing cost for such systems is obtained, and an optimal procedure for decreasing the value of guaranteeing cost is put forward. Two examples are used to illustrate the efficiency of the results.
Algebraic convergence for discrete-time ergodic Markov chains
Institute of Scientific and Technical Information of China (English)
MAO; Yonghua(毛永华)
2003-01-01
This paper studies the e-ergodicity for discrete-time recurrent Markov chains. It proves that thee-order deviation matrix exists and is finite if and only if the chain is (e + 2)-ergodic, and then the algebraicdecay rates of the n-step transition probability to the stationary distribution are obtained. The criteria fore-ergodicity are given in terms of existence of solution to an equation. The main results are illustrated by some examples.
Identifying the topology of networks with discrete-time dynamics
Guo, Shu-Juan; Fu, Xin-Chu
2010-07-01
We suggest a method for identifying the topology of networks with discrete-time dynamics based on the dynamical evolution supported by the networks. The Frobenius matrix norm and Lasalle's invariance principle are used in this work. The network concerned can be directed or undirected, weighted or unweighted, and the local dynamics of each node can be nonidentical. The connections among the nodes can be all unknown or partially known. Finally, several examples are illustrated to verify the theoretical results.
Identifying the topology of networks with discrete-time dynamics
Energy Technology Data Exchange (ETDEWEB)
Guo Shujuan [School of Physics and Mathematics, Changzhou University, Changzhou 213164 (China); Fu Xinchu, E-mail: sjguo1@gmail.co, E-mail: enxcfu@gmail.co [Department of Mathematics, Shanghai University, Shanghai 200444 (China)
2010-07-23
We suggest a method for identifying the topology of networks with discrete-time dynamics based on the dynamical evolution supported by the networks. The Frobenius matrix norm and Lasalle's invariance principle are used in this work. The network concerned can be directed or undirected, weighted or unweighted, and the local dynamics of each node can be nonidentical. The connections among the nodes can be all unknown or partially known. Finally, several examples are illustrated to verify the theoretical results.
Discrete-Time Controllability for Feedback Quantum Dynamics
Albertini, Francesca
2010-01-01
Controllability properties for discrete-time, Markovian quantum dynamics are investigated. We find that, while in general the controlled system is not finite-time controllable, feedback control allows for arbitrary asymptotic state-to-state transitions. Under further assumption on the form of the measurement, we show that finite-time controllability can be achieved in a time that scales linearly with the dimension of the system, and we provide an iterative procedure to design the unitary control actions.
H∞ controller synthesis of piecewise discrete time linear systems
Institute of Scientific and Technical Information of China (English)
Gang FENG
2003-01-01
This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ perfomance and the controller can be obtained by solvng a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapnnov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.
Application of Chance-Constrained Stochastic Optimization for Mitigating Downstream Flood Risks
Alvarado Montero, Rodolfo; Schwanenberg, Dirk; Mainardi Fan, Fernando; Assis dos Reis, Alberto
2015-04-01
Ensemble forecasting is a growing field in the operation of multi-purpose reservoirs and mitigation of flood risks in downstream river reaches. The assessment of uncertainty over the prediction horizon provides added value to the operational flow forecasting system. It provides probabilistic inflow forecasts which, combined with decision support systems, determine optimum release strategies. One way of doing this is through scenario tree-based stochastic optimization. The representation of the ensemble forecasted is converted into a scenario-tree and optimized based on an adaptive multi-stage stochastic optimization. Typical inequality constraints applied over this problem require a full compliance of each ensemble's trajectory and neglect the uncertainty distribution. We propose the application of chance constrained optimization to overcome such problem, allowing a more flexible approach that does not depend on the number of ensembles but rather on the distribution of uncertainty. This technique is used to compute release trajectories of the reservoirs over a finite forecast horizon of up to 14 days by integrating a nonlinear gradient-based optimization algorithm and a model of the water system. The latter consists of simulation components for pool routing and kinematic or diffusive wave models for the downstream river reaches including a simulation mode and a reverse adjoint mode for the efficient computation of first-order derivatives. This framework has been implemented for a reservoir system operated by the Brazilian Companhia Energética de Minas Gerais S.A. (CEMIG). We present results obtained for the operation of the Tres Marias reservoir in the Brazilian state of Minas Gerais with a catchment area of near 55,000 km2. The focus of our discussion is the impact of chance constrains on the optimization procedure and its flexibility for extending the number of ensemble forecasts thus providing a more accurate representation of uncertainty. We compare the
Stability-Constrained Aerodynamic Shape Optimization with Applications to Flying Wings
Mader, Charles Alexander
A set of techniques is developed that allows the incorporation of flight dynamics metrics as an additional discipline in a high-fidelity aerodynamic optimization. Specifically, techniques for including static stability constraints and handling qualities constraints in a high-fidelity aerodynamic optimization are demonstrated. These constraints are developed from stability derivative information calculated using high-fidelity computational fluid dynamics (CFD). Two techniques are explored for computing the stability derivatives from CFD. One technique uses an automatic differentiation adjoint technique (ADjoint) to efficiently and accurately compute a full set of static and dynamic stability derivatives from a single steady solution. The other technique uses a linear regression method to compute the stability derivatives from a quasi-unsteady time-spectral CFD solution, allowing for the computation of static, dynamic and transient stability derivatives. Based on the characteristics of the two methods, the time-spectral technique is selected for further development, incorporated into an optimization framework, and used to conduct stability-constrained aerodynamic optimization. This stability-constrained optimization framework is then used to conduct an optimization study of a flying wing configuration. This study shows that stability constraints have a significant impact on the optimal design of flying wings and that, while static stability constraints can often be satisfied by modifying the airfoil profiles of the wing, dynamic stability constraints can require a significant change in the planform of the aircraft in order for the constraints to be satisfied.
Optimizing on multiple constrained QoS multicast routing algorithms based on GA
Institute of Scientific and Technical Information of China (English)
孙宝林; 李腊元
2004-01-01
With the rapid development of Internet, mobile networks and high-performance networking technology,multiple constrained QoS multicast routing optimization in networks with uncertain parameters has become a very important research issue in the areas of networks and distributed systems. It is also a challenging and hard problem to the next generation Internet and high-performance networks, and has attracted the interests of many people. This paper discusses the multiple constrained QoS multicast routing problem, which may deal with the delay, delay jitter,bandwidth and packet loss metrics, and describes a network model for researching the routing problem. The paper mainly presents multiple constrained QoS multicast routing algorithm (MCQMRA), a QoS multicast routing policy for Internet,mobile network or other high-performance networks, which is based on the genetic algorithm (GA) and can provide QoS-sensitive paths in a scalable and flexible wayin the network environment with uncertain parameters. The MCQMRA can also optimize the network resources such as bandwidth, delay, packet loss metrics and can converge to the optimal or near-optimal solution within few iterations, even for the network environment with uncertain parameters. Simulation results show that MCQMRA is an available approach to QoS multicast routing decision.
Stabilizing Solution for a Discrete-Time Modified Algebraic Riccati Equation in Infinite Dimensions
Directory of Open Access Journals (Sweden)
Viorica Mariela Ungureanu
2015-01-01
Full Text Available We provide necessary and sufficient conditions for the existence of stabilizing solutions for a class of modified algebraic discrete-time Riccati equations (MAREs defined on ordered Banach spaces of sequences of linear and bounded operators. These MAREs arise in the study of linear quadratic (LQ optimal control problems for infinite-dimensional discrete-time linear systems (DTLSs affected simultaneously by multiplicative white noise (MN and Markovian jumps (MJs. Unlike most of the previous works, where the detectability and observability notions are key tools for studying the global solvability of MAREs, in this paper the conditions of existence of mean-square stabilizing solutions are given directly in terms of system parameters. The methods we have used are based on the spectral theory of positive operators and the properties of trace class and compact operators. Our results generalise similar ones obtained for finite-dimensional MAREs associated with stochastic DTLSs without MJs. Also they complete and extend (in the autonomous case former investigations concerning the existence of certain global solutions (as minimal, maximal, and stabilizing solutions for generalized discrete-time Riccati type equations defined on infinite-dimensional ordered Banach spaces.
Institute of Scientific and Technical Information of China (English)
史忠科
2003-01-01
提出了一种离散系统的优化鲁棒滤波方法.为了得到滤波的逼近计算式,通过优化加权矩阵得到了上界不等式逼近和等效系统矩阵,得到了鲁棒滤波的时间更新算法;通过优化加权矩阵得到了下界不等式逼近和等效观测矩阵,得到了鲁棒滤波的测量更新算法,并且给出了鲁棒滤波算法收敛的条件.飞行试验数据处理的结果表明,提出的方法是有效的.%An optimized robust filtering algorithm for uncertain discrete-time systems is presented.To get a series of computational equations, the uncertain part generated by the uncertain systematic matrix in the expression of the error-covariance matrix of time update state estimation is optimized and the least upper bound of the uncertain part is given.By means of these results, the equivalent systematic matrix is obtained and a robust time update algorithm is built up.On the other hand, uncertain parts generated by the uncertain observation matrix in the expression of the error-covariance matrix of measurement update state estimation are optimized, and the largest lower bound of the uncertain part is given.Thus both the time update and measurement update algorithms are developed.By means of the matrix inversion formula, the expression structures of both time update and measurement update algorithms are all simplified.Moreover, the convergence condition of a robust filter is developed to make the results easy to application.The results of flight data processing show that the method presented in this paper is efficient.
Beri, Rajan; Chattopadhyay, Aditi; Nam, Changho
2000-06-01
A rigorous multi-objective optimization procedure, is developed to address the integrated structures/control design of composite plates with surface bonded segmented active constrained layer (ACL) damping treatment. The Kresselmeier- Steinhauser function approach is used to formulate this multidisciplinary problem. The goal is to control vibration without incorporating a weight penalty. Objective functions and constraints include damping ratios, structural weight and natural frequencies. Design variables include the ply stacking sequence, dimensions and placement of segmented ACL. The optimal designs show improved plate vibratory characteristics and reduced structural weight. The results of the multi- objective optimization problem are compared to those of a single objective optimization with vibration control as the objective. Results establish the necessity for developing the integrated structures/controls optimization procedure.
Optimizing Data Locality for Fork/Join Programs Using Constrained Work Stealing
Energy Technology Data Exchange (ETDEWEB)
Lifflander, Jonathan; Krishnamoorthy, Sriram; Kale, Laxmikant
2014-11-16
We present an approach to improving data locality across different phases of fork/join programs scheduled using work stealing. The approach consists of: (1) user-specified and automated approaches to constructing a steal tree, the schedule of steal operations and (2) constrained work stealing algorithms that constrain the actions of the scheduler to mirror a given steal tree. These are combined to construct work stealing schedules that maximize data locality across computation phases while ensuring load balance within each phase. These algorithms are also used to demonstrate dynamic coarsening, an optimization to improve spatial locality and sequential overheads by combining many finer-grained tasks into coarser tasks while ensuring sufficient concurrency for locality-optimized load balance. Implementation and evaluation in Cilk demonstrate performance improvements of up to 2.5x on 80 cores. We also demonstrate that dynamic coarsening can combine the performance benefits of coarse task specification with the adaptability of finer tasks.
Institute of Scientific and Technical Information of China (English)
Tao CHENG; Frank L.LEWIS
2007-01-01
In this paper,neural networks are used to approximately solve the finite-horizon constrained input H-infiniy state feedback control problem.The method is based on solving a related Hamilton-Jacobi-Isaacs equation of the corresponding finite-horizon zero-sum game.The game value function is approximated by a neural network wlth timevarying weights.It is shown that the neural network approximation converges uniformly to the game-value function and the resulting almost optimal constrained feedback controller provides closed-loop stability and bounded L2 gain.The result is an almost optimal H-infinity feedback controller with time-varying coefficients that is solved a priori off-line.The effectiveness of the method is shown on the Rotational/Translational Actuator benchmark nonlinear control problem.
Speed up Training of the Recurrent Neural Network Based on Constrained Optimization Techniques
Institute of Scientific and Technical Information of China (English)
陈珂; 包威权; 等
1996-01-01
In this paper,the constrained optimization technique for a substantial problem is explored,that is accelerating training the globally recurrent neural network.Unlike most of the previous methods in feedforware neural networks,the authors adopt the constrained optimization technique to improve the gradientbased algorithm of the globally recurrent neural network for the adaptive learning rate during tracining.Using the recurrent network with the improved algorithm,some experiments in two real-world problems,namely,filtering additive noises in acoustic data and classification of temporat signals for speaker identification,have been performed.The experimental results show that the recurrent neural network with the improved learning algorithm yields significantly faster training and achieves the satisfactory performance.
Institute of Scientific and Technical Information of China (English)
Ningning YAN; Zhaojie ZHOU
2008-01-01
In this paper,we study a posteriori error estimates of the edge stabilization Galerkin method for the constrained optimal control problem governed by convection-dominated diffusion equations.The residual-type a posteriori error estimators yield both upper and lower bounds for control u measured in L2-norm and for state y and costate p measured in energy norm.Two numerical examples are presented to illustrate the effectiveness of the error estimators provided in this paper.
Optimal Stabilization of A Quadrotor UAV by a Constrained Fuzzy Control and PSO
Directory of Open Access Journals (Sweden)
Boubertakh Hamid
2017-01-01
Full Text Available This work aims to design an optimal fuzzy PD (FPD control for the attitude and altitude stabilization of a quadrotor. The control design is done by mean of the particle swarm optimization (PSO under the constraints of the controller interpretability and the saturation of the actuators. Concretely, a decentralized control structure is adopted where four FPD controllers are used to stabilize the quadrotor angles (roll, pitch and yaw and height. A PSO-based algorithm is used to simultaneously tune the four constrained controllers regarding a cost function quantifying the whole system performances. The simulation results are presented to show the efficiency of the proposed approach.
A Bi-Projection Neural Network for Solving Constrained Quadratic Optimization Problems.
Xia, Youshen; Wang, Jun
2016-02-01
In this paper, a bi-projection neural network for solving a class of constrained quadratic optimization problems is proposed. It is proved that the proposed neural network is globally stable in the sense of Lyapunov, and the output trajectory of the proposed neural network will converge globally to an optimal solution. Compared with existing projection neural networks (PNNs), the proposed neural network has a very small model size owing to its bi-projection structure. Furthermore, an application to data fusion shows that the proposed neural network is very effective. Numerical results demonstrate that the proposed neural network is much faster than the existing PNNs.
Policy iteration adaptive dynamic programming algorithm for discrete-time nonlinear systems.
Liu, Derong; Wei, Qinglai
2014-03-01
This paper is concerned with a new discrete-time policy iteration adaptive dynamic programming (ADP) method for solving the infinite horizon optimal control problem of nonlinear systems. The idea is to use an iterative ADP technique to obtain the iterative control law, which optimizes the iterative performance index function. The main contribution of this paper is to analyze the convergence and stability properties of policy iteration method for discrete-time nonlinear systems for the first time. It shows that the iterative performance index function is nonincreasingly convergent to the optimal solution of the Hamilton-Jacobi-Bellman equation. It is also proven that any of the iterative control laws can stabilize the nonlinear systems. Neural networks are used to approximate the performance index function and compute the optimal control law, respectively, for facilitating the implementation of the iterative ADP algorithm, where the convergence of the weight matrices is analyzed. Finally, the numerical results and analysis are presented to illustrate the performance of the developed method.
Indian Academy of Sciences (India)
DEEPAK KUMAR; A G RAMAKRISHNAN
2016-03-01
Particle swarm optimization (PSO) is used in several combinatorial optimization problems. In this work, particle swarms are used to solve quadratic programming problems with quadratic constraints. The central idea is to use PSO to move in the direction towards optimal solution rather than searching the entire feasibleregion. Binary classification is posed as a quadratically constrained quadratic problem and solved using the proposed method. Each class in the binary classification problem is modeled as a multidimensional ellipsoid to forma quadratic constraint in the problem. Particle swarms help in determining the optimal hyperplane or classification boundary for a data set. Our results on the Iris, Pima, Wine, Thyroid, Balance, Bupa, Haberman, and TAE datasets show that the proposed method works better than a neural network and the performance is close to that of a support vector machine
Feedback control design for discrete-time piecewise affine systems
Institute of Scientific and Technical Information of China (English)
XU Jun; XIE Li-hua
2007-01-01
This paper investigates the design of state feedback and dynamic output feedback stabilizing controllers for discrete-time piecewise affine (PWA) systems. The main objective is to derive design methods that will incorporate the partition information of the PWA systems so as to reduce the design conservatism embedded in existing design methods. We first introduce a transformation that converts the feedback control design problem into a bilinear matrix inequality (BMI) problem. Then, two iterative algorithms are proposed to compute the feedback controllers characterized by the BMI. Several simulation examples are given to demonstrate the advantages of the proposed design.
Satisfactory control of discrete-time linear periodic systems
Institute of Scientific and Technical Information of China (English)
Shiqian LIU; Jihong ZHU; JinChun HU
2007-01-01
In this paper satisfactory control for discrete-time linear periodic systems is studied.Based on a suitable time-invariant state sampled reformulation,periodic state feedback controller has been designed such that desired requirements of steady state covariance,H-infinity rejection bound and regional pole assignment for the periodic system are met simultaneously.By using satisfactory control theory,the problem of satisfactory periodic controller can be transformed into a linear programming problem subject to a set of linear matrix inequalities(LMIs).and a feasible designing approach is presented via LMI technique.Numeric example validates the obtained conclusion.
Simulation of neutrino oscillations using discrete-time quantum walk
Mallick, Arindam; Chandrashekar, C M
2016-01-01
Neutrino oscillation is a well-known phenomenon observed in high energy physics. Here starting from a one-spatial dimensional discrete-time quantum walk we present a method to simulate neutrino oscillation. We present the set of walk parameters with which we can obtain the same oscillation probability profile obtained in both, long range and short range neutrino experiment. Our scheme to simulate three-generation neutrino oscillation from quantum walk evolution operators can be physically realized in any low energy experimental setup with access to control a single six-level system, a multiparticle three-qubits or a qubit-qutrit system.
On reevaluation rate in discrete time Hogg-Huberman model
Tanaka, Toshijiro; Shibata, Junko; Inoue, Masayoshi
2002-06-01
The discrete time Hogg-Huberman model is extended to a case with time-dependent reevaluation rate at which agents using one resource decide to evaluate their resource choice. In this paper the time dependence of the reevaluation rate is determined by states of the system. The dynamical behavior of the extended Hogg-Huberman model is discussed. It is found that the change of fraction of agents using resource 1 is suppressed to be smaller than that in the case of constant reevaluation rate.
A parametric LTR solution for discrete-time systems
DEFF Research Database (Denmark)
Niemann, Hans Henrik; Jannerup, Ole Erik
1989-01-01
and the full loop transfer function, is manipulated into a general form involving the target loop transfer matrix and the fundamental recovery matrix. A parametric LTR solution based on the recovery matrix is developed. It is shown that the LQR/LTR (linear quadratic Gaussian/loop transfer recovery) solution......A parametric LTR (loop transfer recovery) solution for discrete-time compensators incorporating filtering observers which achieve exact recovery is presented for both minimum- and non-minimum-phase systems. First the recovery error, which defines the difference between the target loop transfer...
New Results in Discrete-Time Loop Transfer Recovery
DEFF Research Database (Denmark)
Niemann, Hans Henrik; Søgaard-Andersen, Per
1988-01-01
in terms of the system zeros and the corresponding zero-directions. Full-order as well as minimal-order observers are treated. Further it is shown how exact recovery is also applicable to non-minimum phase plants. In this case the achievable performance is parameterized explicitly.......For discrete-time compensators incorporating prediction observers asymptotic loop transfer recovery is not feasible. Instead loop transfer recovery objectives must be satisfied via exact recovery techniques. In this note the model-based compensators which achieves exact recovery are parametrized...
Control problems of discrete-time dynamical systems
Hasegawa, Yasumichi
2013-01-01
This monograph deals with control problems of discrete-time dynamical systems which include linear and nonlinear input/output relations. It will be of popular interest to researchers, engineers and graduate students who specialized in system theory. A new method which produces manipulated inputs is presented in the sense of state control and output control. This monograph provides new results and their extensions which can also be more applicable for nonlinear dynamical systems. To present the effectiveness of the method, many numerical examples of control problems are provided as well.
LARGE SIGNAL DISCRETE-TIME MODEL FOR PARALLELED BUCK CONVERTERS
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
As a number of switch-combinations are involved in operation of multi-converter-system, conventional methods for obtaining discrete-time large signal model of these converter systems result in a very complex solution. A simple sampled-data technique for modeling distributed dc-dc PWM converters system (DCS) was proposed. The resulting model is nonlinear and can be linearized for analysis and design of DCS. These models are also suitable for fast simulation of these networks. As the input and output of dc-dc converters are slow varying, suitable model for DCS was obtained in terms of the finite order input/output approximation.
Discrete-Time LPV Current Control of an Induction Motor
DEFF Research Database (Denmark)
Bendtsen, Jan Dimon; Trangbæk, Klaus
2003-01-01
In this paper we apply a new method for gain-scheduled output feedback control of nonlinear systems to current control of an induction motor. The method relies on recently developed controller synthesis results for linear parameter-varying (LPV) systems, where the controller synthesis is formulated...... as a set of linear matrix inequalities with full-block multipliers. A standard nonlinear model of the motor is constructed and written on LPV form. We then show that, although originally developed in continuous time, the controller synthesis results can be applied to a discrete-time model as well without...
Synchronization of Discrete-Time Chaotic Systems in Bandlimited Channels
Directory of Open Access Journals (Sweden)
Marcio Eisencraft
2009-01-01
Full Text Available Over the last couple of decades, many methods for synchronizing chaotic systems have been proposed with communications applications in view. Yet their performance has proved disappointing in face of the nonideal character of usual channels linking transmitter and receiver, that is, due to both noise and signal propagation distortion. Here we consider a discrete-time master-slave system that synchronizes despite channel bandwidth limitations and an allied communication system. Synchronization is achieved introducing a digital filter that limits the spectral content of the feedback loop responsible for producing the transmitted signal.
Passive Fault-tolerant Control of Discrete-time Piecewise Affine Systems against Actuator Faults
DEFF Research Database (Denmark)
Tabatabaeipour, Seyed Mojtaba; Izadi-Zamanabadi, Roozbeh; Bak, Thomas
2012-01-01
In this paper, we propose a new method for passive fault-tolerant control of discrete time piecewise affine systems. Actuator faults are considered. A reliable piecewise linear quadratic regulator (LQR) state feedback is designed such that it can tolerate actuator faults. A sufficient condition...... for the exis- tence of a passive fault-tolerant controller is derived and formulated as the feasibility of a set of linear matrix inequalities (LMIs). The upper bound on the performance cost can be minimized using a convex optimization problem with LMI constraints which can be solved efficiently. The approach...
Institute of Scientific and Technical Information of China (English)
ZHANG Yan-hu; YAN Wen-jun; LU Jian-ning; ZHAO Guang-zhou
2005-01-01
Multi-objective robust state-feedback controller synthesis problems for linear discrete-time uncertain systems are addressed. Based on parameter-dependent Lyapunov functions, the Gl2 and GH2 norm expressed in terms of LMI (Linear Matrix Inequality) characterizations are further generalized to cope with the robust analysis for convex polytopic uncertain system.Robust state-feedback controller synthesis conditions are also derived for this class of uncertain systems. Using the above results,multi-objective state-feedback controller synthesis procedures which involve the LMI optimization technique are developed and less conservative than the existing one. An illustrative example verified the validity of the approach.
H-infinity filtering for discrete-time switched linear systems under arbitrary switching
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
This paper is concerned with the problem of H-infinity filtering for discrete-time switched linear systems under arbitrary switching laws.New sufficient conditions for the solvability of the problem are given via switched quadratic Lyapunov functions.Based on Finsler's lemma,two sets of slack variables with special structure are introduced to provide extra degrees of freedom in optimizing the guaranteed H-infinity performance.Compared to the existing methods,the proposed one has better performances and less...
Simultaneous Robust Fault and State Estimation for Linear Discrete-Time Uncertain Systems
Directory of Open Access Journals (Sweden)
Feten Gannouni
2017-01-01
Full Text Available We consider the problem of robust simultaneous fault and state estimation for linear uncertain discrete-time systems with unknown faults which affect both the state and the observation matrices. Using transformation of the original system, a new robust proportional integral filter (RPIF having an error variance with an optimized guaranteed upper bound for any allowed uncertainty is proposed to improve robust estimation of unknown time-varying faults and to improve robustness against uncertainties. In this study, the minimization problem of the upper bound of the estimation error variance is formulated as a convex optimization problem subject to linear matrix inequalities (LMI for all admissible uncertainties. The proportional and the integral gains are optimally chosen by solving the convex optimization problem. Simulation results are given in order to illustrate the performance of the proposed filter, in particular to solve the problem of joint fault and state estimation.
Delay-Constrained Optimized Packet Aggregation in High-Speed Wireless Networks
Institute of Scientific and Technical Information of China (English)
Peyman Teymoori; Nasser Yazdani
2013-01-01
High-speed wireless networks such as IEEE 802.11n have been introduced based on IEEE 802.11 to meet the growing demand for high-throughput and multimedia applications.It is known that the medium access control (MAC) efficiency of IEEE 802.11 decreases with increasing the physical rate.To improve efficiency,few solutions have been proposed such as Aggregation to concatenate a number of packets into a larger frame and send it at once to reduce the protocol overhead.Since transmitting larger frames eventuates to dramatic delay and jitter increase in other nodes,bounding the maximum aggregated frame size is important to satisfy delay requirements of especially multimedia applications.In this paper,we propose a scheme called Optimized Packet Aggregation (OPA) which models the network by constrained convex optimization to obtain the optimal aggregation size of each node regarding to delay constraints of other nodes.OPA attains proportionally fair sharing of the channel while satisfying delay constrains.Furthermore,reaching the optimal point is guaranteed in OPA with low complexity.Simulation results show that OPA can successfully bound delay and meet the requirements of nodes with only an insignificant throughput penalty due to limiting the aggregation size even in dynamic conditions.
Ciaramello, Frank M.; Hemami, Sheila S.
2008-01-01
Sign language users are eager for the freedom and convenience of video communication over cellular devices. Compression of sign language video in this setting offers unique challenges. The low bitrates available make encoding decisions extremely important, while the power constraints of the device limit the encoder complexity. The ultimate goal is to maximize the intelligibility of the conversation given the rate-constrained cellular channel and power constrained encoding device. This paper uses an objective measure of intelligibility, based on subjective testing with members of the Deaf community, for rate-distortion optimization of sign language video within the H.264 framework. Performance bounds are established by using the intelligibility metric in a Lagrangian cost function along with a trellis search to make optimal mode and quantizer decisions for each macroblock. The optimal QP values are analyzed and the unique structure of sign language is exploited in order to reduce complexity by three orders of magnitude relative to the trellis search technique with no loss in rate-distortion performance. Further reductions in complexity are made by eliminating rarely occuring modes in the encoding process. The low complexity SL optimization technique increases the measured intelligibility up to 3.5 dB, at fixed rates, and reduces rate by as much as 60% at fixed levels of intelligibility with respect to a rate control algorithm designed for aesthetic distortion as measured by MSE.
Dynamic optimization and its relation to classical and quantum constrained systems
Contreras, Mauricio; Pellicer, Rely; Villena, Marcelo
2017-08-01
We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist's point of view. By using an analogy to a physical model, we study this system in the classical and quantum frameworks. Classically, the dynamic optimization problem is equivalent to a classical mechanics constrained system, so we must use the Dirac method to analyze it in a correct way. We find that there are two second-class constraints in the model: one fix the momenta associated with the control variables, and the other is a reminder of the optimal control law. The dynamic evolution of this constrained system is given by the Dirac's bracket of the canonical variables with the Hamiltonian. This dynamic results to be identical to the unconstrained one given by the Pontryagin equations, which are the correct classical equations of motion for our physical optimization problem. In the same Pontryagin scheme, by imposing a closed-loop λ-strategy, the optimality condition for the action gives a consistency relation, which is associated to the Hamilton-Jacobi-Bellman equation of the dynamic programming method. A similar result is achieved by quantizing the classical model. By setting the wave function Ψ(x , t) =e iS(x , t) in the quantum Schrödinger equation, a non-linear partial equation is obtained for the S function. For the right-hand side quantization, this is the Hamilton-Jacobi-Bellman equation, when S(x , t) is identified with the optimal value function. Thus, the Hamilton-Jacobi-Bellman equation in Bellman's maximum principle, can be interpreted as the quantum approach of the optimization problem.
Lee, Dae Young
The design of a small satellite is challenging since they are constrained by mass, volume, and power. To mitigate these constraint effects, designers adopt deployable configurations on the spacecraft that result in an interesting and difficult optimization problem. The resulting optimization problem is challenging due to the computational complexity caused by the large number of design variables and the model complexity created by the deployables. Adding to these complexities, there is a lack of integration of the design optimization systems into operational optimization, and the utility maximization of spacecraft in orbit. The developed methodology enables satellite Multidisciplinary Design Optimization (MDO) that is extendable to on-orbit operation. Optimization of on-orbit operations is possible with MDO since the model predictive controller developed in this dissertation guarantees the achievement of the on-ground design behavior in orbit. To enable the design optimization of highly constrained and complex-shaped space systems, the spherical coordinate analysis technique, called the "Attitude Sphere", is extended and merged with an additional engineering tools like OpenGL. OpenGL's graphic acceleration facilitates the accurate estimation of the shadow-degraded photovoltaic cell area. This technique is applied to the design optimization of the satellite Electric Power System (EPS) and the design result shows that the amount of photovoltaic power generation can be increased more than 9%. Based on this initial methodology, the goal of this effort is extended from Single Discipline Optimization to Multidisciplinary Optimization, which includes the design and also operation of the EPS, Attitude Determination and Control System (ADCS), and communication system. The geometry optimization satisfies the conditions of the ground development phase; however, the operation optimization may not be as successful as expected in orbit due to disturbances. To address this issue
DEFF Research Database (Denmark)
Wang, Yong; Cai, Zixing; Zhou, Yuren
2009-01-01
A novel approach to deal with numerical and engineering constrained optimization problems, which incorporates a hybrid evolutionary algorithm and an adaptive constraint-handling technique, is presented in this paper. The hybrid evolutionary algorithm simultaneously uses simplex crossover and two...... mutation operators to generate the offspring population. Additionally, the adaptive constraint-handling technique consists of three main situations. In detail, at each situation, one constraint-handling mechanism is designed based on current population state. Experiments on 13 benchmark test functions...... and four well-known constrained design problems verify the effectiveness and efficiency of the proposed method. The experimental results show that integrating the hybrid evolutionary algorithm with the adaptive constraint-handling technique is beneficial, and the proposed method achieves competitive...
A First-order Prediction-Correction Algorithm for Time-varying (Constrained) Optimization: Preprint
Energy Technology Data Exchange (ETDEWEB)
Dall-Anese, Emiliano [National Renewable Energy Laboratory (NREL), Golden, CO (United States)
2017-07-25
This paper focuses on the design of online algorithms based on prediction-correction steps to track the optimal solution of a time-varying constrained problem. Existing prediction-correction methods have been shown to work well for unconstrained convex problems and for settings where obtaining the inverse of the Hessian of the cost function can be computationally affordable. The prediction-correction algorithm proposed in this paper addresses the limitations of existing methods by tackling constrained problems and by designing a first-order prediction step that relies on the Hessian of the cost function (and do not require the computation of its inverse). Analytical results are established to quantify the tracking error. Numerical simulations corroborate the analytical results and showcase performance and benefits of the algorithms.
Fuzzy chance constrained linear programming model for scrap charge optimization in steel production
DEFF Research Database (Denmark)
Rong, Aiying; Lahdelma, Risto
2008-01-01
the uncertainty based on fuzzy set theory and constrain the failure risk based on a possibility measure. Consequently, the scrap charge optimization problem is modeled as a fuzzy chance constrained linear programming problem. Since the constraints of the model mainly address the specification of the product......, the crisp equivalent of the fuzzy constraints should be less relaxed than that purely based on the concept of soft constraints. Based on the application context we adopt a strengthened version of soft constraints to interpret fuzzy constraints and form a crisp model with consistent and compact constraints...... for solution. Simulation results based on realistic data show that the failure risk can be managed by proper combination of aspiration levels and confidence factors for defining fuzzy numbers. There is a tradeoff between failure risk and material cost. The presented approach applies also for other scrap...
Directory of Open Access Journals (Sweden)
Zhanpeng Fang
2015-01-01
Full Text Available A topology optimization method is proposed to minimize the resonant response of plates with constrained layer damping (CLD treatment under specified broadband harmonic excitations. The topology optimization problem is formulated and the square of displacement resonant response in frequency domain at the specified point is considered as the objective function. Two sensitivity analysis methods are investigated and discussed. The derivative of modal damp ratio is not considered in the conventional sensitivity analysis method. An improved sensitivity analysis method considering the derivative of modal damp ratio is developed to improve the computational accuracy of the sensitivity. The evolutionary structural optimization (ESO method is used to search the optimal layout of CLD material on plates. Numerical examples and experimental results show that the optimal layout of CLD treatment on the plate from the proposed topology optimization using the conventional sensitivity analysis or the improved sensitivity analysis can reduce the displacement resonant response. However, the optimization method using the improved sensitivity analysis can produce a higher modal damping ratio than that using the conventional sensitivity analysis and develop a smaller displacement resonant response.
Robust and Reliable Portfolio Optimization Formulation of a Chance Constrained Problem
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Sengupta Raghu Nandan
2017-02-01
Full Text Available We solve a linear chance constrained portfolio optimization problem using Robust Optimization (RO method wherein financial script/asset loss return distributions are considered as extreme valued. The objective function is a convex combination of portfolio’s CVaR and expected value of loss return, subject to a set of randomly perturbed chance constraints with specified probability values. The robust deterministic counterpart of the model takes the form of Second Order Cone Programming (SOCP problem. Results from extensive simulation runs show the efficacy of our proposed models, as it helps the investor to (i utilize extensive simulation studies to draw insights into the effect of randomness in portfolio decision making process, (ii incorporate different risk appetite scenarios to find the optimal solutions for the financial portfolio allocation problem and (iii compare the risk and return profiles of the investments made in both deterministic as well as in uncertain and highly volatile financial markets.
Chance-Constrained AC Optimal Power Flow for Distribution Systems With Renewables
Energy Technology Data Exchange (ETDEWEB)
DallAnese, Emiliano; Baker, Kyri; Summers, Tyler
2017-09-01
This paper focuses on distribution systems featuring renewable energy sources (RESs) and energy storage systems, and presents an AC optimal power flow (OPF) approach to optimize system-level performance objectives while coping with uncertainty in both RES generation and loads. The proposed method hinges on a chance-constrained AC OPF formulation where probabilistic constraints are utilized to enforce voltage regulation with prescribed probability. A computationally more affordable convex reformulation is developed by resorting to suitable linear approximations of the AC power-flow equations as well as convex approximations of the chance constraints. The approximate chance constraints provide conservative bounds that hold for arbitrary distributions of the forecasting errors. An adaptive strategy is then obtained by embedding the proposed AC OPF task into a model predictive control framework. Finally, a distributed solver is developed to strategically distribute the solution of the optimization problems across utility and customers.
Fuzzy Constrained Predictive Optimal Control of High Speed Train with Actuator Dynamics
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Xi Wang
2016-01-01
Full Text Available We investigate the problem of fuzzy constrained predictive optimal control of high speed train considering the effect of actuator dynamics. The dynamics feature of the high speed train is modeled as a cascade of cars connected by flexible couplers, and the formulation is mathematically transformed into a Takagi-Sugeno (T-S fuzzy model. The goal of this study is to design a state feedback control law at each decision step to enhance safety, comfort, and energy efficiency of high speed train subject to safety constraints on the control input. Based on Lyapunov stability theory, the problem of optimizing an upper bound on the cruise control cost function subject to input constraints is reduced to a convex optimization problem involving linear matrix inequalities (LMIs. Furthermore, we analyze the influences of second-order actuator dynamics on the fuzzy constrained predictive controller, which shows risk of potentially deteriorating the overall system. Employing backstepping method, an actuator compensator is proposed to accommodate for the influence of the actuator dynamics. The experimental results show that with the proposed approach high speed train can track the desired speed, the relative coupler displacement between the neighbouring cars is stable at the equilibrium state, and the influence of actuator dynamics is reduced, which demonstrate the validity and effectiveness of the proposed approaches.
2014-01-01
Portfolio optimization (selection) problem is an important and hard optimization problem that, with the addition of necessary realistic constraints, becomes computationally intractable. Nature-inspired metaheuristics are appropriate for solving such problems; however, literature review shows that there are very few applications of nature-inspired metaheuristics to portfolio optimization problem. This is especially true for swarm intelligence algorithms which represent the newer branch of nature-inspired algorithms. No application of any swarm intelligence metaheuristics to cardinality constrained mean-variance (CCMV) portfolio problem with entropy constraint was found in the literature. This paper introduces modified firefly algorithm (FA) for the CCMV portfolio model with entropy constraint. Firefly algorithm is one of the latest, very successful swarm intelligence algorithm; however, it exhibits some deficiencies when applied to constrained problems. To overcome lack of exploration power during early iterations, we modified the algorithm and tested it on standard portfolio benchmark data sets used in the literature. Our proposed modified firefly algorithm proved to be better than other state-of-the-art algorithms, while introduction of entropy diversity constraint further improved results. PMID:24991645
OPTIMIZED PARTICLE SWARM OPTIMIZATION BASED DEADLINE CONSTRAINED TASK SCHEDULING IN HYBRID CLOUD
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Dhananjay Kumar
2016-01-01
Full Text Available Cloud Computing is a dominant way of sharing of computing resources that can be configured and provisioned easily. Task scheduling in Hybrid cloud is a challenge as it suffers from producing the best QoS (Quality of Service when there is a high demand. In this paper a new resource allocation algorithm, to find the best External Cloud provider when the intermediate provider’s resources aren’t enough to satisfy the customer’s demand is proposed. The proposed algorithm called Optimized Particle Swarm Optimization (OPSO combines the two metaheuristic algorithms namely Particle Swarm Optimization and Ant Colony Optimization (ACO. These metaheuristic algorithms are used for the purpose of optimization in the search space of the required solution, to find the best resource from the pool of resources and to obtain maximum profit even when the number of tasks submitted for execution is very high. This optimization is performed to allocate job requests to internal and external cloud providers to obtain maximum profit. It helps to improve the system performance by improving the CPU utilization, and handle multiple requests at the same time. The simulation result shows that an OPSO yields 0.1% - 5% profit to the intermediate cloud provider compared with standard PSO and ACO algorithms and it also increases the CPU utilization by 0.1%.
Design and Stability of Discrete-Time Quantum Filters with Measurement Imperfections
Somaraju, Abhinav; Sayrin, Clement; Rouchon, Pierre
2011-01-01
This work considers the theory underlying a discrete-time quantum filter recently used in a quantum feedback experiment. It proves that this filter taking into account decoherence and measurement errors is optimal and stable. We present the general framework underlying this filter and show that it corresponds to a recursive expression of the least-square optimal estimation of the density operator in the presence of measurement imperfections. By measurement imperfections, we mean in a very general sense unread measurement performed by the environment (decoherence) and active measurement performed by non-ideal detectors. However, we assume to know precisely all the Kraus operators and also the detection error rates. Such recursive expressions combine well known methods from quantum filtering theory and classical probability theory (Bayes' law). We then demonstrate that such a recursive filter is always stable with respect to its initial condition: the fidelity between the optimal filter state (when the initial ...
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...... function. Most known examples of time-inconsistent stochastic control problems 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 coincide with the equilibrium control and value function, respectively for the time-inconsistent problem. To exemplify the theory, we study some concrete examples, such as hyperbolic discounting and mean–variance control....
Estimating Periodic Software Rejuvenation Schedules under Discrete-Time Operation Circumstance
Iwamoto, Kazuki; Dohi, Tadashi; Kaio, Naoto
Software rejuvenation is a preventive and proactive solution that is particularly useful for counteracting the phenomenon of software aging. In this article, we consider periodic software rejuvenation models based on the expected cost per unit time in the steady state under discrete-time operation circumstance. By applying the discrete renewal reward processes, we describe the stochastic behavior of a telecommunication billing application with a degradation mode, and determine the optimal periodic software rejuvenation schedule minimizing the expected cost. Similar to the earlier work by the same authors, we develop a statistically non-parametric algorithm to estimate the optimal software rejuvenation schedule, by applying the discrete total time on test concept. Numerical examples are presented to estimate the optimal software rejuvenation schedules from the simulation data. We discuss the asymptotic behavior of estimators developed in this paper.
Topology Optimization of Passive Constrained Layer Damping with Partial Coverage on Plate
Directory of Open Access Journals (Sweden)
Weiguang Zheng
2013-01-01
Full Text Available The potential of using topology optimization as a tool to optimize the passive constrained layer damping (PCLD layouts with partial coverage on flat plates is investigated. The objective function is defined as a combination of several modal loss factors solved by finite element-modal strain energy (FE-MSE method. An interface finite element is introduced to modeling the viscoelastic core of PCLD patch to save the computational space and time in the optimization procedure. Solid isotropic material with penalization (SIMP method is used as the material interpolation scheme and the parameters are well selected to avoid local pseudo modes. Then, the method of moving asymptote (MMA is employed as an optimizer to search the optimal topologies of PCLD patch on plates. Applications of two flat plates with different shapes have been applied to demonstrate the validation of the proposed approach. The results show that the objective function is in a steady convergence process and the damping effect of the plates can be enhanced by the optimized PCLD layouts.
A TRUST REGION ALGORITHM WITH NULL SPACE TECHNIQUE FOR EQUALITY CONSTRAINED OPTIMIZATION
Institute of Scientific and Technical Information of China (English)
TONG Xiaojiao; LI Donghui
2004-01-01
This paper presents a trust region algorithm with null space technique fornonlinear equality constrained optimizationConsidering in the null space methods that,the convergent rate of range space step is faster than the null space step for the most cases,the proposed algorithm computes null steps more often than range space stepMoreover,the new algorithm is based on the reduced Hessian SQP methodGlobal convergence ofthe proposed algorithm is provedThe effectiveness of the method is demonstrated bysome numerical examples.
Institute of Scientific and Technical Information of China (English)
ZHU Detong
2000-01-01
This paper proposes projected gradient algorithms in association with using both trust region and line search techniques for convex constrained optimization problems.The mixed strategy is adopted which switches to back tracking steps when a trial projected gradient step produced by the trust region subproblem is unacceptable. A nonmonotone criterion is used to speed up the convergence progress in some curves with large curvature.A theoretical analysis is given which proves that the proposed algorithms are globally convergent and have local superlinear convergence rate under some reasonable conditions.The results of numerical experiments are reported to show the effectiveness of the proposed algorithms.
Constrained time-optimal control of double-integrator system and its application in MPC
Fehér, Marek; Straka, Ondřej; Šmídl, Václav
2017-01-01
The paper deals with the design of a time-optimal controller for systems subject to both state and control constraints. The focus is laid on a double-integrator system, for which the time-to-go function is calculated. The function is then used as a part of a model predictive control criterion where it represents the long-horizon part. The designed model predictive control algorithm is then used in a constrained control problem of permanent magnet synchronous motor model, which behavior can be approximated by a double integrator model. Accomplishments of the control goals are illustrated in a numerical example.
Formal methods for discrete-time dynamical systems
Belta, Calin; Aydin Gol, Ebru
2017-01-01
This book bridges fundamental gaps between control theory and formal methods. Although it focuses on discrete-time linear and piecewise affine systems, it also provides general frameworks for abstraction, analysis, and control of more general models. The book is self-contained, and while some mathematical knowledge is necessary, readers are not expected to have a background in formal methods or control theory. It rigorously defines concepts from formal methods, such as transition systems, temporal logics, model checking and synthesis. It then links these to the infinite state dynamical systems through abstractions that are intuitive and only require basic convex-analysis and control-theory terminology, which is provided in the appendix. Several examples and illustrations help readers understand and visualize the concepts introduced throughout the book.
Coordination Frictions and Job Heterogeneity: A Discrete Time Analysis
DEFF Research Database (Denmark)
Kennes, John; Le Maire, Christian Daniel
This paper develops and extends a dynamic, discrete time, job to worker matching model in which jobs are heterogeneous in equilibrium. The key assumptions of this economic environment are (i) matching is directed and (ii) coordination frictions lead to heterogeneous local labor markets. We de- rive...... a number of new theoretical results, which are essential for the empirical application of this type of model to matched employer-employee microdata. First, we o¤er a robust equilibrium concept in which there is a continu- ous dispersion of job productivities and wages. Second, we show that our model can...... be readily solved with continuous exogenous worker heterogene- ity, where high type workers (high outside options and productivity) earn higher wages in high type jobs and are hired at least as frequently to the better job types as low type workers (low outside options and productivity). Third, we...
COMPONENTWISE STABILITY OF DISCRETE-TIME INTERVAL BIDIRECTIONAL ASSOCIATIVE MEMORIES
Directory of Open Access Journals (Sweden)
Mihaela-Hanako MATCOVSCHI
2004-12-01
Full Text Available The componentwise stability is a special type of asymptotic stability, which incorporates the positive invariance of certain time-dependent rectangular sets with respect to the state space trajectories. The paper develops the analysis of componentwise stability for discrete-time Bidirectional Associative Memory (BAM neural networks with interval type parameters, providing criteria that allow monitoring the evolution of each state-space variable towards the equilibrium point. These criteria are formulated in terms of Schur stability of a test matrix adequately built from the intervals expressing the parameter uncertainties. Our approach represents a refinement of the classical results in stability theory, since the time-dependence of the considered invariant sets makes it possible to give a qualitative characterization of the dynamics at the level of the state vector components.
Hopf Bifurcation in a Cobweb Model with Discrete Time Delays
Directory of Open Access Journals (Sweden)
Luca Gori
2014-01-01
Full Text Available We develop a cobweb model with discrete time delays that characterise the length of production cycle. We assume a market comprised of homogeneous producers that operate as adapters by taking the (expected profit-maximising quantity as a target to adjust production and consumers with a marginal willingness to pay captured by an isoelastic demand. The dynamics of the economy is characterised by a one-dimensional delay differential equation. In this context, we show that (1 if the elasticity of market demand is sufficiently high, the steady-state equilibrium is locally asymptotically stable and (2 if the elasticity of market demand is sufficiently low, quasiperiodic oscillations emerge when the time lag (that represents the length of production cycle is high enough.
Recurrence plots of discrete-time Gaussian stochastic processes
Ramdani, Sofiane; Bouchara, Frédéric; Lagarde, Julien; Lesne, Annick
2016-09-01
We investigate the statistical properties of recurrence plots (RPs) of data generated by discrete-time stationary Gaussian random processes. We analytically derive the theoretical values of the probabilities of occurrence of recurrence points and consecutive recurrence points forming diagonals in the RP, with an embedding dimension equal to 1. These results allow us to obtain theoretical values of three measures: (i) the recurrence rate (REC) (ii) the percent determinism (DET) and (iii) RP-based estimation of the ε-entropy κ(ε) in the sense of correlation entropy. We apply these results to two Gaussian processes, namely first order autoregressive processes and fractional Gaussian noise. For these processes, we simulate a number of realizations and compare the RP-based estimations of the three selected measures to their theoretical values. These comparisons provide useful information on the quality of the estimations, such as the minimum required data length and threshold radius used to construct the RP.
Discrete Time Markovian Agents Interacting Through a Potential
Budhiraja, Amarjit; Rubenthaler, Sylvain
2011-01-01
A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition probability kernel that depends on the 'gradient' of the potential field. The particles, in turn, dynamically modify the potential field through their cumulative input. Interacting Markov processes of the above form have been suggested as models for active biological transport in response to external stimulus such as a chemical gradient. One of the basic mathematical challenges is to develop a general theory of stability for such interacting Markovian systems and for the corresponding nonlinear Markov processes that arise in the large agent limit. Such a theory would be key to a mathematical understanding of the interactive structure formation that results from the complex feedback between the agents and the potential field. It will also be a crucial ingredient in developing simulat...
SU-E-I-23: A General KV Constrained Optimization of CNR for CT Abdominal Imaging
Energy Technology Data Exchange (ETDEWEB)
Weir, V; Zhang, J [University of Kentucky, Lexington, KY (United States)
2015-06-15
Purpose: While Tube current modulation has been well accepted for CT dose reduction, kV adjusting in clinical settings is still at its early stage. This is mainly due to the limited kV options of most current CT scanners. kV adjusting can potentially reduce radiation dose and optimize image quality. This study is to optimize CT abdomen imaging acquisition based on the assumption of a continuous kV, with the goal to provide the best contrast to noise ratio (CNR). Methods: For a given dose (CTDIvol) level, the CNRs at different kV and pitches were measured with an ACR GAMMEX phantom. The phantom was scanned in a Siemens Sensation 64 scanner and a GE VCT 64 scanner. A constrained mathematical optimization was used to find the kV which led to the highest CNR for the anatomy and pitch setting. Parametric equations were obtained from polynomial fitting of plots of kVs vs CNRs. A suitable constraint region for optimization was chosen. Subsequent optimization yielded a peak CNR at a particular kV for different collimations and pitch setting. Results: The constrained mathematical optimization approach yields kV of 114.83 and 113.46, with CNRs of 1.27 and 1.11 at the pitch of 1.2 and 1.4, respectively, for the Siemens Sensation 64 scanner with the collimation of 32 x 0.625mm. An optimized kV of 134.25 and 1.51 CNR is obtained for a GE VCT 64 slice scanner with a collimation of 32 x 0.625mm and a pitch of 0.969. At 0.516 pitch and 32 x 0.625 mm an optimized kV of 133.75 and a CNR of 1.14 was found for the GE VCT 64 slice scanner. Conclusion: CNR in CT image acquisition can be further optimized with a continuous kV option instead of current discrete or fixed kV settings. A continuous kV option is a key for individualized CT protocols.
Variance-Constrained Robust Estimation for Discrete-Time Systems with Communication Constraints
Directory of Open Access Journals (Sweden)
Baofeng Wang
2014-01-01
Full Text Available This paper is concerned with a new filtering problem in networked control systems (NCSs subject to limited communication capacity, which includes measurement quantization, random transmission delay, and packets loss. The measurements are first quantized via a logarithmic quantizer and then transmitted through a digital communication network with random delay and packet loss. The three communication constraints phenomena which can be seen as a class of uncertainties are formulated by a stochastic parameter uncertainty system. The purpose of the paper is to design a linear filter such that, for all the communication constraints, the error state of the filtering process is mean square bounded and the steady-state variance of the estimation error for each state is not more than the individual prescribed upper bound. It is shown that the desired filtering can effectively be solved if there are positive definite solutions to a couple of algebraic Riccati-like inequalities or linear matrix inequalities. Finally, an illustrative numerical example is presented to demonstrate the effectiveness and flexibility of the proposed design approach.
Analyzing the Simple Ranking and Selection Process for Constrained Evolutionary Optimization
Institute of Scientific and Technical Information of China (English)
Ehab Z. Elfeky; Ruhul A. Sarker; Daryl L. Essam
2008-01-01
Many optimization problems that involve practical applications have functional constraints, and some of these constraints are active, meaning that they prevent any solution from improving the objective function value to the one that is better than any solution lying beyond the constraint limits. Therefore, the optimal solution usually lies on the boundary of the feasible region. In order to converge faster when solving such problems, a new ranking and selection scheme is introduced which exploits this feature of constrained problems. In conjunction with selection, a new crossover method is also presented based on three parents. When comparing the results of this new algorithm with six other evolutionary based methods, using 12 benchmark problems from the literature, it shows very encouraging performance. T-tests have been applied in this research to show if there is any statistically significance differences between the algorithms. A study has also been carried out in order to show the effect of each component of the proposed algorithm.
Institute of Scientific and Technical Information of China (English)
蔡绍洪; 龙文; 焦建军
2015-01-01
A novel hybrid algorithm named ABC-BBO, which integrates artificial bee colony (ABC) algorithm with biogeography-based optimization (BBO) algorithm, is proposed to solve constrained mechanical design problems. ABC-BBO combined the exploration of ABC algorithm with the exploitation of BBO algorithm effectively, and hence it can generate the promising candidate individuals. The proposed hybrid algorithm speeds up the convergence and improves the algorithm’s performance. Several benchmark test functions and mechanical design problems are applied to verifying the effects of these improvements and it is demonstrated that the performance of this proposed ABC-BBO is superior to or at least highly competitive with other population-based optimization approaches.
Duda, Jarek
2007-01-01
In this paper it is shown how to almost optimally encode information in valuations of discrete lattice with some translational invariant constrains. The method is based on finding statistical description of such valuations and changing it into statistical algorithm: which allow to construct deterministically valuation with given statistics. Optimal statistic allows to generate valuations with uniform distribution - we get this way maximum information capacity. It will be shown that in this approach we practically can get as close to capacity of the model as we want (found numerically: lost 1e-10 bit/node for Hard Square). There will be presented an alternative to Huffman coding too, which is more precise and practice with changing probability distributions.
Reinforcement learning solution for HJB equation arising in constrained optimal control problem.
Luo, Biao; Wu, Huai-Ning; Huang, Tingwen; Liu, Derong
2015-11-01
The constrained optimal control problem depends on the solution of the complicated Hamilton-Jacobi-Bellman equation (HJBE). In this paper, a data-based off-policy reinforcement learning (RL) method is proposed, which learns the solution of the HJBE and the optimal control policy from real system data. One important feature of the off-policy RL is that its policy evaluation can be realized with data generated by other behavior policies, not necessarily the target policy, which solves the insufficient exploration problem. The convergence of the off-policy RL is proved by demonstrating its equivalence to the successive approximation approach. Its implementation procedure is based on the actor-critic neural networks structure, where the function approximation is conducted with linearly independent basis functions. Subsequently, the convergence of the implementation procedure with function approximation is also proved. Finally, its effectiveness is verified through computer simulations.
A Probability Collectives Approach with a Feasibility-Based Rule for Constrained Optimization
Directory of Open Access Journals (Sweden)
Anand J. Kulkarni
2011-01-01
Full Text Available This paper demonstrates an attempt to incorporate a simple and generic constraint handling technique to the Probability Collectives (PC approach for solving constrained optimization problems. The approach of PC optimizes any complex system by decomposing it into smaller subsystems and further treats them in a distributed and decentralized way. These subsystems can be viewed as a Multi-Agent System with rational and self-interested agents optimizing their local goals. However, as there is no inherent constraint handling capability in the PC approach, a real challenge is to take into account constraints and at the same time make the agents work collectively avoiding the tragedy of commons to optimize the global/system objective. At the core of the PC optimization methodology are the concepts of Deterministic Annealing in Statistical Physics, Game Theory and Nash Equilibrium. Moreover, a rule-based procedure is incorporated to handle solutions based on the number of constraints violated and drive the convergence towards feasibility. Two specially developed cases of the Circle Packing Problem with known solutions are solved and the true optimum results are obtained at reasonable computational costs. The proposed algorithm is shown to be sufficiently robust, and strengths and weaknesses of the methodology are also discussed.
Truong, Binh Duc; Phu Le, Cuong; Halvorsen, Einar
2015-12-01
This paper presents experiments on how to approach the physical limits on power from vibration energy harvesting under displacement-constrained operation. A MEMS electrostatic vibration energy harvester with voltage-control of the system stiffness is used for this purpose. The power saturation problem, when the proof mass displacement reaches maximum amplitude for sufficient acceleration amplitude, is shifted to higher accelerations by use of load optimization and tunable electromechanical coupling k2. Measurement results show that harvested power can be made to follow the optimal velocity-damped generator also for a range of accelerations that implies displacement constraints. Comparing to the saturated power, the power increases 1.5 times with the optimal load and an electromechanical coupling k2=8.7%. This value is 2.3 times for a higher coupling k2=17.9%. The obtained system effectiveness is beyond 60% under the optimization. This work also shows a first demonstration of reaching optimal power in the intermediate acceleration-range between the two extremes of maximum efficiency and maximum power transfer.
Su, Yonggang; Tang, Chen; Chen, Xia; Li, Biyuan; Xu, Wenjun; Lei, Zhenkun
2017-01-01
We propose an image encryption scheme using chaotic phase masks and cascaded Fresnel transform holography based on a constrained optimization algorithm. In the proposed encryption scheme, the chaotic phase masks are generated by Henon map, and the initial conditions and parameters of Henon map serve as the main secret keys during the encryption and decryption process. With the help of multiple chaotic phase masks, the original image can be encrypted into the form of a hologram. The constrained optimization algorithm makes it possible to retrieve the original image from only single frame hologram. The use of chaotic phase masks makes the key management and transmission become very convenient. In addition, the geometric parameters of optical system serve as the additional keys, which can improve the security level of the proposed scheme. Comprehensive security analysis performed on the proposed encryption scheme demonstrates that the scheme has high resistance against various potential attacks. Moreover, the proposed encryption scheme can be used to encrypt video information. And simulations performed on a video in AVI format have also verified the feasibility of the scheme for video encryption.
Institute of Scientific and Technical Information of China (English)
LIU MeiQin
2007-01-01
A novel model, termed the standard neural network model (SNNM), is advanced to describe some delayed (or non-delayed) discrete-time intelligent systems composed of neural networks and Takagi and Sugeno (T-S) fuzzy models. The SNNM is composed of a discrete-time linear dynamic system and a bounded static nonlinear operator. Based on the global asymptotic stability analysis of the SNNMs, linear and nonlinear dynamic output feedback controllers are designed for the SNNMs to stabilize the closed-loop systems, respectively. The control design equations are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms to determine the control signals. Most neural-network-based (or fuzzy) discrete-time intelligent systems with time delays or without time delays can be transformed into the SNNMs for controller synthesis in a unified way. Three application examples show that the SNNMs not only make controller synthesis of neural-network-based (or fuzzy) discrete-time intelligent systems much easier, but also provide a new approach to the synthesis of the controllers for the other type of nonlinear systems.
Observer-based fault detection scheme for a class of discrete time-delay systems
Institute of Scientific and Technical Information of China (English)
Zhong Maiying(钟麦英); Zhang Chenghui(张承慧); Ding Steven X; Lam James
2004-01-01
In this contribution, robust fault detection problems for discrete time-delay systems with l2-norm bounded un-known inputs are studied. The basic idea of our study is first to introduce a state-memoryless observer-based fault detec-tion filter (FDF) as the residual generator and then to formulate such a FDF design problem as an H∞ optimization prob-lem in the sense of increasing the sensitivity of residual to the faults, while simultaneously enhancing the robustness of residual to unknown input as well as plant input. The main results consist of the formulation of such a residual generation optimization problem, solvability conditions and the derivation of an analytic solution. The residual evaluation problem is also considered, which includes the determination of residual evaluation function and threshold. A numerical example is used to demonstrate the proposed fault detection scheme.
H2 control of discrete-time periodic systems with Markovian jumps and multiplicative noise
Ma, Hongji; Jia, Yingmin
2013-10-01
This paper addresses the problem of optimal and robust H2 control for discrete-time periodic systems with Markov jump parameters and multiplicative noise. To analyse the system performance in the presence of exogenous random disturbance, an H2 norm is firstly established on the basis of Gramian matrices. Further, under the condition of exact observability, a necessary and sufficient condition is presented for the solvability of H2 optimal control problem by means of a generalised Riccati equation. When the transition probabilities of jump parameter are incompletely measurable, an H2-guaranteed cost norm is exploited and the robust H2 controller is designed through a linear matrix inequality (LMI) optimisation approach. An example of a networked control system is supplied to illustrate the proposed results.
Preventive Security-Constrained Optimal Power Flow Considering UPFC Control Modes
Directory of Open Access Journals (Sweden)
Xi Wu
2017-08-01
Full Text Available The successful application of the unified power flow controller (UPFC provides a new control method for the secure and economic operation of power system. In order to make the full use of UPFC and improve the economic efficiency and static security of a power system, a preventive security-constrained power flow optimization method considering UPFC control modes is proposed in this paper. Firstly, an iterative method considering UPFC control modes is deduced for power flow calculation. Taking into account the influence of different UPFC control modes on the distribution of power flow after N-1 contingency, the optimization model is then constructed by setting a minimal system operation cost and a maximum static security margin as the objective. Based on this model, the particle swarm optimization (PSO algorithm is utilized to optimize power system operating parameters and UPFC control modes simultaneously. Finally, a standard IEEE 30-bus system is utilized to demonstrate that the proposed method fully exploits the potential of static control of UPFC and significantly increases the economic efficiency and static security of the power system.
He, L.; Huang, G. H.; Lu, H. W.
2008-12-01
In this study a simulation-based fuzzy chance-constrained programming (SFCCP) model is developed based on possibility theory. The model is solved through an indirect search approach which integrates fuzzy simulation, artificial neural network and simulated annealing techniques. This approach has the advantages of: (1) handling simulation and optimization problems under uncertainty associated with fuzzy parameters, (2) providing additional information (i.e. possibility of constraint satisfaction) indicating that how likely one can believe the decision results, (3) alleviating computational burdens in the optimization process, and (4) reducing the chances of being trapped in local optima. The model is applied to a petroleum-contaminated aquifer located in western Canada for supporting the optimal design of groundwater remediation systems. The model solutions provide optimal groundwater pumping rates for the 3, 5 and 10 years of pumping schemes. It is observed that the uncertainty significantly affects the remediation strategies. To mitigate such impacts, additional cost is required either for increased pumping rate or for reinforced site characterization.
Advanced discrete-time control designs and applications
Abidi, Khalid
2015-01-01
This book covers a wide spectrum of systems such as linear and nonlinear multivariable systems as well as control problems such as disturbance, uncertainty and time-delays. The purpose of this book is to provide researchers and practitioners a manual for the design and application of advanced discrete-time controllers. The book presents six different control approaches depending on the type of system and control problem. The first and second approaches are based on Sliding Mode control (SMC) theory and are intended for linear systems with exogenous disturbances. The third and fourth approaches are based on adaptive control theory and are aimed at linear/nonlinear systems with periodically varying parametric uncertainty or systems with input delay. The fifth approach is based on Iterative learning control (ILC) theory and is aimed at uncertain linear/nonlinear systems with repeatable tasks and the final approach is based on fuzzy logic control (FLC) and is intended for highly uncertain systems with heuristi...
Multiple Estimation Architecture in Discrete-Time Adaptive Mixing Control
Directory of Open Access Journals (Sweden)
Simone Baldi
2013-05-01
Full Text Available Adaptive mixing control (AMC is a recently developed control scheme for uncertain plants, where the control action coming from a bank of precomputed controller is mixed based on the parameter estimates generated by an on-line parameter estimator. Even if the stability of the control scheme, also in the presence of modeling errors and disturbances, has been shown analytically, its transient performance might be sensitive to the initial conditions of the parameter estimator. In particular, for some initial conditions, transient oscillations may not be acceptable in practical applications. In order to account for such a possible phenomenon and to improve the learning capability of the adaptive scheme, in this paper a new mixing architecture is developed, involving the use of parallel parameter estimators, or multi-estimators, each one working on a small subset of the uncertainty set. A supervisory logic, using performance signals based on the past and present estimation error, selects the parameter estimate to determine the mixing of the controllers. The stability and robustness properties of the resulting approach, referred to as multi-estimator adaptive mixing control (Multi-AMC, are analytically established. Besides, extensive simulations demonstrate that the scheme improves the transient performance of the original AMC with a single estimator. The control scheme and the analysis are carried out in a discrete-time framework, for easier implementation of the method in digital control.
Various Synchronization Phenomena in Discrete-Time Coupled Chaotic Rotors
Morino, K.; Horita, T.; Miyazaki, S.
2010-06-01
Various synchronizations and related phenomena in discrete-time coupled chaotic rotors are studied. For unidirectional and bidirectional couplings, various dynamical forms of chaotic phase synchronization (CPS) and their relation to the Lyapunov spectra are shown. For a small positive maximum Lyapunov exponent of the coupled element in the case of the unidirectional coupling, the coupling strength at which CPS is achieved almost coincides with the coupling strength at which generalized synchronization (GS) is achieved. On the other hand, for a large positive maximum Lyapunov exponent, the coupling strength is much smaller on the CPS transition point than on the GS transition point. Statistical properties of the phase difference are analytically and numerically studied by large-deviation analysis. On the basis of the grand canonical formalism, the fluctuation spectrum is theoretically derived, which is compared with the numerical results. These agree with the theoretical es timation, and large deviations are detected out of the domain in which the central limit theorem cannot be applied.
Constant pressure and temperature discrete-time Langevin molecular dynamics.
Grønbech-Jensen, Niels; Farago, Oded
2014-11-21
We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems-a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation.
Analyzing neuronal networks using discrete-time dynamics
Ahn, Sungwoo; Smith, Brian H.; Borisyuk, Alla; Terman, David
2010-05-01
We develop mathematical techniques for analyzing detailed Hodgkin-Huxley like models for excitatory-inhibitory neuronal networks. Our strategy for studying a given network is to first reduce it to a discrete-time dynamical system. The discrete model is considerably easier to analyze, both mathematically and computationally, and parameters in the discrete model correspond directly to parameters in the original system of differential equations. While these networks arise in many important applications, a primary focus of this paper is to better understand mechanisms that underlie temporally dynamic responses in early processing of olfactory sensory information. The models presented here exhibit several properties that have been described for olfactory codes in an insect’s Antennal Lobe. These include transient patterns of synchronization and decorrelation of sensory inputs. By reducing the model to a discrete system, we are able to systematically study how properties of the dynamics, including the complex structure of the transients and attractors, depend on factors related to connectivity and the intrinsic and synaptic properties of cells within the network.
Maintaining information online in discrete time; rethinking working memory processes.
Stephane, Massoud
2012-06-21
Linguistic operations occur with verbal information maintained online for a discrete time. It is posited that online maintenance of information is accomplished by verbal working memory (WM), a system that is: (a) independent from the linguistic operations carried out with the information (specialized), and (b) consists of a holding place where information is held in a phonological code (phonological loop) and a rehearsal mechanism that refreshes the phonological loop. This model does not account for the serial position effects associated with information maintenance and additional models are needed to explain the latter effects, which leaves us with a disjointed understanding of online maintenance of information. In this study, 36 middle-aged, healthy subjects (33 males and 3 females) were required to maintain linguistic information (letters) online. The letters called upon different cognitive operations (orthographic; orthographic and phonetic; or orthographic, phonetic and semantic). It was found that online maintenance capacity depends on the cognitive operations associated with the letters and on their serial position. Additionally, the cognitive operation effect on online maintenance was modulated by the serial position. These data favor a model for WM consisting of a simple holding place where verbal information maintenance depends on what the information is used for. We will discuss an integrated model for online information maintenance that accounts for the serial position effects. Published by Elsevier Ireland Ltd.
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available This paper presents sufficient conditions of asymptotic stability for discrete-time linear systems subject to actuator saturations with an output feedback law. The derived stability results are given in terms of LMIs. A new proof is presented to obtain previous conditions of asymptotic stability. A numerical example is used to illustrate this technique by using a linear optimization problem subject to LMI constraints.
Ma, Jun; Chen, Si-Lu; Kamaldin, Nazir; Teo, Chek Sing; Tay, Arthur; Mamun, Abdullah Al; Tan, Kok Kiong
2017-08-18
The biaxial gantry is widely used in many industrial processes that require high precision Cartesian motion. The conventional rigid-link version suffers from breaking down of joints if any de-synchronization between the two carriages occurs. To prevent above potential risk, a flexure-linked biaxial gantry is designed to allow a small rotation angle of the cross-arm. Nevertheless, the chattering of control signals and inappropriate design of the flexure joint will possibly induce resonant modes of the end-effector. Thus, in this work, the design requirements in terms of tracking accuracy, biaxial synchronization, and resonant mode suppression are achieved by integrated optimization of the stiffness of flexures and PID controller parameters for a class of point-to-point reference trajectories with same dynamics but different steps. From here, an H2 optimization problem with defined constraints is formulated, and an efficient iterative solver is proposed by hybridizing direct computation of constrained projection gradient and line search of optimal step. Comparative experimental results obtained on the testbed are presented to verify the effectiveness of the proposed method. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Wang, Gang; Chen, Changzheng; Yu, Shenbo
2016-09-01
In this paper, the static output-feedback control problem of active suspension systems with information structure constraints is investigated. In order to simultaneously improve the ride comfort and stability, a half car model is used. Other constraints such as suspension deflection, actuator saturation, and controller constrained information are also considered. A novel static output-feedback design method based on the variable substitution is employed in the controller design. A single-step linear matrix inequality (LMI) optimization problem is solved to derive the initial feasible solution with a sparsity constraint. The initial infeasibility issue of the static output-feedback is resolved by using state-feedback information. Specifically, an optimization algorithm is proposed to search for less conservative results based on the feasible controller gain matrix. Finally, the validity of the designed controller for different road profiles is illustrated through numerical examples. The simulation results indicate that the optimized static output-feedback controller can achieve better suspension performances when compared with the feasible static output-feedback controller.
Optimal Load and Stiffness for Displacement-Constrained Vibration Energy Harvesters
Halvorsen, Einar
2016-01-01
The power electronic interface to a vibration energy harvester not only provides ac-dc conversion, but can also set the electrical damping to maximize output power under displacement-constrained operation. This is commonly exploited for linear two-port harvesters by synchronous switching to realize a Coulomb-damped resonant generator, but has not been fully explored when the harvester is asynchronously switched to emulate a resistive load. In order to understand the potential of such an approach, the optimal values of load resistance and other control parameters need to be known. In this paper we determine analytically the optimal load and stiffness of a harmonically driven two-port harvester with displacement constraints. For weak-coupling devices, we do not find any benefit of load and stiffness adjustment beyond maintaining a saturated power level. For strong coupling we find that the power can be optimized to agree with the velocity damped generator beyond the first critical force for displacement-constra...
Solution of Constrained Optimal Control Problems Using Multiple Shooting and ESDIRK Methods
DEFF Research Database (Denmark)
Capolei, Andrea; Jørgensen, John Bagterp
2012-01-01
In this paper, we describe a novel numerical algorithm for solution of constrained optimal control problems of the Bolza type for stiff and/or unstable systems. The numerical algorithm combines explicit singly diagonally implicit Runge-Kutta (ESDIRK) integration methods with a multiple shooting...... algorithm. As we consider stiff systems, implicit solvers with sensitivity computation capabilities for initial value problems must be used in the multiple shooting algorithm. Traditionally, multi-step methods based on the BDF algorithm have been used for such problems. The main novel contribution...... of this paper is the use of ESDIRK integration methods for solution of the initial value problems and the corresponding sensitivity equations arising in the multiple shooting algorithm. Compared to BDF-methods, ESDIRK-methods are advantageous in multiple shooting algorithms in which restarts and frequent...
Institute of Scientific and Technical Information of China (English)
ZHU Detong
2006-01-01
In this paper,we propose a new trust-region-projected Hessian algorithm with nonmonotonic backtracking interior point technique for linear constrained optimization.By performing the QR decomposition of an affine scaling equality constraint matrix,the conducted subproblem in the algorithm is changed into the general trust-region subproblem defined by minimizing a quadratic function subject only to an ellipsoidal constraint.By using both the trust-region strategy and the line-search technique,each iteration switches to a backtracking interior point step generated by the trustregion subproblem.The global convergence and fast local convergence rates for the proposed algorithm are established under some reasonable assumptions.A nonmonotonic criterion is used to speed up the convergence in some ill-conditioned cases.
Optimal Financing Decisions of Two Cash-Constrained Supply Chains with Complementary Products
Directory of Open Access Journals (Sweden)
Yuting Li
2016-04-01
Full Text Available In recent years; financing difficulties have been obsessed small and medium enterprises (SMEs; especially emerging SMEs. Inter-members’ joint financing within a supply chain is one of solutions for SMEs. How about members’ joint financing of inter-supply chains? In order to answer the question, we firstly employ the Stackelberg game to propose three kinds of financing decision models of two cash-constrained supply chains with complementary products. Secondly, we analyze qualitatively these models and find the joint financing decision of the two supply chains is the most optimal one. Lastly, we conduct some numerical simulations not only to illustrate above results but also to find that the larger are cross-price sensitivity coefficients; the higher is the motivation for participants to make joint financing decisions; and the more are profits for them to gain.
Directory of Open Access Journals (Sweden)
Kai Yang
2016-01-01
Full Text Available This work investigates a bioinspired microimmune optimization algorithm to solve a general kind of single-objective nonlinear constrained expected value programming without any prior distribution. In the study of algorithm, two lower bound sample estimates of random variables are theoretically developed to estimate the empirical values of individuals. Two adaptive racing sampling schemes are designed to identify those competitive individuals in a given population, by which high-quality individuals can obtain large sampling size. An immune evolutionary mechanism, along with a local search approach, is constructed to evolve the current population. The comparative experiments have showed that the proposed algorithm can effectively solve higher-dimensional benchmark problems and is of potential for further applications.
A SUPERLINEARLY CONVERGENT TRUST REGION ALGORITHM FOR LC1 CONSTRAINED OPTIMIZATION PROBLEMS
Institute of Scientific and Technical Information of China (English)
Ou Yigui; Hou Dingpi
2005-01-01
In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subproblem with a trust region bound, but by solving a system of linear equations. Since the computational complexity of a QP-Problem is in general much larger than that of a system of linear equations, this method proposed in this paper may reduce the computational complexity and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and super-linearly convergent to a solution of the original problem. Some numerical examples are reported, showing the proposed algorithm can be beneficial from a computational point of view.
Analysis of Constrained Optimization Variants of the Map-Seeking Circuit Algorithm
Energy Technology Data Exchange (ETDEWEB)
S.R. Harker; C.R. Vogel; T. Gedeon
2005-09-05
The map-seeking circuit algorithm (MSC) was developed by Arathorn to efficiently solve the combinatorial problem of correspondence maximization, which arises in applications like computer vision, motion estimation, image matching, and automatic speech recognition [D. W. Arathorn, Map-Seeking Circuits in Visual Cognition: A Computational Mechanism for Biological and Machine Vision, Stanford University Press, 2002]. Given an input image, a template image, and a discrete set of transformations, the goal is to find a composition of transformations which gives the best fit between the transformed input and the template. We imbed the associated combinatorial search problem within a continuous framework by using superposition, and we analyze a resulting constrained optimization problem. We present several numerical schemes to compute local solutions, and we compare their performance on a pair of test problems: an image matching problem and the challenging problem of automatically solving a Rubik's cube.
Hinze, J. F.; Klein, S. A.; Nellis, G. F.
2015-12-01
Mixed refrigerant (MR) working fluids can significantly increase the cooling capacity of a Joule-Thomson (JT) cycle. The optimization of MRJT systems has been the subject of substantial research. However, most optimization techniques do not model the recuperator in sufficient detail. For example, the recuperator is usually assumed to have a heat transfer coefficient that does not vary with the mixture. Ongoing work at the University of Wisconsin-Madison has shown that the heat transfer coefficients for two-phase flow are approximately three times greater than for a single phase mixture when the mixture quality is between 15% and 85%. As a result, a system that optimizes a MR without also requiring that the flow be in this quality range may require an extremely large recuperator or not achieve the performance predicted by the model. To ensure optimal performance of the JT cycle, the MR should be selected such that it is entirely two-phase within the recuperator. To determine the optimal MR composition, a parametric study was conducted assuming a thermodynamically ideal cycle. The results of the parametric study are graphically presented on a contour plot in the parameter space consisting of the extremes of the qualities that exist within the recuperator. The contours show constant values of the normalized refrigeration power. This ‘map’ shows the effect of MR composition on the cycle performance and it can be used to select the MR that provides a high cooling load while also constraining the recuperator to be two phase. The predicted best MR composition can be used as a starting point for experimentally determining the best MR.
RECONFIGURABLE CONTROL SYSTEM WITH DISCRETE-TIME CONTROLLERS
Directory of Open Access Journals (Sweden)
A. G. Strizhnev
2015-01-01
Full Text Available The paper considers a synthesis problem for automatic control systems, which operate in various modes, for example, tracking step-wise effects and slowly changing input signals. Generally, one controller cannot ensure the required qualitative characteristics in all operational modes. One of the methods to solve this problem is to create a reconfigurable control system. The authors propose a reconfigurable control system with two discrete-time controllers. The first one is placed in series with the forward path and the second one is connected in parallel with the reverse path having additional gain and unity feedback. Such system structure is characterized by its simplicity and qualitative operational ability to track step-wise and sinusoidal inputs with different amplitudes.The paper presents a developed block diagram of the reconfigurable system and describes its operational principle. Three various plants have been chosen with the purpose to check the operation of the system. Digital controllers have been selected and their parameters have been determined in accordance with the requirements to qualitative operational characteristics of the system. Mathematical modeling has been executed in order to check the operation of the proposed system with various plants and digital controllers. The modeling confirms good –speed performance of the automatic control system while tracking stepwise signals, provision of minimum dynamic error for the given controllers and time delay while tracking harmonic signals with various amplitudes. The obtained results have been successfully tested and can be used for development of automatic control systems that contain other plants and digital controllers, if there are various and occasionally contradictory requirements to their operational quality.
Neural-network-based approximate output regulation of discrete-time nonlinear systems.
Lan, Weiyao; Huang, Jie
2007-07-01
The existing approaches to the discrete-time nonlinear output regulation problem rely on the offline solution of a set of mixed nonlinear functional equations known as discrete regulator equations. For complex nonlinear systems, it is difficult to solve the discrete regulator equations even approximately. Moreover, for systems with uncertainty, these approaches cannot offer a reliable solution. By combining the approximation capability of the feedforward neural networks (NNs) with an online parameter optimization mechanism, we develop an approach to solving the discrete nonlinear output regulation problem without solving the discrete regulator equations explicitly. The approach of this paper can be viewed as a discrete counterpart of our previous paper on approximately solving the continuous-time nonlinear output regulation problem.
Performance limitations in the tracking and regulation problem for discrete-time systems.
Jiang, Xiao-Wei; Guan, Zhi-Hong; Yuan, Fu-Shun; Zhang, Xian-He
2014-03-01
In this paper, the optimal tracking and regulation performance of discrete-time, multi-input multi-output, linear time-invariant systems is investigated. The control signal is influenced by the external disturbance, and the output feedback is subjected to an additive white Gaussian noise (AWGN) corruption. The tracking error with channel input power constraint and the output regulation with control energy constraint are adopted as the measure of tracking and regulation performance respectively, which can be obtained by searching through all stabilizing two-parameter controllers. Both results demonstrate that the performance is closely related to locations and directions of the nonminimum phase zeros, unstable poles of the plant and may be badly degraded by external disturbance and AWGN.
DEFF Research Database (Denmark)
Tabatabaeipour, Seyed Mojtaba; Bak, Thomas
2012-01-01
In this paper we consider the problem of fault estimation and accommodation for discrete time piecewise linear systems. A robust fault estimator is designed to estimate the fault such that the estimation error converges to zero and H∞ performance of the fault estimation is minimized. Then......, the estimate of fault is used to compensate for the effect of the fault. Hence, using the estimate of fault, a fault tolerant controller using a piecewise linear static output feedback is designed such that it stabilizes the system and provides an upper bound on the H∞ performance of the faulty system....... Sufficient conditions for the existence of robust fault estimator and fault tolerant controller are derived in terms of linear matrix inequalities. Upper bounds on the H∞ performance can be minimized by solving convex optimization problems with linear matrix inequality constraints. The efficiency...
Guaranteed cost control with constructing switching law of uncertain discrete-time switched systems
Institute of Scientific and Technical Information of China (English)
Zhang Ying; Duan Guangren
2007-01-01
A guaranteed cost control problem for a class of linear discrete-time switched systems with normbounded uncertainties is considered in this article. The purpose is to construct a switching rule and design a state feedback control law, such that, the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties under the constructed switching rule.A sufficient condition for the existence of guaranteed cost controllers and switching rules is derived based on the Lyapunov theory together with the linear matrix inequality (LMI) approach. Furthermore, a convex optimization problem with LMI constraints is formulated to select the suboptimal guaranteed cost controller. A numerical example demonstrates the validity of the proposed design approach.
Guaranteed cost control with pole constraints for uncertain discrete-time switched systems
Institute of Scientific and Technical Information of China (English)
Ying ZHANG; Guangren DUAN; Liyan CHEN
2009-01-01
For a class of discrete-time switched systems with norm-bounded uncertainties and a quadratic cost index, the problem of designing a guaranteed cost state feedback controller with pole constraints is considered. A sufficient condition on the existence of robust guaranteed controllers is derived by a quadratic Lyapunov function approach together with linear matrix inequality (LMI)technique. Based on a constructed switching law, the closed-loop system is quadratic D-stable and the closedloop cost function value is not more than a specified upper bound. Furthermore, the design of suboptimal guaranteed cost controllers is turned into a convex optimization problem with linear matrix inequalities constraints. A numerical example demonstrates the effect of the proposed design approach.
New approaches to robust l2-l∞ and H∞ filtering for uncertain discrete-time systems
Institute of Scientific and Technical Information of China (English)
高会军; 王常虹
2003-01-01
The problems of robust l2-l∞ and H∞ filtering for discrete-time systems with parameter uncer- tainty residing in a polytope are investigated in this paper. The filtering strategies are based on new ro- bust performance criteria derived from a new result of parameter-dependent Lyapunov stability condition, which exhibit less conservativeness than previous results in the quadratic framework. The designed filters guaranteeing a prescribed l2-l∞ or H∞ noise attenuation level can be obtained from the solution of convex optimization problems, which can be solved via efficient interior point methods. Numerical examples have shown that the filter design procedures proposed in this paper are much less conservative than earlier results.
A Discrete-Time Queue with Balking, Reneging, and Working Vacations
Directory of Open Access Journals (Sweden)
Veena Goswami
2014-01-01
Full Text Available This paper presents an analysis of balking and reneging in finite-buffer discrete-time single server queue with single and multiple working vacations. An arriving customer may balk with a probability or renege after joining according to a geometric distribution. The server works with different service rates rather than completely stopping the service during a vacation period. The service times during a busy period, vacation period, and vacation times are assumed to be geometrically distributed. We find the explicit expressions for the stationary state probabilities. Various system performance measures and a cost model to determine the optimal service rates are presented. Moreover, some queueing models presented in the literature are derived as special cases of our model. Finally, the influence of various parameters on the performance characteristics is shown numerically.
Dynamic Tracking with Zero Variation and Disturbance Rejection Applied to Discrete-Time Systems
Directory of Open Access Journals (Sweden)
Renato de Aguiar Teixeira Mendes
2010-01-01
Full Text Available The problem of signal tracking in discrete linear time invariant systems, in the presence of a disturbance signal in the plant, is solved using a new zero-variation methodology. A discrete-time dynamic output feedback controller is designed in order to minimize the H∞ norm between the exogen input and the output signal of the system, such that the effect of the disturbance is attenuated. Then, the zeros modification is used to minimize the H∞ norm from the reference input signal to the error signal. The error is taken as the difference between the reference and the output signal. The proposed design is formulated in linear matrix inequalities (LMIs framework, such that the optimal solution of the stated problem is obtained. The method can be applied to plants with delay. The control of a delayed system illustrates the effectiveness of the proposed method.
A Discrete Time Markov Chain Model for High Throughput Bidirectional Fano Decoders
Xu, Ran; Morris, Kevin; Kocak, Taskin
2010-01-01
The bidirectional Fano algorithm (BFA) can achieve at least two times decoding throughput compared to the conventional unidirectional Fano algorithm (UFA). In this paper, bidirectional Fano decoding is examined from the queuing theory perspective. A Discrete Time Markov Chain (DTMC) is employed to model the BFA decoder with a finite input buffer. The relationship between the input data rate, the input buffer size and the clock speed of the BFA decoder is established. The DTMC based modelling can be used in designing a high throughput parallel BFA decoding system. It is shown that there is a tradeoff between the number of BFA decoders and the input buffer size, and an optimal input buffer size can be chosen to minimize the hardware complexity for a target decoding throughput in designing a high throughput parallel BFA decoding system.
Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System
Directory of Open Access Journals (Sweden)
Jie Ran
2015-01-01
Full Text Available The dynamics of a discrete-time hyperchaotic system and the amplitude control of Hopf bifurcation for a stochastic discrete-time hyperchaotic system are investigated in this paper. Numerical simulations are presented to exhibit the complex dynamical behaviors in the discrete-time hyperchaotic system. Furthermore, the stochastic discrete-time hyperchaotic system with random parameters is transformed into its equivalent deterministic system with the orthogonal polynomial theory of discrete random function. In addition, the dynamical features of the discrete-time hyperchaotic system with random disturbances are obtained through its equivalent deterministic system. By using the Hopf bifurcation conditions of the deterministic discrete-time system, the specific conditions for the existence of Hopf bifurcation in the equivalent deterministic system are derived. And the amplitude control with random intensity is discussed in detail. Finally, the feasibility of the control method is demonstrated by numerical simulations.
High resolution quantitative phase imaging of live cells with constrained optimization approach
Pandiyan, Vimal Prabhu; Khare, Kedar; John, Renu
2016-03-01
Quantitative phase imaging (QPI) aims at studying weakly scattering and absorbing biological specimens with subwavelength accuracy without any external staining mechanisms. Use of a reference beam at an angle is one of the necessary criteria for recording of high resolution holograms in most of the interferometric methods used for quantitative phase imaging. The spatial separation of the dc and twin images is decided by the reference beam angle and Fourier-filtered reconstructed image will have a very poor resolution if hologram is recorded below a minimum reference angle condition. However, it is always inconvenient to have a large reference beam angle while performing high resolution microscopy of live cells and biological specimens with nanometric features. In this paper, we treat reconstruction of digital holographic microscopy images as a constrained optimization problem with smoothness constraint in order to recover only complex object field in hologram plane even with overlapping dc and twin image terms. We solve this optimization problem by gradient descent approach iteratively and the smoothness constraint is implemented by spatial averaging with appropriate size. This approach will give excellent high resolution image recovery compared to Fourier filtering while keeping a very small reference angle. We demonstrate this approach on digital holographic microscopy of live cells by recovering the quantitative phase of live cells from a hologram recorded with nearly zero reference angle.
Directory of Open Access Journals (Sweden)
Longfei He
2014-01-01
Full Text Available We focus on the joint production planning of complex supply chains facing stochastic demands and being constrained by carbon emission reduction policies. We pick two typical carbon emission reduction policies to research how emission regulation influences the profit and carbon footprint of a typical supply chain. We use the input-output model to capture the interrelated demand link between an arbitrary pair of two nodes in scenarios without or with carbon emission constraints. We design optimization algorithm to obtain joint optimal production quantities combination for maximizing overall profit under regulatory policies, respectively. Furthermore, numerical studies by featuring exponentially distributed demand compare systemwide performances in various scenarios. We build the “carbon emission elasticity of profit (CEEP” index as a metric to evaluate the impact of regulatory policies on both chainwide emissions and profit. Our results manifest that by facilitating the mandatory emission cap in proper installation within the network one can balance well effective emission reduction and associated acceptable profit loss. The outcome that CEEP index when implementing Carbon emission tax is elastic implies that the scale of profit loss is greater than that of emission reduction, which shows that this policy is less effective than mandatory cap from industry standpoint at least.
Smoothing neural network for constrained non-Lipschitz optimization with applications.
Bian, Wei; Chen, Xiaojun
2012-03-01
In this paper, a smoothing neural network (SNN) is proposed for a class of constrained non-Lipschitz optimization problems, where the objective function is the sum of a nonsmooth, nonconvex function, and a non-Lipschitz function, and the feasible set is a closed convex subset of . Using the smoothing approximate techniques, the proposed neural network is modeled by a differential equation, which can be implemented easily. Under the level bounded condition on the objective function in the feasible set, we prove the global existence and uniform boundedness of the solutions of the SNN with any initial point in the feasible set. The uniqueness of the solution of the SNN is provided under the Lipschitz property of smoothing functions. We show that any accumulation point of the solutions of the SNN is a stationary point of the optimization problem. Numerical results including image restoration, blind source separation, variable selection, and minimizing condition number are presented to illustrate the theoretical results and show the efficiency of the SNN. Comparisons with some existing algorithms show the advantages of the SNN.
Adaptive Control and Function Projective Synchronization in 2D Discrete-Time Chaotic Systems
Institute of Scientific and Technical Information of China (English)
LI Yin; CHEN Yong; LI Biao
2009-01-01
This study addresses the adaptive control and function projective synchronization problems between 2D Rulkov discrete-time system and Network discrete-time system.Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate the function projective synchronization of discrete-time chaotic systems.In addition, the adaptive control function is applied to achieve the state synchronization of two discrete-time systems.Numerical results demonstrate the effectiveness of the proposed control scheme.
Discrete-time nonlinear HJB solution using approximate dynamic programming: convergence proof.
Al-Tamimi, Asma; Lewis, Frank L; Abu-Khalaf, Murad
2008-08-01
Convergence of the value-iteration-based heuristic dynamic programming (HDP) algorithm is proven in the case of general nonlinear systems. That is, it is shown that HDP converges to the optimal control and the optimal value function that solves the Hamilton-Jacobi-Bellman equation appearing in infinite-horizon discrete-time (DT) nonlinear optimal control. It is assumed that, at each iteration, the value and action update equations can be exactly solved. The following two standard neural networks (NN) are used: a critic NN is used to approximate the value function, whereas an action network is used to approximate the optimal control policy. It is stressed that this approach allows the implementation of HDP without knowing the internal dynamics of the system. The exact solution assumption holds for some classes of nonlinear systems and, specifically, in the specific case of the DT linear quadratic regulator (LQR), where the action is linear and the value quadratic in the states and NNs have zero approximation error. It is stressed that, for the LQR, HDP may be implemented without knowing the system A matrix by using two NNs. This fact is not generally appreciated in the folklore of HDP for the DT LQR, where only one critic NN is generally used.
Moreenthaler, George W.; Khatib, Nader; Kim, Byoungsoo
2003-08-01
For two decades now, the use of Remote Sensing/Precision Agriculture to improve farm yields while reducing the use of polluting chemicals and the limited water supply has been a major goal. With world population growing exponentially, arable land being consumed by urbanization, and an unfavorable farm economy, farm efficiency must increase to meet future food requirements and to make farming a sustainable, profitable occupation. "Precision Agriculture" refers to a farming methodology that applies nutrients and moisture only where and when they are needed in the field. The real goal is to increase farm profitability by identifying the additional treatments of chemicals and water that increase revenues more than they increase costs and do no exceed pollution standards (constrained optimization). Even though the economic and environmental benefits appear to be great, Remote Sensing/Precision Agriculture has not grown as rapidly as early advocates envisioned. Technology for a successful Remote Sensing/Precision Agriculture system is now in place, but other needed factors have been missing. Commercial satellite systems can now image the Earth (multi-spectrally) with a resolution as fine as 2.5 m. Precision variable dispensing systems using GPS are now available and affordable. Crop models that predict yield as a function of soil, chemical, and irrigation parameter levels have been developed. Personal computers and internet access are now in place in most farm homes and can provide a mechanism for periodically disseminating advice on what quantities of water and chemicals are needed in specific regions of each field. Several processes have been selected that fuse the disparate sources of information on the current and historic states of the crop and soil, and the remaining resource levels available, with the critical decisions that farmers are required to make. These are done in a way that is easy for the farmer to understand and profitable to implement. A "Constrained
Infinite Horizon Discrete Time Control Problems for Bounded Processes
Directory of Open Access Journals (Sweden)
Hayek Naïla
2008-01-01
Full Text Available We establish Pontryagin Maximum Principles in the strong form for infinite horizon optimal control problems for bounded processes, for systems governed by difference equations. Results due to Ioffe and Tihomirov are among the tools used to prove our theorems. We write necessary conditions with weakened hypotheses of concavity and without invertibility, and we provide new results on the adjoint variable. We show links between bounded problems and nonbounded ones. We also give sufficient conditions of optimality.
Infinite Horizon Discrete Time Control Problems for Bounded Processes
Directory of Open Access Journals (Sweden)
2009-03-01
Full Text Available We establish Pontryagin Maximum Principles in the strong form for infinite horizon optimal control problems for bounded processes, for systems governed by difference equations. Results due to Ioffe and Tihomirov are among the tools used to prove our theorems. We write necessary conditions with weakened hypotheses of concavity and without invertibility, and we provide new results on the adjoint variable. We show links between bounded problems and nonbounded ones. We also give sufficient conditions of optimality.
Augmented Lagrangian methods for constrained optimization: the role of the penalty constant
Energy Technology Data Exchange (ETDEWEB)
Tapia, R.A.
1979-01-01
In recent years there has been considerable research activity in the area of penalty function and augmented Lagrangian methods for constrained optimization. The role that the penalty constant plays with respect to local convergence and rate of convergence is reviewed here. As the emphasis has changed from the penalty function methods to the multiplier methods, and lately to the quasi-Newton methods, there has been a corresponding decrease in the importance of the penalty constant. Specifically, in the penalty function method one obtains local convergence if and only if the penalty constant becomes infinite. It is possible to obtain local convergence in the multiplier method for a fixed penalty constant, provided that this constant is sufficiently large. However, one obtains superlinear convergence if and only if the penalty constant becomes infinite. Finally, the quasi-Newton methods are locally superlinearly convergent for fixed values of the penalty constant, and actually the most natural formulation gives an algorithm that is independent of the penalty constant.
Kawano, Yu; Ohtsuka, Toshiyuki
2011-01-01
In this paper, we consider local observability at an initial state for discrete-time autonomous polynomial systems. When testing for observability, for discrete-time nonlinear systems, a condition based on the inverse function theorem is commonly used. However, it is a sufficient condition. In this
Discrete-time delayed standard neural network model and its application
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A novel neural network model, termed the discrete-time delayed standard neural network model (DDSNNM), and similar to the nominal model in linear robust control theory, is suggested to facilitate the stability analysis of discrete-time recurrent neural networks (RNNs) and to ease the synthesis of controllers for discrete-time nonlinear systems. The model is composed of a discrete-time linear dynamic system and a bounded static delayed (or non-delayed) nonlinear operator. By combining various Lyapunov functionals with the S-procedure, sufficient conditions for the global asymptotic stability and global exponential stability of the DDSNNM are derived, which are formulated as linear or nonlinear matrix inequalities. Most discrete-time delayed or non-delayed RNNs, or discrete-time neural-network-based nonlinear control systems can be transformed into the DDSNNMs for stability analysis and controller synthesis in a unified way. Two application examples are given where the DDSNNMs are employed to analyze the stability of the discrete-time cellular neural networks (CNNs) and to synthesize the neuro-controllers for the discrete-time nonlinear systems, respectively. Through these examples, it is demonstrated that the DDSNNM not only makes the stability analysis of the RNNs much easier, but also provides a new approach to the synthesis of the controllers for the nonlinear systems.
Controllability of Linear Discrete-Time Systems with Both Delayed States and Delayed Inputs
Directory of Open Access Journals (Sweden)
Hong Shi
2013-01-01
Full Text Available The controllability issues for discrete-time linear systems with delay in state and control are addressed. By introducing a new concept, the controllability realization index (CRI, the characteristic of controllability is revealed. An easily testable necessary and sufficient condition for the controllability of discrete-time linear systems with state and control delay is established.
Shorikov, A. F.
2016-12-01
This article discusses the discrete-time dynamical system consisting from two controlled objects and described by a linear recurrent vector equations in the presence of uncertain perturbations. This dynamical system has two levels of a control: dominant level (the first level or the level I) and subordinate level (the second level or the level II) and both have different linear terminal criterions of functioning and united a priori by determined information and control connections. It is assumed that the sets constraining all a priori undefined parameters are known and they are a finite sets or convex, closed and bounded polyhedrons in the corresponding finite-dimensional vector spaces. For the dynamical system in question, we propose a mathematical formalization in the form of solving two-level hierarchical minimax program control problem with incomplete information. In this article for solving of the investigated problem is proposed the algorithm that has a form of a recurrent procedure of solving a linear programming and a finite optimization problems. The results obtained in this article can be used for computer simulation of an actual dynamical processes and for designing controlling and navigation systems.
Roselyn, J. Preetha; Devaraj, D.; Dash, Subhransu Sekhar
2013-11-01
Voltage stability is an important issue in the planning and operation of deregulated power systems. The voltage stability problems is a most challenging one for the system operators in deregulated power systems because of the intense use of transmission line capabilities and poor regulation in market environment. This article addresses the congestion management problem avoiding offline transmission capacity limits related to voltage stability by considering Voltage Security Constrained Optimal Power Flow (VSCOPF) problem in deregulated environment. This article presents the application of Multi Objective Differential Evolution (MODE) algorithm to solve the VSCOPF problem in new competitive power systems. The maximum of L-index of the load buses is taken as the indicator of voltage stability and is incorporated in the Optimal Power Flow (OPF) problem. The proposed method in hybrid power market which also gives solutions to voltage stability problems by considering the generation rescheduling cost and load shedding cost which relieves the congestion problem in deregulated environment. The buses for load shedding are selected based on the minimum eigen value of Jacobian with respect to the load shed. In the proposed approach, real power settings of generators in base case and contingency cases, generator bus voltage magnitudes, real and reactive power demands of selected load buses using sensitivity analysis are taken as the control variables and are represented as the combination of floating point numbers and integers. DE/randSF/1/bin strategy scheme of differential evolution with self-tuned parameter which employs binomial crossover and difference vector based mutation is used for the VSCOPF problem. A fuzzy based mechanism is employed to get the best compromise solution from the pareto front to aid the decision maker. The proposed VSCOPF planning model is implemented on IEEE 30-bus system, IEEE 57 bus practical system and IEEE 118 bus system. The pareto optimal
Adaptive Dynamic Programming for Discrete-Time Zero-Sum Games.
Wei, Qinglai; Liu, Derong; Lin, Qiao; Song, Ruizhuo
2017-01-27
In this paper, a novel adaptive dynamic programming (ADP) algorithm, called "iterative zero-sum ADP algorithm," is developed to solve infinite-horizon discrete-time two-player zero-sum games of nonlinear systems. The present iterative zero-sum ADP algorithm permits arbitrary positive semidefinite functions to initialize the upper and lower iterations. A novel convergence analysis is developed to guarantee the upper and lower iterative value functions to converge to the upper and lower optimums, respectively. When the saddle-point equilibrium exists, it is emphasized that both the upper and lower iterative value functions are proved to converge to the optimal solution of the zero-sum game, where the existence criteria of the saddle-point equilibrium are not required. If the saddle-point equilibrium does not exist, the upper and lower optimal performance index functions are obtained, respectively, where the upper and lower performance index functions are proved to be not equivalent. Finally, simulation results and comparisons are shown to illustrate the performance of the present method.
Benjamini, Dan; Basser, Peter J.
2016-10-01
Measuring multidimensional (e.g., 2D) relaxation spectra in NMR and MRI clinical applications is a holy grail of the porous media and biomedical MR communities. The main bottleneck is the inversion of Fredholm integrals of the first kind, an ill-conditioned problem requiring large amounts of data to stabilize a solution. We suggest a novel experimental design and processing framework to accelerate and improve the reconstruction of such 2D spectra that uses a priori information from the 1D projections of spectra, or marginal distributions. These 1D marginal distributions provide powerful constraints when 2D spectra are reconstructed, and their estimation requires an order of magnitude less data than a conventional 2D approach. This marginal distributions constrained optimization (MADCO) methodology is demonstrated here with a polyvinylpyrrolidone-water phantom that has 3 distinct peaks in the 2D D-T1 space. The stability, sensitivity to experimental parameters, and accuracy of this new approach are compared with conventional methods by serially subsampling the full data set. While the conventional, unconstrained approach performed poorly, the new method had proven to be highly accurate and robust, only requiring a fraction of the data. Additionally, synthetic T1 -T2 data are presented to explore the effects of noise on the estimations, and the performance of the proposed method with a smooth and realistic 2D spectrum. The proposed framework is quite general and can also be used with a variety of 2D MRI experiments (D-T2,T1 -T2, D -D, etc.), making these potentially feasible for preclinical and even clinical applications for the first time.
Bakir, Pelin Gundes; Reynders, Edwin; De Roeck, Guido
2007-08-01
The use of changes in dynamic system characteristics to detect damage has received considerable attention during the last years. Within this context, FE model updating technique, which belongs to the class of inverse problems in classical mechanics, is used to detect, locate and quantify damage. In this study, a sensitivity-based finite element (FE) model updating scheme using a trust region algorithm is developed and implemented in a complex structure. A damage scenario is applied on the structure in which the stiffness values of the beam elements close to the beam-column joints are decreased by stiffness reduction factors. A worst case and complex damage pattern is assumed such that the stiffnesses of adjacent elements are decreased by substantially different stiffness reduction factors. The objective of the model updating is to minimize the differences between the eigenfrequency and eigenmodes residuals. The updating parameters of the structure are the stiffness reduction factors. The changes of these parameters are determined iteratively by solving a nonlinear constrained optimization problem. The FE model updating algorithm is also tested in the presence of two levels of noise in simulated measurements. In all three cases, the updated MAC values are above 99% and the relative eigenfrequency differences improve substantially after model updating. In cases without noise and with moderate levels of noise; detection, localization and quantification of damage are successfully accomplished. In the case with substantially noisy measurements, detection and localization of damage are successfully realized. Damage quantification is also promising in the presence of high noise as the algorithm can still predict 18 out of 24 damage parameters relatively accurately in that case.
Universal fuzzy models and universal fuzzy controllers for discrete-time nonlinear systems.
Gao, Qing; Feng, Gang; Dong, Daoyi; Liu, Lu
2015-05-01
This paper investigates the problems of universal fuzzy model and universal fuzzy controller for discrete-time nonaffine nonlinear systems (NNSs). It is shown that a kind of generalized T-S fuzzy model is the universal fuzzy model for discrete-time NNSs satisfying a sufficient condition. The results on universal fuzzy controllers are presented for two classes of discrete-time stabilizable NNSs. Constructive procedures are provided to construct the model reference fuzzy controllers. The simulation example of an inverted pendulum is presented to illustrate the effectiveness and advantages of the proposed method. These results significantly extend the approach for potential applications in solving complex engineering problems.
Generalized computer-aided discrete time domain modeling and analysis of dc-dc converters
Lee, F. C.; Iwens, R. P.; Yu, Y.; Triner, J. E.
1977-01-01
A generalized discrete time domain modeling and analysis technique is presented for all types of switching regulators using any type of duty-cycle controller, and operating in both continuous and discontinuous inductor current. State space techniques are employed to derive an equivalent nonlinear discrete time model that describes the converter exactly. The system is linearized about its equilibrium state to obtain a linear discrete time model for small signal performance evaluations, such as stability, audiosusceptibility and transient response. The analysis makes extensive use of the digital computer as an analytical tool. It is universal, exact and easy to use.
Improved robustness and performance of discrete time sliding mode control systems.
Chakrabarty, Sohom; Bartoszewicz, Andrzej
2016-11-01
This paper presents a theoretical analysis along with simulations to show that increased robustness can be achieved for discrete time sliding mode control systems by choosing the sliding variable, or the output, to be of relative degree two instead of relative degree one. In other words it successfully reduces the ultimate bound of the sliding variable compared to the ultimate bound for standard discrete time sliding mode control systems. It is also found out that for such a selection of relative degree two output of the discrete time system, the reduced order system during sliding becomes finite time stable in absence of disturbance. With disturbance, it becomes finite time ultimately bounded.
DEFF Research Database (Denmark)
Jørgensen, John Bagterp; Jørgensen, Sten Bay
2007-01-01
model is realized from a continuous-discrete-time linear stochastic system specified using transfer functions with time-delays. It is argued that the prediction-error criterion should be selected such that it is compatible with the objective function of the predictive controller in which the model......A Prediction-error-method tailored for model based predictive control is presented. The prediction-error method studied are based on predictions using the Kalman filter and Kalman predictors for a linear discrete-time stochastic state space model. The linear discrete-time stochastic state space...
Robust H∞ filtering for discrete-time impulsive systems with uncertainty
Institute of Scientific and Technical Information of China (English)
Sheng-tao PAN; Ji-tao SUN
2009-01-01
This paper investigates robust filter design for linear discrete-time impulsive systems with uncertainty under H∞ performance. First, an impulsive linear filter and a robust H∞ filtering problem are introduced for a discrete-time impulsive systems. Then,a sufficient condition of asymptotical stability and H∞ performance for the filtering error systems are provided by the discrete-time Lyapunov function method. The filter gains can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example is presented to show effectiveness of the obtained result.
Energy Technology Data Exchange (ETDEWEB)
Huang Zhenkun [Department of Mathematics, School of Sciences, Zhejiang University, Hangzhou, Zhejiang 310027 (China) and School of Sciences, Jimei University, Xiamen, Fujian 361021 (China)]. E-mail: huangdoc@tom.com; Wang Xinghua [Department of Mathematics, School of Sciences, Zhejiang University, Hangzhou, Zhejiang 310027 (China); Gao Feng [School of Sciences, Jimei University, Xiamen, Fujian 361021 (China)
2006-02-06
In this Letter, we discuss discrete-time analogue of a continuous-time cellular neural network. Sufficient conditions are obtained for the existence of a unique almost periodic sequence solution which is globally attractive. Our results demonstrate dynamics of the formulated discrete-time analogue as mathematical models for the continuous-time cellular neural network in almost periodic case. Finally, a computer simulation illustrates the suitability of our discrete-time analogue as numerical algorithms in simulating the continuous-time cellular neural network conveniently.
Stability analysis of a general family of nonlinear positive discrete time-delay systems
Nam, P. T.; Phat, V. N.; Pathirana, P. N.; Trinh, H.
2016-07-01
In this paper, we propose a new approach to analyse the stability of a general family of nonlinear positive discrete time-delay systems. First, we introduce a new class of nonlinear positive discrete time-delay systems, which generalises some existing discrete time-delay systems. Second, through a new technique that relies on the comparison and mathematical induction method, we establish explicit criteria for stability and instability of the systems. Three numerical examples are given to illustrate the feasibility of the obtained results.
Dynamics of Uncertain Discrete-Time Neural Network with Delay and Impulses
Directory of Open Access Journals (Sweden)
Xuehui Mei
2015-01-01
Full Text Available The stability of discrete-time impulsive delay neural networks with and without uncertainty is investigated. First, by using Razumikhin-type theorem, a new less conservative condition for the exponential stability of discrete-time neural network with delay and impulse is proposed. Moreover, some new sufficient conditions are derived to guarantee the stability of uncertain discrete-time neural network with delay and impulse by using Lyapunov function and linear matrix inequality (LMI. Finally, several examples with numerical simulation are presented to demonstrate the effectiveness of the obtained results.
Song, Haiyu; Yu, Li; Zhang, Dan; Zhang, Wen-An
2012-12-01
This paper is concerned with the finite-time quantized H∞ control problem for a class of discrete-time switched time-delay systems with time-varying exogenous disturbances. By using the sector bound approach and the average dwell time method, sufficient conditions are derived for the switched system to be finite-time bounded and ensure a prescribed H∞ disturbance attenuation level, and a mode-dependent quantized state feedback controller is designed by solving an optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the proposed theoretical results.
Hu, Han; Ding, Yulin; Zhu, Qing; Wu, Bo; Xie, Linfu; Chen, Min
2016-08-01
Least-squares matching is a standard procedure in photogrammetric applications for obtaining sub-pixel accuracies of image correspondences. However, least-squares matching has also been criticized for its instability, which is primarily reflected by the requests for the initial correspondence and favorable image quality. In image matching between oblique images, due to the blur, illumination differences and other effects, the image attributes of different views are notably different, which results in a more severe convergence problem. Aiming at improving the convergence rate and robustness of least-squares matching of oblique images, we incorporated prior geometric knowledge in the optimization process, which is reflected as the bounded constraints on the optimizing parameters that constrain the search for a solution to a reasonable region. Furthermore, to be resilient to outliers, we substituted the square loss with a robust loss function. To solve the composite problem, we reformulated the least-squares matching problem as a bound constrained optimization problem, which can be solved with bounds constrained Levenberg-Marquardt solver. Experimental results consisting of images from two different penta-view oblique camera systems confirmed that the proposed method shows guaranteed final convergences in various scenarios compared to the approximately 20-50% convergence rate of classical least-squares matching.
Directory of Open Access Journals (Sweden)
R. Venkata Rao
2016-01-01
Full Text Available The teaching-learning-based optimization (TLBO algorithm is finding a large number of applications in different fields of engineering and science since its introduction in 2011. The major applications are found in electrical engineering, mechanical design, thermal engineering, manufacturing engineering, civil engineering, structural engineering, computer engineering, electronics engineering, physics, chemistry, biotechnology and economics. This paper presents a review of applications of TLBO algorithm and a tutorial for solving the unconstrained and constrained optimization problems. The tutorial is expected to be useful to the beginners.
Parameter estimation for the subcritical Heston model based on discrete time observations
2014-01-01
We study asymptotic properties of some (essentially conditional least squares) parameter estimators for the subcritical Heston model based on discrete time observations derived from conditional least squares estimators of some modified parameters.
A dynamic model of mobile concrete pump boom based on discrete time transfer matrix method
Ren, Wu; Wu, Yunxin; Zhang, Zhaowei
2013-12-01
Mobile concrete pump boom is typical multibody large-scale motion manipulator. Due to posture constantly change in working process, kinematic rule and dynamic characteristic are difficult to solve. A dynamics model of a mobile concrete pump boom is established based on discrete time transfer matrix method (DTTMM). The boom system is divided into sub-structure A and substructure B. Sub-structure A is composed by the 1st boom and hydraulic actuator as well as the support. And substructure B is consists of the other three booms and corresponding hydraulic actuators. In the model, the booms and links are regarded as rigid elements and the hydraulic cylinders are equivalent to spring-damper. The booms are driven by the controllable hydraulic actuators. The overall dynamic equation and transfer matrix of the model can be assembled by sub-structures A and B. To get a precise result, step size and integration parameters are studied then. Next the tip displacement is calculated and compared with the result of ADAMS software. The displacement and rotation angle curves of the proposed method fit well with the ADAMS model. Besides it is convenient in modeling and saves time. So it is suitable for mobile concrete pump boom real-time monitoring and dynamic analysis. All of these provide reference to boom optimize and engineering application of such mechanisms.
Chun, Tae Yoon; Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho
2016-03-01
In this paper, we analyse the convergence and stability properties of generalised policy iteration (GPI) applied to discrete-time linear quadratic regulation problems. GPI is one kind of the generalised adaptive dynamic programming methods used for solving optimal control problems, and is composed of policy evaluation and policy improvement steps. To analyse the convergence and stability of GPI, the dynamic programming (DP) operator is defined. Then, GPI and its equivalent formulas are presented based on the notation of DP operator. The convergence of the approximate value function to the exact one in policy evaluation is proven based on the equivalent formulas. Furthermore, the positive semi-definiteness, stability, and the monotone convergence (PI-mode and VI-mode convergence) of GPI are presented under certain conditions on the initial value function. The online least square method is also presented for the implementation of GPI. Finally, some numerical simulations are carried out to verify the effectiveness of GPI as well as to further investigate the convergence and stability properties.
Robust Proactive Project Scheduling Model for the Stochastic Discrete Time/Cost Trade-Off Problem
Directory of Open Access Journals (Sweden)
Hongbo Li
2015-01-01
Full Text Available We study the project budget version of the stochastic discrete time/cost trade-off problem (SDTCTP-B from the viewpoint of the robustness in the scheduling. Given the project budget and a set of activity execution modes, each with uncertain activity time and cost, the objective of the SDTCTP-B is to minimize the expected project makespan by determining each activity’s mode and starting time. By modeling the activity time and cost using interval numbers, we propose a proactive project scheduling model for the SDTCTP-B based on robust optimization theory. Our model can generate robust baseline schedules that enable a freely adjustable level of robustness. We convert our model into its robust counterpart using a form of the mixed-integer programming model. Extensive experiments are performed on a large number of randomly generated networks to validate our model. Moreover, simulation is used to investigate the trade-off between the advantages and the disadvantages of our robust proactive project scheduling model.
A polynomial criterion for adaptive stabilizability of discrete-time nonlinear systems
Li, Chanying; Xie, Liang-Liang; Guo, Lei
2006-01-01
In this paper, we will investigate the maximum capability of adaptive feedback in stabilizing a basic class of discrete-time nonlinear systems with both multiple unknown parameters and bounded noises. We will present a complete proof of the polynomial criterion for feedback capability as stated in "Robust stability of discrete-time adaptive nonlinear control" (C. Li, L.-L. Xie. and L. Guo, IFAC World Congress, Prague, July 3-8, 2005), by providing both the necessity and sufficiency analyze...
An Audio Data Encryption with Single and Double Dimension Discrete-Time Chaotic Systems
AKGÜL, Akif; KAÇAR, Sezgin; Pehlivan, İhsan
2015-01-01
— In this article, a study on increasing security of audio data encryption with single and double dimension discrete-time chaotic systems was carried out and application and security analyses were executed. Audio data samples of both mono and stereo types were encrypted. In the application here, single and double dimension discrete-time chaotic systems were used. In order to enhance security during encryption, a different method was applied by also using a non-linear function. In the chaos ba...
Simple stability conditions of linear discrete time systems with multiple delay
Directory of Open Access Journals (Sweden)
Stojanović Sreten B.
2010-01-01
Full Text Available In this paper we have established a new Lyapunov-Krasovskii method for linear discrete time systems with multiple time delay. Based on this method, two sufficient conditions for delay-independent asymptotic stability of the linear discrete time systems with multiple delays are derived in the shape of Lyapunov inequality. Numerical examples are presented to demonstrate the applicability of the present approach.
BI-DIRECTIONAL COHEN-GROSSBERG NEURAL NETWORK WITH DISCRETE TIME
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Discrete-time version of the bi-directional Cohen-Grossberg neural network is stud-ied in this paper. Some sufficient conditions are obtained to ensure the global exponen-tial stability of such networks with discrete time based on Lyapunov method. These results do not require the symmetry of the connection matrix and the monotonicity, boundedness and differentiability of the activation function.
BI-DIRECTIONAL COHEN-GROSSBERG NEURAL NETWORK WITH DISCRETE TIME
Institute of Scientific and Technical Information of China (English)
Du Dejun; Chen Anping
2009-01-01
Discrete-time version of the bi-directional Cohen-Grossberg neural network is stu-died in this paper. Some sufficient conditions are obtained to ensure the global ex-ponential stability of such" networks with discrete time based on Lyapunov method. These results do not require the symmetry of the connection matrix and the monoto-nicity, boundedness and differentiability of the activation function.
A continuous-time/discrete-time mixed audio-band sigma delta ADC
Institute of Scientific and Technical Information of China (English)
Liu Yan; Hua Siliang; Wang Donghui; Hou Chaohuan
2011-01-01
This paper introduces a mixed continuous-time/discrete-time, single-loop, fourth-order, 4-bit audioband sigma delta ADC that combines the benefits of continuous-time and discrete-time circuits, while mitigating the challenges associated with continuous-time design. Measurement results show that the peak SNR of this ADC reaches 100 dB and the total power consumption is less than 30 mW.
Nonlinear Maps for Design of Discrete-Time Models of Neuronal Network Dynamics
2016-03-31
responsive tiring patterns . We propose to use modern DSP ideas to develop new efficient approaches to the design of such discrete-time models for...2016 Performance/Technic~ 03-01-2016- 03-31-2016 4. TITLE AND SUBTITLE Sa. CONTRACT NUMBER Nonlinear Maps for Design of Discrete-Time Models of...simulations is to design a neuronal model in the form of difference equations that generates neuronal states in discrete moments of time. In this
Function Projective Synchronization in Discrete-Time Chaotic System with Uncertain Parameters
Institute of Scientific and Technical Information of China (English)
CHEN Yong; LI Xin
2009-01-01
The function projective synchronization of discrete-time chaotic systems is presented. Based on backstep-ping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate function projective synchronization (FPS) of discrete-time chaotic systems with uncertain parameters. With the aid of symbolic-numeric computation, we use the proposed scheme to illustrate FPS between two identical 3D Henon-like maps with uncertain parameters. Numeric simulations are used to verify the effectiveness of our scheme.
Shinano, Yuji; Yoshihara, Toshiyuki; Miyashiro, Ryuhei; Fukagawa, Youzou
The present paper considers optimization of lens adjustment in semiconductor lithography equipment. For improving productivity, the laser irradiation power of recent semiconductor lithography equipment has been boosted, which causes significant aberration due to heating during exposure. The aberration of the equipment must be measured or estimated in order to adjust the positions and orientations of the lenses. Since this adjustment is performed sequentially during exposure, the optimization problem to obtain optimal lens adjustment should be solved within a time as short as 100 ms. Although the problem of calculating the optimal lens adjustment can be naturally formulated as a convex minimization problem, in such a formulation the objective function is convex but includes several nondifferentiable points. Hence, optimization methods based on derivatives cannot be applied. Other approaches using derivative-free optimization or meta-heuristic methods cannot guarantee that the obtained solutions are truly optimal. Therefore, we formulate the optimization problem as quadratically constrained and second-order cone programming problems, which can be handled by solvers using an interior point method. Using the proposed formulations, computational experiments demonstrate that the optimal lens adjustment is obtained in a practical computational time, which is much less than 100 ms.
Directory of Open Access Journals (Sweden)
Arnaut Dierck
2015-01-01
Full Text Available Designing textile antennas for real-life applications requires a design strategy that is able to produce antennas that are optimized over a wide bandwidth for often conflicting characteristics, such as impedance matching, axial ratio, efficiency, and gain, and, moreover, that is able to account for the variations that apply for the characteristics of the unconventional materials used in smart textile systems. In this paper, such a strategy, incorporating a multiobjective constrained Pareto optimization, is presented and applied to the design of a Galileo E6-band antenna with optimal return loss and wide-band axial ratio characteristics. Subsequently, different prototypes of the optimized antenna are fabricated and measured to validate the proposed design strategy.
Analysis of Nonlinear Discrete Time Active Control System with Boring Chatter
Directory of Open Access Journals (Sweden)
Shujing Wu
2014-03-01
Full Text Available In this work we study the design and analysis for nonlinear discrete time active control system with boring charter. It is shown that most analysis result for continuous time nonlinear system can be extended to the discrete time case. In previous studies, a method of nonlinear Model Following Control System (MFCS was proposed by Okubo (1985. In this study, the method of nonlinear MFCS will be extended to nonlinear discrete time system with boring charter. Nonlinear systems which are dealt in this study have the property of norm constraints ║ƒ (v (k║&le&alpha+&betaβ║v (k║&gamma, where &alpha&ge0, &beta&ge0, 0&le&gamma&le1. When 0&le&gamma&le1. It is easy to extend the method to discrete time systems. But in the case &gamma = 1 discrete time systems, the proof becomes difficult. In this case, a new criterion is proposed to ensure that internal states are stable. We expect that this method will provide a useful tool in areas related to stability analysis and design for nonlinear discrete time systems as well.
Rose, Sean; Sidky, Emil Y; Pan, Xiaochuan
2016-01-01
This article is intended to supplement our 2015 paper in Medical Physics titled "Noise properties of CT images reconstructed by use of constrained total-variation, data-discrepancy minimization", in which ordered subsets methods were employed to perform total-variation constrained data-discrepancy minimization for image reconstruction in X-ray computed tomography. Here we provide details regarding implementation of the ordered subsets algorithms and suggestions for selection of algorithm parameters. Detailed pseudo-code is included for every algorithm implemented in the original manuscript.
Energy Technology Data Exchange (ETDEWEB)
Park, Moon Kyu; Kim, Yong Hee; Cha, Kune Ho; Kim, Myung Ki [KEPCO, KEPRI, Taejon (Korea, Republic of)
1998-10-01
A method is described to develop an H{infinity} filtering method for the dynamic compensation of self-powered neutron detectors normally used for fixed incore instruments. An H{infinity} norm of the filter transfer matrix is used as the optimization criteria in the worst-case estimation error sense. Filter modeling is performed for discrete-time model. The filter gains are optimized in the sense of noise attenuation level of H{infinity} setting. By introducing Bounded Real Lemma, the conventional algebraic Riccati inequalities are converted into Linear Matrix Inequalities (LMIs). Finally, the filter design problem is solved via the convex optimization framework using LMIs. The simulation results show that remarkable improvements are achieved in view of the filter response time and the filter design efficiency.
Zhang, Chenglong; Guo, Ping
2017-10-01
The vague and fuzzy parametric information is a challenging issue in irrigation water management problems. In response to this problem, a generalized fuzzy credibility-constrained linear fractional programming (GFCCFP) model is developed for optimal irrigation water allocation under uncertainty. The model can be derived from integrating generalized fuzzy credibility-constrained programming (GFCCP) into a linear fractional programming (LFP) optimization framework. Therefore, it can solve ratio optimization problems associated with fuzzy parameters, and examine the variation of results under different credibility levels and weight coefficients of possibility and necessary. It has advantages in: (1) balancing the economic and resources objectives directly; (2) analyzing system efficiency; (3) generating more flexible decision solutions by giving different credibility levels and weight coefficients of possibility and (4) supporting in-depth analysis of the interrelationships among system efficiency, credibility level and weight coefficient. The model is applied to a case study of irrigation water allocation in the middle reaches of Heihe River Basin, northwest China. Therefore, optimal irrigation water allocation solutions from the GFCCFP model can be obtained. Moreover, factorial analysis on the two parameters (i.e. λ and γ) indicates that the weight coefficient is a main factor compared with credibility level for system efficiency. These results can be effective for support reasonable irrigation water resources management and agricultural production.
Liu, Xing; Hou, Kun Mean; de Vaulx, Christophe; Xu, Jun; Yang, Jianfeng; Zhou, Haiying; Shi, Hongling; Zhou, Peng
2015-01-01
Memory and energy optimization strategies are essential for the resource-constrained wireless sensor network (WSN) nodes. In this article, a new memory-optimized and energy-optimized multithreaded WSN operating system (OS) LiveOS is designed and implemented. Memory cost of LiveOS is optimized by using the stack-shifting hybrid scheduling approach. Different from the traditional multithreaded OS in which thread stacks are allocated statically by the pre-reservation, thread stacks in LiveOS are allocated dynamically by using the stack-shifting technique. As a result, memory waste problems caused by the static pre-reservation can be avoided. In addition to the stack-shifting dynamic allocation approach, the hybrid scheduling mechanism which can decrease both the thread scheduling overhead and the thread stack number is also implemented in LiveOS. With these mechanisms, the stack memory cost of LiveOS can be reduced more than 50% if compared to that of a traditional multithreaded OS. Not is memory cost optimized, but also the energy cost is optimized in LiveOS, and this is achieved by using the multi-core “context aware” and multi-core “power-off/wakeup” energy conservation approaches. By using these approaches, energy cost of LiveOS can be reduced more than 30% when compared to the single-core WSN system. Memory and energy optimization strategies in LiveOS not only prolong the lifetime of WSN nodes, but also make the multithreaded OS feasible to run on the memory-constrained WSN nodes. PMID:25545264
Directory of Open Access Journals (Sweden)
Xing Liu
2014-12-01
Full Text Available Memory and energy optimization strategies are essential for the resource-constrained wireless sensor network (WSN nodes. In this article, a new memory-optimized and energy-optimized multithreaded WSN operating system (OS LiveOS is designed and implemented. Memory cost of LiveOS is optimized by using the stack-shifting hybrid scheduling approach. Different from the traditional multithreaded OS in which thread stacks are allocated statically by the pre-reservation, thread stacks in LiveOS are allocated dynamically by using the stack-shifting technique. As a result, memory waste problems caused by the static pre-reservation can be avoided. In addition to the stack-shifting dynamic allocation approach, the hybrid scheduling mechanism which can decrease both the thread scheduling overhead and the thread stack number is also implemented in LiveOS. With these mechanisms, the stack memory cost of LiveOS can be reduced more than 50% if compared to that of a traditional multithreaded OS. Not is memory cost optimized, but also the energy cost is optimized in LiveOS, and this is achieved by using the multi-core “context aware” and multi-core “power-off/wakeup” energy conservation approaches. By using these approaches, energy cost of LiveOS can be reduced more than 30% when compared to the single-core WSN system. Memory and energy optimization strategies in LiveOS not only prolong the lifetime of WSN nodes, but also make the multithreaded OS feasible to run on the memory-constrained WSN nodes.
Liu, Xing; Hou, Kun Mean; de Vaulx, Christophe; Xu, Jun; Yang, Jianfeng; Zhou, Haiying; Shi, Hongling; Zhou, Peng
2014-12-23
Memory and energy optimization strategies are essential for the resource-constrained wireless sensor network (WSN) nodes. In this article, a new memory-optimized and energy-optimized multithreaded WSN operating system (OS) LiveOS is designed and implemented. Memory cost of LiveOS is optimized by using the stack-shifting hybrid scheduling approach. Different from the traditional multithreaded OS in which thread stacks are allocated statically by the pre-reservation, thread stacks in LiveOS are allocated dynamically by using the stack-shifting technique. As a result, memory waste problems caused by the static pre-reservation can be avoided. In addition to the stack-shifting dynamic allocation approach, the hybrid scheduling mechanism which can decrease both the thread scheduling overhead and the thread stack number is also implemented in LiveOS. With these mechanisms, the stack memory cost of LiveOS can be reduced more than 50% if compared to that of a traditional multithreaded OS. Not is memory cost optimized, but also the energy cost is optimized in LiveOS, and this is achieved by using the multi-core "context aware" and multi-core "power-off/wakeup" energy conservation approaches. By using these approaches, energy cost of LiveOS can be reduced more than 30% when compared to the single-core WSN system. Memory and energy optimization strategies in LiveOS not only prolong the lifetime of WSN nodes, but also make the multithreaded OS feasible to run on the memory-constrained WSN nodes.
Global Optimization of a Class of Nonconvex Quadratically Constrained Quadratic Programming Problems
Institute of Scientific and Technical Information of China (English)
Yong XIA
2011-01-01
In this paper we study a class of nonconvex quadratically constrained quadratic programming problems generalized from relaxations of quadratic assignment problems.We show that each problem is polynomially solved.Strong duality holds if a redundant constraint is introduced.As an application,a new lower bound is proposed for the quadratic assignment problem.
Optimal clustering of frequency-constrained maintenance jobs with shared set-ups
Dijkhuizen, van Gerhard; Harten, van Aart
1997-01-01
Since maintenance jobs often require one or more set-up activities, joint execution or clustering of maintenance jobs is a powerful instrument to reduce shut-down costs. We consider a clustering problem for frequency-constrained maintenance jobs, i.e. maintenance jobs that must be carried out with a
Directory of Open Access Journals (Sweden)
Chocat Rudy
2015-01-01
Full Text Available The design of complex systems often induces a constrained optimization problem under uncertainty. An adaptation of CMA-ES(λ, μ optimization algorithm is proposed in order to efficiently handle the constraints in the presence of noise. The update mechanisms of the parametrized distribution used to generate the candidate solutions are modified. The constraint handling method allows to reduce the semi-principal axes of the probable research ellipsoid in the directions violating the constraints. The proposed approach is compared to existing approaches on three analytic optimization problems to highlight the efficiency and the robustness of the algorithm. The proposed method is used to design a two stage solid propulsion launch vehicle.
DEFF Research Database (Denmark)
Liu, Zhaoxi; Wu, Qiuwei; Oren, Shmuel S.
2016-01-01
This paper presents a distribution locational marginal pricing (DLMP) method through chance constrained mixed-integer programming designed to alleviate the possible congestion in the future distribution network with high penetration of electric vehicles (EVs). In order to represent the stochastic...... the driving requirement is below the predetermined confidence parameter. The efficacy of the proposed approach was demonstrated by case studies using a 33-bus distribution system of the Bornholm power system and the Danish driving data. The case study results show that the DLMP method through chance...... constrained MIP can successfully alleviate the congestion in the distribution network due to the EV charging while keeping the failure probability of EV charging not meeting driving needs below the predefined confidence....
Directory of Open Access Journals (Sweden)
Nebojsa Bacanin
2014-01-01
portfolio model with entropy constraint. Firefly algorithm is one of the latest, very successful swarm intelligence algorithm; however, it exhibits some deficiencies when applied to constrained problems. To overcome lack of exploration power during early iterations, we modified the algorithm and tested it on standard portfolio benchmark data sets used in the literature. Our proposed modified firefly algorithm proved to be better than other state-of-the-art algorithms, while introduction of entropy diversity constraint further improved results.
Mirzaei, Mahmood; Tibaldi, Carlo; Hansen, Morten H.
2016-09-01
PI/PID controllers are the most common wind turbine controllers. Normally a first tuning is obtained using methods such as pole-placement or Ziegler-Nichols and then extensive aeroelastic simulations are used to obtain the best tuning in terms of regulation of the outputs and reduction of the loads. In the traditional tuning approaches, the properties of different open loop and closed loop transfer functions of the system are not normally considered. In this paper, an assessment of the pole-placement tuning method is presented based on robustness measures. Then a constrained optimization setup is suggested to automatically tune the wind turbine controller subject to robustness constraints. The properties of the system such as the maximum sensitivity and complementary sensitivity functions (Ms and Mt ), along with some of the responses of the system, are used to investigate the controller performance and formulate the optimization problem. The cost function is the integral absolute error (IAE) of the rotational speed from a disturbance modeled as a step in wind speed. Linearized model of the DTU 10-MW reference wind turbine is obtained using HAWCStab2. Thereafter, the model is reduced with model order reduction. The trade-off curves are given to assess the tunings of the poles- placement method and a constrained optimization problem is solved to find the best tuning.
Causal inference for continuous-time processes when covariates are observed only at discrete times
Zhang, Mingyuan; Small, Dylan S; 10.1214/10-AOS830
2011-01-01
Most of the work on the structural nested model and g-estimation for causal inference in longitudinal data assumes a discrete-time underlying data generating process. However, in some observational studies, it is more reasonable to assume that the data are generated from a continuous-time process and are only observable at discrete time points. When these circumstances arise, the sequential randomization assumption in the observed discrete-time data, which is essential in justifying discrete-time g-estimation, may not be reasonable. Under a deterministic model, we discuss other useful assumptions that guarantee the consistency of discrete-time g-estimation. In more general cases, when those assumptions are violated, we propose a controlling-the-future method that performs at least as well as g-estimation in most scenarios and which provides consistent estimation in some cases where g-estimation is severely inconsistent. We apply the methods discussed in this paper to simulated data, as well as to a data set c...
Directory of Open Access Journals (Sweden)
Huiying Sun
2014-01-01
Full Text Available We mainly consider the stability of discrete-time Markovian jump linear systems with state-dependent noise as well as its linear quadratic (LQ differential games. A necessary and sufficient condition involved with the connection between stochastic Tn-stability of Markovian jump linear systems with state-dependent noise and Lyapunov equation is proposed. And using the theory of stochastic Tn-stability, we give the optimal strategies and the optimal cost values for infinite horizon LQ stochastic differential games. It is demonstrated that the solutions of infinite horizon LQ stochastic differential games are concerned with four coupled generalized algebraic Riccati equations (GAREs. Finally, an iterative algorithm is presented to solve the four coupled GAREs and a simulation example is given to illustrate the effectiveness of it.
Wang, Dong; Liu, Tao; Sun, Ximing; Zhong, Chongquan
2016-07-01
A discrete-time domain two-degree-of-freedom (2DOF) design method is proposed for integrating and unstable processes with time delay. Based on a 2DOF control structure recently developed, a controller is analytically designed in terms of the H2 optimal control performance specification for the set-point tracking, and another controller is derived by proposing the desired closed-loop transfer function for load disturbance rejection. Both controllers can be tuned relatively independent to realize control optimization. Analytical expression of the set-point response is given for quantitatively tuning the single adjustable parameter in the set-point tracking controller. At the meantime, sufficient and necessary conditions for holding robust stability of the closed-loop control system are established for tuning another adjustable parameter in the disturbance rejection controller, along with numerical tuning guidelines. Illustrative examples from the literature are used to demonstrate the effectiveness of the proposed method.
Qi, Donglian; Liu, Meiqin; Qiu, Meikang; Zhang, Senlin
2010-08-01
This brief studies exponential H(infinity) synchronization of a class of general discrete-time chaotic neural networks with external disturbance. On the basis of the drive-response concept and H(infinity) control theory, and using Lyapunov-Krasovskii (or Lyapunov) functional, state feedback controllers are established to not only guarantee exponential stable synchronization between two general chaotic neural networks with or without time delays, but also reduce the effect of external disturbance on the synchronization error to a minimal H(infinity) norm constraint. The proposed controllers can be obtained by solving the convex optimization problems represented by linear matrix inequalities. Most discrete-time chaotic systems with or without time delays, such as Hopfield neural networks, cellular neural networks, bidirectional associative memory networks, recurrent multilayer perceptrons, Cohen-Grossberg neural networks, Chua's circuits, etc., can be transformed into this general chaotic neural network to be H(infinity) synchronization controller designed in a unified way. Finally, some illustrated examples with their simulations have been utilized to demonstrate the effectiveness of the proposed methods.
Adaptive band-limited disturbance rejection in linear discrete-time systems
Directory of Open Access Journals (Sweden)
Foued Ben-Amara
1995-01-01
Full Text Available The problem of adaptively rejecting a disturbance consisting of a linear combination of sinusoids with unknown and/or time varying frequencies for SISO LTI discrete-time systems is considered. The rejection of the disturbance input is achieved by constructing the set of stabilizing controllers using the Youla parametrization and adjusting the Youla parameter to achieve asymptotic disturbance rejection. The first main result in this paper concerns off-line controller design where a controller that achieves regulation is numerically designed off-line based on the assumption that only the sequence of discrete disturbance input values (as opposed to a model of the disturbance is available. A least squares based optimization algorithm is used in the controller design. As expected, it is shown, under some mild assumptions, that if the off-line designed controller achieves regulation, then it must include a model of the disturbance input. The second main result concerns on-line controller design where recursive versions of the off-line algorithm used above for controller design are presented and their convergence properties analyzed. Conditions under which the on-line algorithms yield an asymptotic controller that achieves regulation are presented. Conditions both for the case where the disturbance input properties are constant but unknown and for the case where they are unknown and time-varying are given. The on-line controller construction amounts to an adaptive implementation of the Internal Model Principle. The performance robustness of the off-line designed controller in the face of plant model uncertainties is investigated. It is shown, under some mild assumptions, that performance robustness is realized provided internal stability is maintained. The performance of the adaptation algorithms is illustrated through a simulation example.
Joint modeling of longitudinal data and discrete-time survival outcome.
Qiu, Feiyou; Stein, Catherine M; Elston, Robert C
2016-08-01
A predictive joint shared parameter model is proposed for discrete time-to-event and longitudinal data. A discrete survival model with frailty and a generalized linear mixed model for the longitudinal data are joined to predict the probability of events. This joint model focuses on predicting discrete time-to-event outcome, taking advantage of repeated measurements. We show that the probability of an event in a time window can be more precisely predicted by incorporating the longitudinal measurements. The model was investigated by comparison with a two-step model and a discrete-time survival model. Results from both a study on the occurrence of tuberculosis and simulated data show that the joint model is superior to the other models in discrimination ability, especially as the latent variables related to both survival times and the longitudinal measurements depart from 0.
Wang, Tong; Ding, Yongsheng; Zhang, Lei; Hao, Kuangrong
2016-08-01
This paper considered the synchronisation of continuous complex dynamical networks with discrete-time communications and delayed nodes. The nodes in the dynamical networks act in the continuous manner, while the communications between nodes are discrete-time; that is, they communicate with others only at discrete time instants. The communication intervals in communication period can be uncertain and variable. By using a piecewise Lyapunov-Krasovskii function to govern the characteristics of the discrete communication instants, we investigate the adaptive feedback synchronisation and a criterion is derived to guarantee the existence of the desired controllers. The globally exponential synchronisation can be achieved by the controllers under the updating laws. Finally, two numerical examples including globally coupled network and nearest-neighbour coupled networks are presented to demonstrate the validity and effectiveness of the proposed control scheme.
Li, Shaobao; Feng, Gang; Luo, Xiaoyuan; Guan, Xinping
2015-12-01
This paper investigates the output consensus problem of heterogeneous discrete-time multiagent systems with individual agents subject to structural uncertainties and different disturbances. A novel distributed control law based on internal reference models is first presented for output consensus of heterogeneous discrete-time multiagent systems without structural uncertainties, where internal reference models embedded in controllers are designed with the objective of reducing communication costs. Then based on the distributed internal reference models and the well-known internal model principle, a distributed control law is further presented for output consensus of heterogeneous discrete-time multiagent systems with structural uncertainties. It is shown in both cases that the consensus trajectory of the internal reference models determines the output trajectories of agents. Finally, numerical simulation results are provided to illustrate the effectiveness of the proposed control schemes.
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Chellaboina Vijaysekhar
2005-01-01
Full Text Available We develop thermodynamic models for discrete-time large-scale dynamical systems. Specifically, using compartmental dynamical system theory, we develop energy flow models possessing energy conservation, energy equipartition, temperature equipartition, and entropy nonconservation principles for discrete-time, large-scale dynamical systems. Furthermore, we introduce a new and dual notion to entropy; namely, ectropy, as a measure of the tendency of a dynamical system to do useful work and grow more organized, and show that conservation of energy in an isolated thermodynamic system necessarily leads to nonconservation of ectropy and entropy. In addition, using the system ectropy as a Lyapunov function candidate, we show that our discrete-time, large-scale thermodynamic energy flow model has convergent trajectories to Lyapunov stable equilibria determined by the system initial subsystem energies.
Permitted and forbidden sets in discrete-time linear threshold recurrent neural networks.
Yi, Zhang; Zhang, Lei; Yu, Jiali; Tan, Kok Kiong
2009-06-01
The concepts of permitted and forbidden sets enable a new perspective of the memory in neural networks. Such concepts exhibit interesting dynamics in recurrent neural networks. This paper studies the basic theories of permitted and forbidden sets of the linear threshold discrete-time recurrent neural networks. The linear threshold transfer function has been regarded as an adequate transfer function for recurrent neural networks. Networks with this transfer function form a class of hybrid analog and digital networks which are especially useful for perceptual computations. Networks in discrete time can directly provide algorithms for efficient implementation in digital hardware. The main contribution of this paper is to establish foundations of permitted and forbidden sets. Necessary and sufficient conditions for the linear threshold discrete-time recurrent neural networks are obtained for complete convergence, existence of permitted and forbidden sets, as well as conditionally multiattractivity, respectively. Simulation studies explore some possible interesting practical applications.
Control of discrete time systems based on recurrent Super-Twisting-like algorithm.
Salgado, I; Kamal, S; Bandyopadhyay, B; Chairez, I; Fridman, L
2016-09-01
Most of the research in sliding mode theory has been carried out to in continuous time to solve the estimation and control problems. However, in discrete time, the results in high order sliding modes have been less developed. In this paper, a discrete time super-twisting-like algorithm (DSTA) was proposed to solve the problems of control and state estimation. The stability proof was developed in terms of the discrete time Lyapunov approach and the linear matrix inequalities theory. The system trajectories were ultimately bounded inside a small region dependent on the sampling period. Simulation results tested the DSTA. The DSTA was applied as a controller for a Furuta pendulum and for a DC motor supplied by a DSTA signal differentiator.
On Extended Dissipativity of Discrete-Time Neural Networks With Time Delay.
Feng, Zhiguang; Zheng, Wei Xing
2015-12-01
In this brief, the problem of extended dissipativity analysis for discrete-time neural networks with time-varying delay is investigated. The definition of extended dissipativity of discrete-time neural networks is proposed, which unifies several performance measures, such as the H∞ performance, passivity, l2 - l∞ performance, and dissipativity. By introducing a triple-summable term in Lyapunov function, the reciprocally convex approach is utilized to bound the forward difference of the triple-summable term and then the extended dissipativity criterion for discrete-time neural networks with time-varying delay is established. The derived condition guarantees not only the extended dissipativity but also the stability of the neural networks. Two numerical examples are given to demonstrate the reduced conservatism and effectiveness of the obtained results.
Liao, Bolin; Zhang, Yunong; Jin, Long
2016-02-01
In this paper, a new Taylor-type numerical differentiation formula is first presented to discretize the continuous-time Zhang neural network (ZNN), and obtain higher computational accuracy. Based on the Taylor-type formula, two Taylor-type discrete-time ZNN models (termed Taylor-type discrete-time ZNNK and Taylor-type discrete-time ZNNU models) are then proposed and discussed to perform online dynamic equality-constrained quadratic programming. For comparison, Euler-type discrete-time ZNN models (called Euler-type discrete-time ZNNK and Euler-type discrete-time ZNNU models) and Newton iteration, with interesting links being found, are also presented. It is proved herein that the steady-state residual errors of the proposed Taylor-type discrete-time ZNN models, Euler-type discrete-time ZNN models, and Newton iteration have the patterns of O(h(3)), O(h(2)), and O(h), respectively, with h denoting the sampling gap. Numerical experiments, including the application examples, are carried out, of which the results further substantiate the theoretical findings and the efficacy of Taylor-type discrete-time ZNN models. Finally, the comparisons with Taylor-type discrete-time derivative model and other Lagrange-type discrete-time ZNN models for dynamic equality-constrained quadratic programming substantiate the superiority of the proposed Taylor-type discrete-time ZNN models once again.
Constrained Run-to-Run Optimization for Batch Process Based on Support Vector Regression Model
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
An iterative (run-to-run) optimization method was presented for batch processes under input constraints. Generally it is very difficult to acquire an accurate mechanistic model for a batch process. Because support vector machine is powerful for the problems characterized by small samples, nonlinearity, high dimension and local minima, support vector regression models were developed for the end-point optimization of batch processes. Since there is no analytical way to find the optimal trajectory, an iterative method was used to exploit the repetitive nature of batch processes to determine the optimal operating policy. The optimization algorithm is proved convergent. The numerical simulation shows that the method can improve the process performance through iterations.
Optimization of constrained multiple-objective reliability problems using evolutionary algorithms
Energy Technology Data Exchange (ETDEWEB)
Salazar, Daniel [Instituto de Sistemas Inteligentes y Aplicaciones Numericas en Ingenieria (IUSIANI), Division de Computacion Evolutiva y Aplicaciones (CEANI), Universidad de Las Palmas de Gran Canaria, Islas Canarias (Spain) and Facultad de Ingenieria, Universidad Central Venezuela, Caracas (Venezuela)]. E-mail: danielsalazaraponte@gmail.com; Rocco, Claudio M. [Facultad de Ingenieria, Universidad Central Venezuela, Caracas (Venezuela)]. E-mail: crocco@reacciun.ve; Galvan, Blas J. [Instituto de Sistemas Inteligentes y Aplicaciones Numericas en Ingenieria (IUSIANI), Division de Computacion Evolutiva y Aplicaciones (CEANI), Universidad de Las Palmas de Gran Canaria, Islas Canarias (Spain)]. E-mail: bgalvan@step.es
2006-09-15
This paper illustrates the use of multi-objective optimization to solve three types of reliability optimization problems: to find the optimal number of redundant components, find the reliability of components, and determine both their redundancy and reliability. In general, these problems have been formulated as single objective mixed-integer non-linear programming problems with one or several constraints and solved by using mathematical programming techniques or special heuristics. In this work, these problems are reformulated as multiple-objective problems (MOP) and then solved by using a second-generation Multiple-Objective Evolutionary Algorithm (MOEA) that allows handling constraints. The MOEA used in this paper (NSGA-II) demonstrates the ability to identify a set of optimal solutions (Pareto front), which provides the Decision Maker with a complete picture of the optimal solution space. Finally, the advantages of both MOP and MOEA approaches are illustrated by solving four redundancy problems taken from the literature.
A Novel Analytic Technique for the Service Station Reliability in a Discrete-Time Repairable Queue
Directory of Open Access Journals (Sweden)
Renbin Liu
2013-01-01
Full Text Available This paper presents a decomposition technique for the service station reliability in a discrete-time repairable GeomX/G/1 queueing system, in which the server takes exhaustive service and multiple adaptive delayed vacation discipline. Using such a novel analytic technique, some important reliability indices and reliability relation equations of the service station are derived. Furthermore, the structures of the service station indices are also found. Finally, special cases and numerical examples validate the derived results and show that our analytic technique is applicable to reliability analysis of some complex discrete-time repairable bulk arrival queueing systems.
Institute of Scientific and Technical Information of China (English)
阮炯; 王军平; 郭德典
2004-01-01
In this paper, we first introduce the model of discrete-time neural networks with generalized input-output function and present a proof of the existence of a fixed point by Schauder fixed-point principle. Secondly, we study the uniformly asymptotical stability of equilibrium in non-autonomous discrete-time neural networks and give some sufficient conditions that guarantee the stability of it by using the converse theorem of Lyapunov function. Finally, several examples and numerical simulations are given to illustrate and reinforce our theories.
Explicit G 2-constrained Merging of a Pair of B´ezier Curves by Control Point Optimization
Institute of Scientific and Technical Information of China (English)
LU Li-Zheng; QIU Yu-Yang
2014-01-01
This paper presents a simple and explicit method for G2-constrained merging of a pair of B´ezier curves by mini-mizing the l2 distance defined in terms of control points. After expressing the l2 distance as a quadratic function of two param-eters, the optimally merged curve can be explicitly obtained, which is achieved by control point optimization such that the l2 distance is minimized. The existence of the unique solution is shown by proving that the l2 distance is convex. The pro-posed method is explicit and eﬃcient since it is non-iterative and expressed by known control points. Numerical examples demonstrate the effectiveness of the new method.
Vysotskiy, Victor P; Boström, Jonas; Veryazov, Valera
2013-11-15
A parallel procedure for an effective optimization of relative position and orientation between two or more fragments has been implemented in the MOLCAS program package. By design, the procedure does not perturb the electronic structure of a system under the study. The original composite system is divided into frozen fragments and internal coordinates linking those fragments are the only optimized parameters. The procedure is capable to handle fully independent (no border atoms) fragments as well as fragments connected by covalent bonds. In the framework of the procedure, the optimization of relative position and orientation of the fragments are carried out in the internal "Z-matrix" coordinates using numerical derivatives. The total number of required single points energy evaluations scales with the number of fragments rather than with the total number of atoms in the system. The accuracy and the performance of the procedure have been studied by test calculations for a representative set of two- and three-fragment molecules with artificially distorted structures. The developed approach exhibits robust and smooth convergence to the reference optimal structures. As only a few internal coordinates are varied during the procedure, the proposed constrained fragment geometry optimization can be afforded even for high level ab initio methods like CCSD(T) and CASPT2. This capability has been demonstrated by applying the method to two larger cases, CCSD(T) and CASPT2 calculations on a positively charged benzene lithium complex and on the oxygen molecule interacting to iron porphyrin molecule, respectively.
Automatic analog IC sizing and optimization constrained with PVT corners and layout effects
Lourenço, Nuno; Horta, Nuno
2017-01-01
This book introduces readers to a variety of tools for automatic analog integrated circuit (IC) sizing and optimization. The authors provide a historical perspective on the early methods proposed to tackle automatic analog circuit sizing, with emphasis on the methodologies to size and optimize the circuit, and on the methodologies to estimate the circuit’s performance. The discussion also includes robust circuit design and optimization and the most recent advances in layout-aware analog sizing approaches. The authors describe a methodology for an automatic flow for analog IC design, including details of the inputs and interfaces, multi-objective optimization techniques, and the enhancements made in the base implementation by using machine leaning techniques. The Gradient model is discussed in detail, along with the methods to include layout effects in the circuit sizing. The concepts and algorithms of all the modules are thoroughly described, enabling readers to reproduce the methodologies, improve the qual...
Make It Go Viral! Rate-optimal Control for Resource-Constrained Branching Processes
Xu, Kuang
2012-01-01
We propose a new class of controlled multi-type branching processes with a per-step linear resource constraint, motivated by applications in quantitative marketing, and study the associated growth-rate maximizing control strategies. We show that the optimal growth rate can be achieved by maintaining a single optimal ratio among different population types, for both deterministic and stochastic branching processes. In the special case of a two-type population and with a symmetric revenue structure, the optimal ratio is obtained in closed-form. As a proof of concept, the methodology is applied to the linkage structure of the 2004 US Presidential Election blogosphere, where the optimal growth rate achieves sizable gains over a uniform selection strategy.
A non-penalty recurrent neural network for solving a class of constrained optimization problems.
Hosseini, Alireza
2016-01-01
In this paper, we explain a methodology to analyze convergence of some differential inclusion-based neural networks for solving nonsmooth optimization problems. For a general differential inclusion, we show that if its right hand-side set valued map satisfies some conditions, then solution trajectory of the differential inclusion converges to optimal solution set of its corresponding in optimization problem. Based on the obtained methodology, we introduce a new recurrent neural network for solving nonsmooth optimization problems. Objective function does not need to be convex on R(n) nor does the new neural network model require any penalty parameter. We compare our new method with some penalty-based and non-penalty based models. Moreover for differentiable cases, we implement circuit diagram of the new neural network.
A one-layer recurrent neural network for constrained nonconvex optimization.
Li, Guocheng; Yan, Zheng; Wang, Jun
2015-01-01
In this paper, a one-layer recurrent neural network is proposed for solving nonconvex optimization problems subject to general inequality constraints, designed based on an exact penalty function method. It is proved herein that any neuron state of the proposed neural network is convergent to the feasible region in finite time and stays there thereafter, provided that the penalty parameter is sufficiently large. The lower bounds of the penalty parameter and convergence time are also estimated. In addition, any neural state of the proposed neural network is convergent to its equilibrium point set which satisfies the Karush-Kuhn-Tucker conditions of the optimization problem. Moreover, the equilibrium point set is equivalent to the optimal solution to the nonconvex optimization problem if the objective function and constraints satisfy given conditions. Four numerical examples are provided to illustrate the performances of the proposed neural network.
Orito, Yukiko; Yamamoto, Hisashi; Tsujimura, Yasuhiro; Kambayashi, Yasushi
The portfolio optimizations are to determine the proportion-weighted combination in the portfolio in order to achieve investment targets. This optimization is one of the multi-dimensional combinatorial optimizations and it is difficult for the portfolio constructed in the past period to keep its performance in the future period. In order to keep the good performances of portfolios, we propose the extended information ratio as an objective function, using the information ratio, beta, prime beta, or correlation coefficient in this paper. We apply the simulated annealing (SA) to optimize the portfolio employing the proposed ratio. For the SA, we make the neighbor by the operation that changes the structure of the weights in the portfolio. In the numerical experiments, we show that our portfolios keep the good performances when the market trend of the future period becomes different from that of the past period.
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...
Trade-offs and efficiencies in optimal budget-constrained multispecies corridor networks
Dilkina, Bistra; Houtman, Rachel; Gomes, Carla P.; Montgomery, Claire A.; McKelvey, Kevin; Kendall, Katherine; Graves, Tabitha A.; Bernstein, Richard; Schwartz, Michael K.
2017-01-01
Conservation biologists recognize that a system of isolated protected areas will be necessary but insufficient to meet biodiversity objectives. Current approaches to connecting core conservation areas through corridors consider optimal corridor placement based on a single optimization goal: commonly, maximizing the movement for a target species across a network of protected areas. We show that designing corridors for single species based on purely ecological criteria leads to extremely expensive linkages that are suboptimal for multispecies connectivity objectives. Similarly, acquiring the least-expensive linkages leads to ecologically poor solutions. We developed algorithms for optimizing corridors for multispecies use given a specific budget. We applied our approach in western Montana to demonstrate how the solutions may be used to evaluate trade-offs in connectivity for 2 species with different habitat requirements, different core areas, and different conservation values under different budgets. We evaluated corridors that were optimal for each species individually and for both species jointly. Incorporating a budget constraint and jointly optimizing for both species resulted in corridors that were close to the individual species movement-potential optima but with substantial cost savings. Our approach produced corridors that were within 14% and 11% of the best possible corridor connectivity for grizzly bears (Ursus arctos) and wolverines (Gulo gulo), respectively, and saved 75% of the cost. Similarly, joint optimization under a combined budget resulted in improved connectivity for both species relative to splitting the budget in 2 to optimize for each species individually. Our results demonstrate economies of scale and complementarities conservation planners can achieve by optimizing corridor designs for financial costs and for multiple species connectivity jointly. We believe that our approach will facilitate corridor conservation by reducing acquisition costs
Dao, Son Duy; Abhary, Kazem; Marian, Romeo
2017-01-01
Integration of production planning and scheduling is a class of problems commonly found in manufacturing industry. This class of problems associated with precedence constraint has been previously modeled and optimized by the authors, in which, it requires a multidimensional optimization at the same time: what to make, how many to make, where to make and the order to make. It is a combinatorial, NP-hard problem, for which no polynomial time algorithm is known to produce an optimal result on a random graph. In this paper, the further development of Genetic Algorithm (GA) for this integrated optimization is presented. Because of the dynamic nature of the problem, the size of its solution is variable. To deal with this variability and find an optimal solution to the problem, GA with new features in chromosome encoding, crossover, mutation, selection as well as algorithm structure is developed herein. With the proposed structure, the proposed GA is able to "learn" from its experience. Robustness of the proposed GA is demonstrated by a complex numerical example in which performance of the proposed GA is compared with those of three commercial optimization solvers.
Dao, Son Duy; Abhary, Kazem; Marian, Romeo
2017-01-01
Integration of production planning and scheduling is a class of problems commonly found in manufacturing industry. This class of problems associated with precedence constraint has been previously modeled and optimized by the authors, in which, it requires a multidimensional optimization at the same time: what to make, how many to make, where to make and the order to make. It is a combinatorial, NP-hard problem, for which no polynomial time algorithm is known to produce an optimal result on a random graph. In this paper, the further development of Genetic Algorithm (GA) for this integrated optimization is presented. Because of the dynamic nature of the problem, the size of its solution is variable. To deal with this variability and find an optimal solution to the problem, GA with new features in chromosome encoding, crossover, mutation, selection as well as algorithm structure is developed herein. With the proposed structure, the proposed GA is able to "learn" from its experience. Robustness of the proposed GA is demonstrated by a complex numerical example in which performance of the proposed GA is compared with those of three commercial optimization solvers.
Chance Constrained Optimal Power Flow: Risk-Aware Network Control under Uncertainty
Bienstock, Daniel; Harnett, Sean
2012-01-01
When uncontrollable resources fluctuate, Optimum Power Flow (OPF), routinely used by the electric power industry to re-dispatch hourly controllable generation (coal, gas and hydro plants) over control areas of transmission networks, can result in grid instability, and, potentially, cascading outages. This risk arises because OPF dispatch is computed without awareness of major uncertainty, in particular fluctuations in renewable output. As a result, grid operation under OPF with renewable variability can lead to frequent conditions where power line flow ratings are significantly exceeded. Such a condition, which is borne by simulations of real grids, would likely resulting in automatic line tripping to protect lines from thermal stress, a risky and undesirable outcome which compromises stability. Smart grid goals include a commitment to large penetration of highly fluctuating renewables, thus calling to reconsider current practices, in particular the use of standard OPF. Our Chance Constrained (CC) OPF correct...
Optimal Coordinated EV Charging with Reactive Power Support in Constrained Distribution Grids
Energy Technology Data Exchange (ETDEWEB)
Paudyal, Sumit; Ceylan, Oğuzhan; Bhattarai, Bishnu P.; Myers, Kurt S.
2017-07-01
Electric vehicle (EV) charging/discharging can take place in any P-Q quadrants, which means EVs could support reactive power to the grid while charging the battery. In controlled charging schemes, distribution system operator (DSO) coordinates with the charging of EV fleets to ensure grid’s operating constraints are not violated. In fact, this refers to DSO setting upper bounds on power limits for EV charging. In this work, we demonstrate that if EVs inject reactive power into the grid while charging, DSO could issue higher upper bounds on the active power limits for the EVs for the same set of grid constraints. We demonstrate the concept in an 33-node test feeder with 1,500 EVs. Case studies show that in constrained distribution grids in coordinated charging, average costs of EV charging could be reduced if the charging takes place in the fourth P-Q quadrant compared to charging with unity power factor.
EXISTENCE OF PERIODIC SOLUTIONS FOR A DISCRETE-TIME MODEL OF TWO-CELL CNNS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
We investigate a class of discrete-time model of two-cell cellular neural networks with symmetric template. By using the Lyapunov direct method, La-Salle's invariance principle, we discuss the existence and the stability of periodic solutions. The model considered has attractive 2-periodic and unstable 2-periodic solutions.
A Note on the Mean-Variance Criteria for Discrete Time Financial Markets
Institute of Scientific and Technical Information of China (English)
Xin-hua Liu
2005-01-01
It was shown in Xia[3] that for incomplete markets with continuous assets' price processes and for complete markets the mean-variance portfolio selection can be viewed as expected utility maximization with non-negative marginal utility. In this paper we show that for discrete time incomplete markets this result is not true.
Oostveen, J
1996-01-01
In this paper we present results about the algebraic Riccati equation (ARE) and a weaker version of the ARE, the algebraic Riccati system (ARS), for infinite-dimensional, discrete-time systems. We introduce an operator pencil, associated with these equations, the so-called extended symplectic Pencil
ON THE ANISOTROPIC NORM OF DISCRETE TIME STOCHASTIC SYSTEMS WITH STATE DEPENDENT NOISE
Directory of Open Access Journals (Sweden)
Isaac Yaesh
2013-01-01
Full Text Available The purpose of this paper is to determine conditions for the bound-edness of the anisotropic norm of discrete-time linear stochastic sys-tems with state dependent noise. It is proved that these conditions canbe expressed in terms of the feasibility of a specific system of matrixinequalities.
Discrete-Time Mixing Receiver Architecture for RF-Sampling Software-Defined Radio
Ru, Z.; Klumperink, Eric A.M.; Nauta, Bram
2010-01-01
Abstract—A discrete-time (DT) mixing architecture for RF-sampling receivers is presented. This architecture makes RF sampling more suitable for software-defined radio (SDR) as it achieves wideband quadrature demodulation and wideband harmonic rejection. The paper consists of two parts. In the first
Linear quadratic Gaussian balancing for discrete-time infinite-dimensional linear systems
Opmeer, MR; Curtain, RF
2004-01-01
In this paper, we study the existence of linear quadratic Gaussian (LQG)-balanced realizations for discrete-time infinite-dimensional systems. LQG-balanced realizations are those for which the smallest nonnegative self-adjoint solutions of the control and filter Riccati equations are equal. We show
From Discrete-Time Models to Continuous-Time, Asynchronous Models of Financial Markets
K. Boer-Sorban (Katalin); U. Kaymak (Uzay); J. Spiering (Jaap)
2006-01-01
textabstractMost agent-based simulation models of financial markets are discrete-time in nature. In this paper, we investigate to what degree such models are extensible to continuous-time, asynchronous modelling of financial markets. We study the behaviour of a learning market maker in a market with
Stabilization of nonlinear sandwich systems via state feedback-Discrete-time systems
Wang, Xu; Stoorvogel, Anton A.; Saberi, Ali; Grip, H°avard Fjær; Sannuti, Peddapullaiah
2011-01-01
A recent paper (IEEE Trans. Aut. Contr. 2010; 55(9):2156–2160) considered stabilization of a class of continuous-time nonlinear sandwich systems via state feedback. This paper is a discrete-time counterpart of it. The class of nonlinear sandwich systems consists of saturation elements sandwiched bet
More relaxed condition for dynamics of discrete time delayed Hopfield neural networks
Institute of Scientific and Technical Information of China (English)
Zhang Qiang
2008-01-01
The dynamics of discrete time delayed Hopfield neural networks is investigated.By using a difference inequality combining with the linear matrix inequality,a sufficient condition ensuring global exponential stability of the unique equilibrium point of the networks is found.The result obtained holds not only for constant delay but also for time-varying delays.
Modeling Repeatable Events Using Discrete-Time Data: Predicting Marital Dissolution
Teachman, Jay
2011-01-01
I join two methodologies by illustrating the application of multilevel modeling principles to hazard-rate models with an emphasis on procedures for discrete-time data that contain repeatable events. I demonstrate this application using data taken from the 1995 National Survey of Family Growth (NSFG) to ascertain the relationship between multiple…
Huang, David Y. C.; Murphy, Debra A.; Hser, Yih-Ing
2011-01-01
We used discrete-time survival mixture modeling to examine 5,305 adolescents from the 1997 National Longitudinal Survey of Youth regarding the impact of parental monitoring during early adolescence (ages 14-16) on initiation of sexual intercourse and problem behavior engagement (ages 14-23). Four distinctive parental-monitoring groups were…
A Lyapunov-Krasovskii methodology for asymptotic stability of discrete time delay systems
Directory of Open Access Journals (Sweden)
Stojanović Sreten B.
2007-01-01
Full Text Available This paper presents a Lyapunov-Krasovskii methodology for asymptotic stability of discrete time delay systems. Based on the methods, delay-independent stability condition is derived. A numerical example has been working out to show the applicability of results derived.
DISCRETE-TIME STOCHASTIC EQUILIBRIUM WITH INFINITE HORIZON INCOMPLETE ASSET MARKETS
Institute of Scientific and Technical Information of China (English)
ZhangShunming
2001-01-01
Abstract. This paper examines the existence of general equilibrium in a discrete time economywith the infinite horizon incomplete markets. There is a single good at each node in the eventtree. The existence of general equilibrium for the infinite horizon economy is proved by takinglimit of equilibria in truncated economies in which trade stops at a sequence of dates.
From Discrete-Time Models to Continuous-Time, Asynchronous Models of Financial Markets
K. Boer-Sorban (Katalin); U. Kaymak (Uzay); J. Spiering (Jaap)
2006-01-01
textabstractMost agent-based simulation models of financial markets are discrete-time in nature. In this paper, we investigate to what degree such models are extensible to continuous-time, asynchronous modelling of financial markets. We study the behaviour of a learning market maker in a market with
MINIMAL INVERSION AND ITS ALGORITHMS OF DISCRETE-TIME NONLINEAR SYSTEMS
Institute of Scientific and Technical Information of China (English)
ZHENG Yufan
2005-01-01
The left-inverse system with minimal order and its algorithms of discrete-time nonlinear systems are studied in a linear algebraic framework. The general structure of left-inverse system is described and computed in symbolic algorithm. Two algorithms are given for constructing left-inverse systems with minimal order.
Directory of Open Access Journals (Sweden)
Xinggui Liu
2011-01-01
Full Text Available In this paper, by using Mawhin's continuation theorem of coincidence degree theory, we establish the existence of at least four positive periodic solutions for a discrete time Lotka-Volterra competitive system with harvesting terms. An example is given to illustrate the effectiveness of our results.
Hick Samuelson Keynes Dynamic Economic Model with Discrete Time and Consumer Sentiment
Dobrescu, Loretti I.; Neamå#U, Mihaela; Opriş, Dumitru
The paper describes the Hick Samuelson Keynes dynamical economic model with discrete time and consumer sentiment. We seek to demonstrate that consumer sentiment may create fluctuations in the economical activities. The model possesses a flip bifurcation and a Neimark-Sacker bifurcation, after which the stable state is replaced by a (quasi-) periodic motion.
Design of nonlinear discrete-time controllers using a parameter space sampling procedure
Young, G. E.; Auslander, D. M.
1983-01-01
The design of nonlinear discrete-time controllers is investigated where the control algorithm assumes a special form. State-dependent control actions are obtained from tables whose values are the design parameters. A new design methodology capable of dealing with nonlinear systems containing parameter uncertainty is used to obtain the controller design. Various controller strategies are presented and illustrated through an example.
Outer-(J1,J2)-lossless factorizations of linear discrete time-varying systems
Yu, Xiaode; Scherpen, Jacqueline M.A.; Veen, Allejan van der; Dewilde, Patrick
1996-01-01
In this paper the outer-J-lossless factorization for linear discrete time-varying systems is treated. Lossless operators and its corresponding J-lossless chain-scattering operators are studied. Then the factorization is treated by first 'taking out' the anticausal part, and then considering the
Robust observer-based fault estimation and accommodation of discrete-time piecewise linear systems
DEFF Research Database (Denmark)
Tabatabaeipour, Mojtaba; Bak, Thomas
2013-01-01
In this paper a new integrated observer-based fault estimation and accommodation strategy for discrete-time piecewise linear (PWL) systems subject to actuator faults is proposed. A robust estimator is designed to simultaneously estimate the state of the system and the actuator fault. Then, the es...
DEFF Research Database (Denmark)
Tabatabaeipour, Seyed Mojtaba; Bak, Thomas
2012-01-01
In this paper we consider the problem of fault estimation and accommodation for discrete time piecewise linear systems. A robust fault estimator is designed to estimate the fault such that the estimation error converges to zero and H∞ performance of the fault estimation is minimized. Then...
Homogeneous Discrete Time Alternating Compound Renewal Process: A Disability Insurance Application
Directory of Open Access Journals (Sweden)
Guglielmo D’Amico
2015-01-01
Full Text Available Discrete time alternating renewal process is a very simple tool that permits solving many real life problems. This paper, after the presentation of this tool, introduces the compound environment in the alternating process giving a systematization to this important tool. The claim costs for a temporary disability insurance contract are presented. The algorithm and an example of application are also provided.
Ratio limits and limiting conditional distributions for discrete-time birth-death processes
Doorn, van Erik A.; Schrijner, Pauline
1995-01-01
We consider discrete-time birth-death processes with an absorbing state and study the conditional state distribution at time n given that absorption has not occurred by that time but will occur eventually. In particular, we establish conditions for the convergence of these distributions to a proper
Outer-(J1,J2)-lossless factorizations of linear discrete time-varying systems
Yu, Xiaode; Scherpen, Jacqueline M.A.; Veen, Allejan van der; Dewilde, Patrick
1996-01-01
In this paper the outer-J-lossless factorization for linear discrete time-varying systems is treated. Lossless operators and its corresponding J-lossless chain-scattering operators are studied. Then the factorization is treated by first 'taking out' the anticausal part, and then considering the oute
The ruin probability of a discrete time risk model under constant interest rate with heavy tails
Tang, Q.
2004-01-01
This paper investigates the ultimate ruin probability of a discrete time risk model with a positive constant interest rate. Under the assumption that the gross loss of the company within one year is subexponentially distributed, a simple asymptotic relation for the ruin probability is derived and co
Single-experiment observability decomposition of discrete-time analytic systems
Kawano, Yu; Kotta, Ülle
2016-01-01
This paper addresses the single-experiment observability decomposition of discrete-time analytic systems. Unlike the continuous-time case, there exist systems which cannot be decomposed into observable and unobservable subsystems due to the fact that the observable space is not integrable. In this p
Stability analysis of extended discrete-time BAM neural networks based on LMI approach
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
We propose a new approach for analyzing the global asymptotic stability of the extended discrete-time bidirectional associative memory (BAM) neural networks. By using the Euler rule, we discretize the continuous-time BAM neural networks as the extended discrete-time BAM neural networks with non-threshold activation functions. Here we present some conditions under which the neural networks have unique equilibrium points. To judge the global asymptotic stability of the equilibrium points, we introduce a new neural network model - standard neural network model (SNNM).For the SNNMs, we derive the sufficient conditions for the global asymptotic stability of the equilibrium points, which are formulated as some linear matrix inequalities (LMIs). We transform the discrete-time BAM into the SNNM and apply the general result about the SNNM to the determination of global asymptotic stability of the discrete-time BAM. The approach proposed extends the known stability results, has lower conservativeness, can be verified easily, and can also be applied to other forms of recurrent neural networks.
Statistical inference for discrete-time samples from affine stochastic delay differential equations
DEFF Research Database (Denmark)
Küchler, Uwe; Sørensen, Michael
2013-01-01
Statistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudo-likelihood estimators, which are easy to calculate in practice. A more general class of prediction-based estimating functions is investigated...
On the Riccati Equations of the H∞ Control Problem for Discrete Time-Varying Systems
Verhaegen, Michel; Scherpen, Jacquelien M.A.; Benedetto, Maria Domenica Di; Bittanti, Sergio; Isidori, Alberto; Luca, Alessandro De; Mosca, Edoardo; Oriolo, Giuseppe
1995-01-01
In this paper we investigate the relationship between the different Riccati equations that appear in the H∞ control problem for linear discrete time-varying systems. Once we obtain this relation we can reformulate the conditions under which the H∞ output feedback problem is solvable. In contrary to
Modeling Repeatable Events Using Discrete-Time Data: Predicting Marital Dissolution
Teachman, Jay
2011-01-01
I join two methodologies by illustrating the application of multilevel modeling principles to hazard-rate models with an emphasis on procedures for discrete-time data that contain repeatable events. I demonstrate this application using data taken from the 1995 National Survey of Family Growth (NSFG) to ascertain the relationship between multiple…
The uniform measure for discrete-time quantum walks in one dimension
Konno, Norio
2013-01-01
We obtain the uniform measure as a stationary measure of the one-dimensional discrete-time quantum walks by solving the corresponding eigenvalue problem. As an application, the uniform probability measure on a finite interval at a time can be given.
A unified aggregation and relaxation approach for stress-constrained topology optimization
DEFF Research Database (Denmark)
Verbart, Alexander; Langelaar, Matthijs; Keulen, Fred van
2017-01-01
optima accessible. The main advantage is that no separate constraint relaxation techniques are necessary, which reduces the parameter dependence of the problem. Furthermore, there is a clear relationship between the original feasible domain and the perturbed feasible domain via this aggregation parameter.......In this paper, we propose a unified aggregation and relaxation approach for topology optimization with stress constraints. Following this approach, we first reformulate the original optimization problem with a design-dependent set of constraints into an equivalent optimization problem with a fixed...... design-independent set of constraints. The next step is to perform constraint aggregation over the reformulated local constraints using a lower bound aggregation function. We demonstrate that this approach concurrently aggregates the constraints and relaxes the feasible domain, thereby making singular...
Directory of Open Access Journals (Sweden)
Syed Asif AliShah
2011-10-01
Full Text Available Load balancing is an efficient technique used to maximize throughput, optimal resource utilization, minimized response time and avoiding congestion. This can be achieved by distributing the workload evenly across two or more network stations, nodes or buffers, links, central processing units, hard drives, or other resources. In this paper, we have modeled and developed a load balancing approach in a discrete-time domain to analyze and evaluate the system of finite network buffers using an early arrival system. Our approach of modeling such a system consists of two steps. The first step is the determination of all system-state stages and their corresponding transition probabilities. Next, we compute various performance measures by utilizing the system state transition probabilities for its steady-state behavior.
Directory of Open Access Journals (Sweden)
Per-Ole Nyman
2010-01-01
Full Text Available In this article we develop a method of solving general one-dimensional Linear Quadratic Regulator (LQR problems in optimal control theory, using a generalized form of Fibonacci numbers. We find the solution R(k of the corresponding discrete-time Riccati equation in terms of ratios of generalized Fibonacci numbers. An explicit Binet type formula for R(k is also found, removing the need for recursively finding the solution at a given timestep. Moreover, we show that it is also possible to express the feedback gain, the penalty functional and the controller state in terms of these ratios. A generalized golden ratio appears in the corresponding infinite horizon problem. Finally, we show the use of the method in a few examples.
Zhang, Huaguang; Jiang, He; Luo, Chaomin; Xiao, Geyang
2016-10-03
In this paper, we investigate the nonzero-sum games for a class of discrete-time (DT) nonlinear systems by using a novel policy iteration (PI) adaptive dynamic programming (ADP) method. The main idea of our proposed PI scheme is to utilize the iterative ADP algorithm to obtain the iterative control policies, which not only ensure the system to achieve stability but also minimize the performance index function for each player. This paper integrates game theory, optimal control theory, and reinforcement learning technique to formulate and handle the DT nonzero-sum games for multiplayer. First, we design three actor-critic algorithms, an offline one and two online ones, for the PI scheme. Subsequently, neural networks are employed to implement these algorithms and the corresponding stability analysis is also provided via the Lyapunov theory. Finally, a numerical simulation example is presented to demonstrate the effectiveness of our proposed approach.
Ultra-fast consensus of discrete-time multi-agent systems with multi-step predictive output feedback
Zhang, Wenle; Liu, Jianchang
2016-04-01
This article addresses the ultra-fast consensus problem of high-order discrete-time multi-agent systems based on a unified consensus framework. A novel multi-step predictive output mechanism is proposed under a directed communication topology containing a spanning tree. By predicting the outputs of a network several steps ahead and adding this information into the consensus protocol, it is shown that the asymptotic convergence factor is improved by a power of q + 1 compared to the routine consensus. The difficult problem of selecting the optimal control gain is solved well by introducing a variable called convergence step. In addition, the ultra-fast formation achievement is studied on the basis of this new consensus protocol. Finally, the ultra-fast consensus with respect to a reference model and robust consensus is discussed. Some simulations are performed to illustrate the effectiveness of the theoretical results.
Preconditioners for state-constrained optimal control problems with Moreau-Yosida penalty function
Pearson, John W.
2012-11-21
Optimal control problems with partial differential equations as constraints play an important role in many applications. The inclusion of bound constraints for the state variable poses a significant challenge for optimization methods. Our focus here is on the incorporation of the constraints via the Moreau-Yosida regularization technique. This method has been studied recently and has proven to be advantageous compared with other approaches. In this paper, we develop robust preconditioners for the efficient solution of the Newton steps associated with the fast solution of the Moreau-Yosida regularized problem. Numerical results illustrate the efficiency of our approach. © 2012 John Wiley & Sons, Ltd.
Ecological monitoring in a discrete-time prey-predator model.
Gámez, M; López, I; Rodríguez, C; Varga, Z; Garay, J
2017-09-21
The paper is aimed at the methodological development of ecological monitoring in discrete-time dynamic models. In earlier papers, in the framework of continuous-time models, we have shown how a systems-theoretical methodology can be applied to the monitoring of the state process of a system of interacting populations, also estimating certain abiotic environmental changes such as pollution, climatic or seasonal changes. In practice, however, there may be good reasons to use discrete-time models. (For instance, there may be discrete cycles in the development of the populations, or observations can be made only at discrete time steps.) Therefore the present paper is devoted to the development of the monitoring methodology in the framework of discrete-time models of population ecology. By monitoring we mean that, observing only certain component(s) of the system, we reconstruct the whole state process. This may be necessary, e.g., when in a complex ecosystem the observation of the densities of certain species is impossible, or too expensive. For the first presentation of the offered methodology, we have chosen a discrete-time version of the classical Lotka-Volterra prey-predator model. This is a minimal but not trivial system where the methodology can still be presented. We also show how this methodology can be applied to estimate the effect of an abiotic environmental change, using a component of the population system as an environmental indicator. Although this approach is illustrated in a simplest possible case, it can be easily extended to larger ecosystems with several interacting populations and different types of abiotic environmental effects. Copyright © 2017 Elsevier Ltd. All rights reserved.
Interpolation techniques in robust constrained model predictive control
Kheawhom, Soorathep; Bumroongsri, Pornchai
2017-05-01
This work investigates interpolation techniques that can be employed on off-line robust constrained model predictive control for a discrete time-varying system. A sequence of feedback gains is determined by solving off-line a series of optimal control optimization problems. A sequence of nested corresponding robustly positive invariant set, which is either ellipsoidal or polyhedral set, is then constructed. At each sampling time, the smallest invariant set containing the current state is determined. If the current invariant set is the innermost set, the pre-computed gain associated with the innermost set is applied. If otherwise, a feedback gain is variable and determined by a linear interpolation of the pre-computed gains. The proposed algorithms are illustrated with case studies of a two-tank system. The simulation results showed that the proposed interpolation techniques significantly improve control performance of off-line robust model predictive control without much sacrificing on-line computational performance.
Constrained Optimization Problems in Cost and Managerial Accounting--Spreadsheet Tools
Amlie, Thomas T.
2009-01-01
A common problem addressed in Managerial and Cost Accounting classes is that of selecting an optimal production mix given scarce resources. That is, if a firm produces a number of different products, and is faced with scarce resources (e.g., limitations on labor, materials, or machine time), what combination of products yields the greatest profit…
A policy iteration approach to online optimal control of continuous-time constrained-input systems.
Modares, Hamidreza; Naghibi Sistani, Mohammad-Bagher; Lewis, Frank L
2013-09-01
This paper is an effort towards developing an online learning algorithm to find the optimal control solution for continuous-time (CT) systems subject to input constraints. The proposed method is based on the policy iteration (PI) technique which has recently evolved as a major technique for solving optimal control problems. Although a number of online PI algorithms have been developed for CT systems, none of them take into account the input constraints caused by actuator saturation. In practice, however, ignoring these constraints leads to performance degradation or even system instability. In this paper, to deal with the input constraints, a suitable nonquadratic functional is employed to encode the constraints into the optimization formulation. Then, the proposed PI algorithm is implemented on an actor-critic structure to solve the Hamilton-Jacobi-Bellman (HJB) equation associated with this nonquadratic cost functional in an online fashion. That is, two coupled neural network (NN) approximators, namely an actor and a critic are tuned online and simultaneously for approximating the associated HJB solution and computing the optimal control policy. The critic is used to evaluate the cost associated with the current policy, while the actor is used to find an improved policy based on information provided by the critic. Convergence to a close approximation of the HJB solution as well as stability of the proposed feedback control law are shown. Simulation results of the proposed method on a nonlinear CT system illustrate the effectiveness of the proposed approach. Copyright © 2013 ISA. All rights reserved.
Delbos, F.; Gilbert, J. Ch.; Glowinski, R.; Sinoquet, D.
2006-03-01
Seismic reflection tomography is a method for determining a subsurface velocity model from the traveltimes of seismic waves reflecting on geological interfaces. From an optimization viewpoint, the problem consists in minimizing a non-linear least-squares function measuring the mismatch between observed traveltimes and those calculated by ray tracing in this model. The introduction of a priori information on the model is crucial to reduce the under-determination. The contribution of this paper is to introduce a technique able to take into account geological a priori information in the reflection tomography problem expressed as inequality constraints in the optimization problem. This technique is based on a Gauss-Newton (GN) sequential quadratic programming approach. At each GN step, a solution to a convex quadratic optimization problem subject to linear constraints is computed thanks to an augmented Lagrangian algorithm. Our choice for this optimization method is motivated and its original aspects are described. First applications on real data sets are presented to illustrate the potential of the approach in practical use of reflection tomography.
Design Optimization of Time- and Cost-Constrained Fault-Tolerant Distributed Embedded Systems
DEFF Research Database (Denmark)
Izosimov, Viacheslav; Pop, Paul; Eles, Petru;
2005-01-01
In this paper we present an approach to the design optimization of fault-tolerant embedded systems for safety-critical applications. Processes are statically scheduled and communications are performed using the time-triggered protocol. We use process re-execution and replication for tolerating...
Trade-Off Analysis vs. Constrained Optimization with an Economic Control Chart Model
1994-01-01
description of this technique can be found in Luenberger (1989) or Reklaitis et al. (1983). Similar to the economic statistical designs, the trade-off...15] Reklaitis , G. V.; Ravindran, A.; and Ragsdell, K. M., Engineering Optimization, Methods and Applications, John Wiley & Sons, New York (1983). [16
Optimal apodization design for medical ultrasound using constrained least squares part I: theory.
Guenther, Drake A; Walker, William F
2007-02-01
Aperture weighting functions are critical design parameters in the development of ultrasound systems because beam characteristics affect the contrast and point resolution of the final output image. In previous work by our group, we developed a metric that quantifies a broadband imaging system's contrast resolution performance. We now use this metric to formulate a novel general ultrasound beamformer design method. In our algorithm, we use constrained least squares (CLS) techniques and a linear algebra formulation to describe the system point spread function (PSF) as a function of the aperture weightings. In one approach, we minimize the energy of the PSF outside a certain boundary and impose a linear constraint on the aperture weights. In a second approach, we minimize the energy of the PSF outside a certain boundary while imposing a quadratic constraint on the energy of the PSF inside the boundary. We present detailed analysis for an arbitrary ultrasound imaging system and discuss several possible applications of the CLS techniques, such as designing aperture weightings to maximize contrast resolution and improve the system depth of field.
A Novel Genetic-based Optimization for Transmission Constrained Generation Expansion Planning
Directory of Open Access Journals (Sweden)
Iman Goroohi Sardou
2013-12-01
Full Text Available Transmission constrained generation expansion planning (TC-GEP problem involves decisions on site, capacity, type of fuel, and etc. of new generation units, which should be installed over a planning horizon to meet the expectations of energy demand. This may lead to adding or lightening transmission lines congestion. This paper presents an application of genetic algorithm (GA to TC-GEP problem for simultaneously determination of new generation site, capacity and fuel type for a multi-period generation expansion plan. The objective function in this paper is to minimize the total generation cost which is composed of generation capital investment costs, operation and maintenance (O&M costs, outage cost, transmission losses costs and transmission enhancement costs. In this paper, also a new method is proposed for computing transmission enhancement costs. In addition a new approach is presented in this paper to determine site and number of combined cycle power plants regarding to candidate units. The GA is applied to solve TC-GEP problem for 4 bus test system from Grainger & Stevenson for a planning horizon of one year and the results are compared and validated against Enumeration Method (EM. Then GA is applied to solve TC-GEP problem for IEEE-RTS 24-bus test system for a planning horizon of three years and results are discussed.
Energy-Constrained Quality Optimization for Secure Image Transmission in Wireless Sensor Networks
Directory of Open Access Journals (Sweden)
Wei Wang
2007-01-01
Full Text Available Resource allocation for multimedia selective encryption and energy efficient transmission has not been fully investigated in literature for wireless sensor networks (WSNs. In this article, we propose a new cross-layer approach to optimize selectively encrypted image transmission quality in WSNs with strict energy constraint. A new selective image encryption approach favorable for unequal error protection (UEP is proposed, which reduces encryption overhead considerably by controlling the structure of image bitstreams. Also, a novel cross-layer UEP scheme based on cipher-plain-text diversity is studied. In this UEP scheme, resources are unequally and optimally allocated in the encrypted bitstream structure, including data position information and magnitude value information. Simulation studies demonstrate that the proposed approach can simultaneously achieve improved image quality and assured energy efficiency with secure transmissions over WSNs.
Model-Constrained Optimization Methods for Reduction of Parameterized Large-Scale Systems
2007-05-01
colorful with his stereo karaoke system. Anh Hai, thanks for helping me move my furnitures many times, and for all the beers too! To all Vietnamese...visit them. My trips to Springfield would have been very boring if Anh Tung (+ Thao) and Anh Danh (+ Thuy) had not turn on their super stereo karaoke ...expensive to solve, e.g. for applications such as optimal design or probabilistic analyses. Model order reduction is a powerful tool that permits the
Stress-constrained truss topology optimization problems that can be solved by linear programming
DEFF Research Database (Denmark)
Stolpe, Mathias; Svanberg, Krister
2004-01-01
We consider the problem of simultaneously selecting the material and determining the area of each bar in a truss structure in such a way that the cost of the structure is minimized subject to stress constraints under a single load condition. We show that such problems can be solved by linear...... programming to give the global optimum, and that two different materials are always sufficient in an optimal structure....
Reuther, James; Jameson, Antony; Alonso, Juan Jose; Rimlinger, Mark J.; Saunders, David
1997-01-01
An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity computational fluid dynamics (CFD), geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on a higher order CFD method. In order to facilitate the integration of these high fidelity CFD approaches into future multi-disciplinary optimization (NW) applications, new methods must be developed which are capable of simultaneously addressing complex geometries, multiple objective functions, and geometric design constraints. In our earlier studies, we coupled the adjoint based design formulations with unconstrained optimization algorithms and showed that the approach was effective for the aerodynamic design of airfoils, wings, wing-bodies, and complex aircraft configurations. In many of the results presented in these earlier works, geometric constraints were satisfied either by a projection into feasible space or by posing the design space parameterization such that it automatically satisfied constraints. Furthermore, with the exception of reference 9 where the second author initially explored the use of multipoint design in conjunction with adjoint formulations, our earlier works have focused on single point design efforts. Here we demonstrate that the same methodology may be extended to treat
Constraining the atmosphere of GJ 1214b using an optimal estimation technique
Barstow, Joanna K; Irwin, Patrick G J; Fletcher, Leigh N; Lee, Jae-Min
2013-01-01
We explore cloudy, extended H2-He atmosphere scenarios for the warm super-Earth GJ 1214b using an optimal estimation retrieval technique. This planet, orbiting an M4.5 star only 13 pc from the Earth, is of particular interest because it lies between the Earth and Neptune in size and may be a member of a new class of planet that is neither terrestrial nor gas giant. Its relatively flat transmission spectrum has so far made atmospheric characterisation difficult. The NEMESIS algorithm (Irwin et al. 2008) is used to explore the degenerate model parameter space for a cloudy, H2-He-dominated atmosphere scenario. Optimal estimation is a data-led approach that allows solutions beyond the range permitted by ab initio equilibrium model atmosphere calculations, and as such prevents restriction from prior expectations. We show that optimal estimation retrieval is a powerful tool for this kind of study, and present an exploration of the degenerate atmospheric scenarios for GJ 1214b. Whilst we find a family of solutions t...
The L_infinity constrained global optimal histogram equalization technique for real time imaging
Ren, Qiongwei; Niu, Yi; Liu, Lin; Jiao, Yang; Shi, Guangming
2015-08-01
Although the current imaging sensors can achieve 12 or higher precision, the current display devices and the commonly used digital image formats are still only 8 bits. This mismatch causes significant waste of the sensor precision and loss of information when storing and displaying the images. For better usage of the precision-budget, tone mapping operators have to be used to map the high-precision data into low-precision digital images adaptively. In this paper, the classic histogram equalization tone mapping operator is reexamined in the sense of optimization. We point out that the traditional histogram equalization technique and its variants are fundamentally improper by suffering from local optimum problems. To overcome this drawback, we remodel the histogram equalization tone mapping task based on graphic theory which achieves the global optimal solutions. Another advantage of the graphic-based modeling is that the tone-continuity is also modeled as a vital constraint in our approach which suppress the annoying boundary artifacts of the traditional approaches. In addition, we propose a novel dynamic programming technique to solve the histogram equalization problem in real time. Experimental results shows that the proposed tone-preserved global optimal histogram equalization technique outperforms the traditional approaches by exhibiting more subtle details in the foreground while preserving the smoothness of the background.
OPTIMAL SELECTION FOR THE WEIGHTED COEFFICIENTS OF THE CONSTRAINED VARIATIONAL PROBLEMS
Institute of Scientific and Technical Information of China (English)
魏鸣; 刘国庆; 王成刚; 葛文忠; 许秦
2003-01-01
The aim is to put forward the optimal selecting of weights in variational problem in which the linear advection equation is used as constraint. The selection of the functional weight coefficients (FWC) is one of the key problems for the relevant research. It was arbitrary and subjective to some extent presently. To overcome this difficulty, the reasonable assumptions were given for the observation field and analyz ed field, variational problems with "weak constraints" and "strong constraints" were considered separately. By solving Euler' s equation with the matrix theory and the finite difference method of partial differential equation, the objective weight coefficients were obtained in the minimum variance of the difference between the analyzed field and ideal field. Deduction results show that theoretically the optimal selection indeed exists in the weighting factors of the cost function in the means of the minimal variance between the analysis and ideal field in terms of the matrix theory and partial differential ( corresponding difference ) equation, if the reasonable assumption from the actual problem is valid and the differnece equation is stable.It may realize the coordination among the weight factors, numerical models and the observational data. With its theoretical basis as well as its prospects of applications, this objective selecting method is probably a way towards the finding of the optimal weighting factors in the variational problem.
Dynamic Control and Optimization of Capital-Constrained Stochastic Inventory Systems
Institute of Scientific and Technical Information of China (English)
ZHAO Xiu-li; WANG Shou-yang
2015-01-01
For most firms, especially the small-and medium-sized ones, the operational decisions are affected by their internal capital and ability to obtain external capital .However , the majority of the current studies on dynamic inventory control ignore the firm ’ s financial status and financing issues completely .An important question that arises is:what are the dynamic optimal inventory and financing policies for firms with limited capital and limited access to external capital ?In this paper , we review some of the latest developments in this area .After a brief review of single period models , we focus on multi-period dynamic control of the firm who aims to optimize its xpected terminal wealth .Two cases are discussed in detail:self-finance and short term finance .In the first case , the firm has to rely on its own capital for all ordering decisions , while in the second , the firm can borrow short term loan from lenders .A detailed characterization of the optimal policy is presented and its managerial insights are discussed .Several possible extensions are suggested .
Energy Technology Data Exchange (ETDEWEB)
Ji-Zheng Chu; Shyan-Shu Shieh; Shi-Shang Jang; Chuan-I Chien; Hou-Peng Wan; Hsu-Hsun Ko [Beijing University of Chemical Technology, Beijing (China). Department of Automation
2003-04-01
Combustion in a boiler is too complex to be analytically described with mathematical models. To meet the needs of operation optimization, on-site experiments guided by the statistical optimization methods are often necessary to achieve the optimum operating conditions. This study proposes a new constrained optimization procedure using artificial neural networks as models for target processes. Information analysis based on random search, fuzzy c-mean clustering, and minimization of information free energy is performed iteratively in the procedure to suggest the location of future experiments, which can greatly reduce the number of experiments needed. The effectiveness of the proposed procedure in searching optima is demonstrated by three case studies: (1) a bench-mark problem, namely minimization of the modified Himmelblau function under a circle constraint; (2) both minimization of NOx and CO emissions and maximization of thermal efficiency for a simulated combustion process of a boiler; (3) maximization of thermal efficiency within NOx and CO emission limits for the same combustion process. The simulated combustion process is based on a commercial software package CHEMKIN, where 78 chemical species and 467 chemical reactions related to the combustion mechanism are incorporated and a plug-flow model and a load-correlated temperature distribution for the combustion tunnel of a boiler are used. 22 refs., 6 figs., 4 tabs.
Directory of Open Access Journals (Sweden)
Yeison Díaz-Mateus
2017-07-01
Full Text Available Decision making in supply chains is influenced by demand variations, and hence sales, purchase orders and inventory levels are therefore concerned. This paper presents a non-linear optimization model for a two-echelon supply chain, for a unique product. In addition, the model includes the consumers’ maximum willingness to pay, taking socioeconomic differences into account. To do so, the constrained multinomial logit for discrete choices is used to estimate demand levels. Then, a metaheuristic approach based on particle swarm optimization is proposed to determine the optimal product sales price and inventory coordination variables. To validate the proposed model, a supply chain of a technological product was chosen and three scenarios are analyzed: discounts, demand segmentation and demand overestimation. Results are analyzed on the basis of profits, lotsizing and inventory turnover and market share. It can be concluded that the maximum willingness to pay must be taken into consideration, otherwise fictitious profits may mislead decision making, and although the market share would seem to improve, overall profits are not in fact necessarily better.
Institute of Scientific and Technical Information of China (English)
Peihua GUO; Detong ZHU
2008-01-01
The authors propose an affine scaling modified gradient path method in association with reduced projective Hessian and nonmonotonic interior backtracking line search techniques for solving the linear equality constrained optimization subject to bounds on variables. By employing the QR decomposition of the constraint matrix and the eigensystem decomposition of reduced projective Hes-sian matrix in the subproblem, the authors form affine scaling modified gradient curvilinear path very easily. By using interior backtracking line search technique, each iterate switches to trial step of strict interior feasibility. The global convergence and fast local superlinear/quadratical convergence rates of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion should bring about speeding up the convergence progress in some ill-conditioned cases. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.
DEFF Research Database (Denmark)
Mirzaei, Mahmood; Tibaldi, Carlo; Hansen, Morten Hartvig
2016-01-01
PI/PID controllers are the most common wind turbine controllers. Normally a first tuning is obtained using methods such as pole-placement or Ziegler-Nichols and then extensive aeroelastic simulations are used to obtain the best tuning in terms of regulation of the outputs and reduction of the loads....... In the traditional tuning approaches, the properties of different open loop and closed loop transfer functions of the system are not normally considered. In this paper, an assessment of the pole-placement tuning method is presented based on robustness measures. Then a constrained optimization setup is suggested...... to automatically tune the wind turbine controller subject to robustness constraints. The properties of the system such as the maximum sensitivity and complementary sensitivity functions (Ms and Mt), along with some of the responses of the system, are used to investigate the controller performance and formulate...
Energy Technology Data Exchange (ETDEWEB)
Rafique, Rashid; Kumar, Sandeep; Luo, Yiqi; Kiely, Gerard; Asrar, Ghassem R.
2015-02-01
he accurate calibration of complex biogeochemical models is essential for the robust estimation of soil greenhouse gases (GHG) as well as other environmental conditions and parameters that are used in research and policy decisions. DayCent is a popular biogeochemical model used both nationally and internationally for this purpose. Despite DayCent’s popularity, its complex parameter estimation is often based on experts’ knowledge which is somewhat subjective. In this study we used the inverse modelling parameter estimation software (PEST), to calibrate the DayCent model based on sensitivity and identifi- ability analysis. Using previously published N2 O and crop yield data as a basis of our calibration approach, we found that half of the 140 parameters used in this study were the primary drivers of calibration dif- ferences (i.e. the most sensitive) and the remaining parameters could not be identified given the data set and parameter ranges we used in this study. The post calibration results showed improvement over the pre-calibration parameter set based on, a decrease in residual differences 79% for N2O fluxes and 84% for crop yield, and an increase in coefficient of determination 63% for N2O fluxes and 72% for corn yield. The results of our study suggest that future studies need to better characterize germination tem- perature, number of degree-days and temperature dependency of plant growth; these processes were highly sensitive and could not be adequately constrained by the data used in our study. Furthermore, the sensitivity and identifiability analysis was helpful in providing deeper insight for important processes and associated parameters that can lead to further improvement in calibration of DayCent model.
Fast Bundle-Level Type Methods for Unconstrained and Ball-Constrained Convex Optimization
2014-12-01
of half- spaces , hence it is convex and closed. Therefore, the subproblem (3.4) always has a unique solution as long as Qk is non-empty. To finish the...pixels in the image. The ‖u‖TV is convex and non-smooth. Table 5.1 Uniformly distributed QP instances A : n = 4000,m = 3000, L = 2.0e6, e0 = 2.89e4 Alg...generation. Mathematical pro- gramming, 118(1):177–206, 2009. [14] G. Lan. Bundle-level type methods uniformly optimal for smooth and non-smooth convex
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
The paper deals with the stochastic optimal control of a wave energy point absorber with strong nonlinear buoyancy forces using the reactive force from the electric generator on the absorber as control force. The considered point absorber has only one degree of freedom, heave motion, which is used...... presented in the paper. The effect of nonlinear buoyancy force – in comparison to linear buoyancy force – and constraints of the controller on the power outtake of the device have been studied in details and supported by numerical simulations....
Wrapper/TAM Co-Optimization and constrained Test Scheduling for SOCs Using Rectangle Bin Packing
Babu, Hafiz Md Hasan; Karim, Muhammad Rezaul; Mahmud, Abdullah Al; Islam, Md Saiful
2010-01-01
This paper describes an integrated framework for SOC test automation. This framework is based on a new approach for Wrapper/TAM co-optimization based on rectangle packing considering the diagonal length of the rectangles to emphasize on both TAM widths required by a core and its corresponding testing time .In this paper, an efficient algorithm has been proposed to construct wrappers that reduce testing time for cores. Rectangle packing has been used to develop an integrated scheduling algorithm that incorporates power constraints in the test schedule. The test power consumption is important to consider since exceeding the system's power limit might damage the system.
Park, Y. C.; Chang, M. H.; Lee, T.-Y.
2007-06-01
A deterministic global optimization method that is applicable to general nonlinear programming problems composed of twice-differentiable objective and constraint functions is proposed. The method hybridizes the branch-and-bound algorithm and a convex cut function (CCF). For a given subregion, the difference of a convex underestimator that does not need an iterative local optimizer to determine the lower bound of the objective function is generated. If the obtained lower bound is located in an infeasible region, then the CCF is generated for constraints to cut this region. The cutting region generated by the CCF forms a hyperellipsoid and serves as the basis of a discarding rule for the selected subregion. However, the convergence rate decreases as the number of cutting regions increases. To accelerate the convergence rate, an inclusion relation between two hyperellipsoids should be applied in order to reduce the number of cutting regions. It is shown that the two-hyperellipsoid inclusion relation is determined by maximizing a quadratic function over a sphere, which is a special case of a trust region subproblem. The proposed method is applied to twelve nonlinear programming test problems and five engineering design problems. Numerical results show that the proposed method converges in a finite calculation time and produces accurate solutions.
Optimization of a constrained linear monochromator design for neutral atom beams.
Kaltenbacher, Thomas
2016-04-01
A focused ground state, neutral atom beam, exploiting its de Broglie wavelength by means of atom optics, is used for neutral atom microscopy imaging. Employing Fresnel zone plates as a lens for these beams is a well established microscopy technique. To date, even for favorable beam source conditions a minimal focus spot size of slightly below 1μm was reached. This limitation is essentially given by the intrinsic spectral purity of the beam in combination with the chromatic aberration of the diffraction based zone plate. Therefore, it is important to enhance the monochromaticity of the beam, enabling a higher spatial resolution, preferably below 100nm. We propose to increase the monochromaticity of a neutral atom beam by means of a so-called linear monochromator set-up - a Fresnel zone plate in combination with a pinhole aperture - in order to gain more than one order of magnitude in spatial resolution. This configuration is known in X-ray microscopy and has proven to be useful, but has not been applied to neutral atom beams. The main result of this work is optimal design parameters based on models for this linear monochromator set-up followed by a second zone plate for focusing. The optimization was performed for minimizing the focal spot size and maximizing the centre line intensity at the detector position for an atom beam simultaneously. The results presented in this work are for, but not limited to, a neutral helium atom beam.
Observation of discrete time-crystalline order in a disordered dipolar many-body system
Choi, Soonwon; Landig, Renate; Kucsko, Georg; Zhou, Hengyun; Isoya, Junichi; Jelezko, Fedor; Onoda, Shinobu; Sumiya, Hitoshi; Khemani, Vedika; von Keyserlingk, Curt; Yao, Norman Y; Demler, Eugene; Lukin, Mikhail D
2016-01-01
Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. It is well known that out-of-equilibrium systems can display a rich array of phenomena, ranging from self-organized synchronization to dynamical phase transitions. More recently, advances in the controlled manipulation of isolated many-body systems have enabled detailed studies of non-equilibrium phases in strongly interacting quantum matter. As a particularly striking example, the interplay of periodic driving, disorder, and strong interactions has recently been predicted to result in exotic "time-crystalline" phases, which spontaneously break the discrete time-translation symmetry of the underlying drive. Here, we report the experimental observation of such discrete time-crystalline order in a driven, disordered ensemble of $\\sim 10^6$ dipolar spin impurities in diamond at room-temperature. We observe long-lived temporal correlations at integer multiples of the fundamental driving period, experi...
Directory of Open Access Journals (Sweden)
He Jiang
2015-01-01
Full Text Available This paper deals with the output consensus regulation problem for discrete-time multiagent systems with state-unmeasurable agents and external disturbances under directed communication network topologies. Firstly, the mathematical model for the output consensus problem of discrete-time multiagent systems is deduced and formulated via making matrix transformation. Then, based on state observers, a novel output consensus protocol with dynamic compensator which is used as observer for the exosystem is proposed to solve this problem. Some knowledge of matrix theory and graph theory is introduced to design protocol parameters and the convergence of output consensus errors is proved. Finally, a numerical simulation example is shown to verify the effectiveness of the proposed protocol design.
LS-based discrete-time adaptive nonlinear control——Feasibility and limitations
Institute of Scientific and Technical Information of China (English)
郭雷; 魏晨Institute of Systems Science; Chinese Academy of Sciences; Beijing 100080; China
1996-01-01
Global stability and instability of a class of discrete-time adaptive nonlinear control systems are investigated.The systems to be controlled are assumed to be linear in unknown parameters but nonlinear in dynamics which are characterizEd by a nonlinear function f(x).It is shown that in the scalar parameter case,when the standard least-squares (LS) method is used in estimation,the certainty equivalence adaptive control is globally stable whenever f(x) has a growth rate |f(x)| =0(||x||b) with b<8.Moreover,in the case where b≥8,it is also shown that the dosed-loop adaptive control system does not have global stability in general.Both the results found and the new analytical methods introduced may be regarded as a basic step for further study of discrete-time adaptive nonlinear control systems.
A discrete-time chaos synchronization system for electronic locking devices
Minero-Ramales, G.; López-Mancilla, D.; Castañeda, Carlos E.; Huerta Cuellar, G.; Chiu Z., R.; Hugo García López, J.; Jaimes Reátegui, R.; Villafaña Rauda, E.; Posadas-Castillo, C.
2016-11-01
This paper presents a novel electronic locking key based on discrete-time chaos synchronization. Two Chen chaos generators are synchronized using the Model-Matching Approach, from non-linear control theory, in order to perform the encryption/decryption of the signal to be transmitted. A model/transmitter system is designed, generating a key of chaotic pulses in discrete-time. A plant/receiver system uses the above mentioned key to unlock the mechanism. Two alternative schemes to transmit the private chaotic key are proposed. The first one utilizes two transmission channels. One channel is used to encrypt the chaotic key and the other is used to achieve output synchronization. The second alternative uses only one transmission channel for obtaining synchronization and encryption of the chaotic key. In both cases, the private chaotic key is encrypted again with chaos to solve secure communication-related problems. The results obtained via simulations contribute to enhance the electronic locking devices.
Leader-follower Formation for Nonholonomic Mobile Robots: Discrete-time Approach
Directory of Open Access Journals (Sweden)
Raul Dali Cruz-Morales
2016-03-01
Full Text Available This paper presents a novel solution for the classical leader-follower formation problem considering the case of nonholonomic mobile robots. A formation control strategy is proposed in a discrete-time context by considering the exact discrete-time discretization of the non-linear continuous-time kinematic model of the vehicle. The geometric formation of the robots allows us to derive an alternative model that describes the time evolution of the relative distance and angle between the robots. These variables are obtained in real-time by a vision-based localization system on board, in which the follower robot is equipped with a Kinect device, together with a recognition board mounted on the leader robot. The boundedness of the relative position error is formally proven by considering a feedback law that is delayed by one sampling period of time. Numerical simulations and real-time experiments are presented to verify the performance of the control strategy.
Robust stability analysis of uncertain discrete-time systems with state delay
Institute of Scientific and Technical Information of China (English)
任正云; 张立群; 邵惠鹤
2004-01-01
The sufficient conditions of stability for uncertain discrete-time systems with state delay have been proposed by some researchers in the past few years, yet these results may be conservative in application. The stability analysis of these systems is discussed, and the necessary and sufficient condition of stability is derived by method other than constructing Lyapunov function and solving Riccati inequality. The root locations of system characteristic polynomial, which is obtained by augmentation approach and Laplace expansion, determine the stability of uncertain discrete-time systems with state delay, the system is stable if and only if all roots lie within the unit circle. In order to analyze robust stability of system characteristic polynomial effectively, Kharitonov theorem and edge theorem are applied. Example shows the practicability of these methods.
H∞ output tracking control of discrete-time nonlinear systems via standard neural network models.
Liu, Meiqin; Zhang, Senlin; Chen, Haiyang; Sheng, Weihua
2014-10-01
This brief proposes an output tracking control for a class of discrete-time nonlinear systems with disturbances. A standard neural network model is used to represent discrete-time nonlinear systems whose nonlinearity satisfies the sector conditions. H∞ control performance for the closed-loop system including the standard neural network model, the reference model, and state feedback controller is analyzed using Lyapunov-Krasovskii stability theorem and linear matrix inequality (LMI) approach. The H∞ controller, of which the parameters are obtained by solving LMIs, guarantees that the output of the closed-loop system closely tracks the output of a given reference model well, and reduces the influence of disturbances on the tracking error. Three numerical examples are provided to show the effectiveness of the proposed H∞ output tracking design approach.
Engineering Stable Discrete-Time Quantum Dynamics via a Canonical QR Decomposition
Bolognani, Saverio
2009-01-01
We analyze the asymptotic behavior of discrete-time, Markovian quantum systems with respect to a subspace of interest. Global asymptotic stability of subspaces is relevant to quantum information processing, in particular for initializing the system in pure states or subspace codes. We provide a linear-algebraic characterization of the dynamical properties leading to invariance and attractivity of a given quantum subspace. We then construct a design algorithm for discrete-time feedback control that allows to stabilize a target subspace, proving that if the control problem is feasible, then the algorithm returns an effective control choice. In order to prove this result, a canonical QR matrix decomposition is derived, and also used to establish the control scheme potential for the simulation of open-system dynamics.
Autonomous learning by simple dynamical systems with a discrete-time formulation
Bilen, Agustín M.; Kaluza, Pablo
2017-05-01
We present a discrete-time formulation for the autonomous learning conjecture. The main feature of this formulation is the possibility to apply the autonomous learning scheme to systems in which the errors with respect to target functions are not well-defined for all times. This restriction for the evaluation of functionality is a typical feature in systems that need a finite time interval to process a unit piece of information. We illustrate its application on an artificial neural network with feed-forward architecture for classification and a phase oscillator system with synchronization properties. The main characteristics of the discrete-time formulation are shown by constructing these systems with predefined functions.
Frequency Weighted Model Order Reduction Technique and Error Bounds for Discrete Time Systems
Directory of Open Access Journals (Sweden)
Muhammad Imran
2014-01-01
for whole frequency range. However, certain applications (like controller reduction require frequency weighted approximation, which introduce the concept of using frequency weights in model reduction techniques. Limitations of some existing frequency weighted model reduction techniques include lack of stability of reduced order models (for two sided weighting case and frequency response error bounds. A new frequency weighted technique for balanced model reduction for discrete time systems is proposed. The proposed technique guarantees stable reduced order models even for the case when two sided weightings are present. Efficient technique for frequency weighted Gramians is also proposed. Results are compared with other existing frequency weighted model reduction techniques for discrete time systems. Moreover, the proposed technique yields frequency response error bounds.
Robust passivity analysis for discrete-time recurrent neural networks with mixed delays
Huang, Chuan-Kuei; Shu, Yu-Jeng; Chang, Koan-Yuh; Shou, Ho-Nien; Lu, Chien-Yu
2015-02-01
This article considers the robust passivity analysis for a class of discrete-time recurrent neural networks (DRNNs) with mixed time-delays and uncertain parameters. The mixed time-delays that consist of both the discrete time-varying and distributed time-delays in a given range are presented, and the uncertain parameters are norm-bounded. The activation functions are assumed to be globally Lipschitz continuous. Based on new bounding technique and appropriate type of Lyapunov functional, a sufficient condition is investigated to guarantee the existence of the desired robust passivity condition for the DRNNs, which can be derived in terms of a family of linear matrix inequality (LMI). Some free-weighting matrices are introduced to reduce the conservatism of the criterion by using the bounding technique. A numerical example is given to illustrate the effectiveness and applicability.
Stability analysis of discrete-time BAM neural networks based on standard neural network models
Institute of Scientific and Technical Information of China (English)
ZHANG Sen-lin; LIU Mei-qin
2005-01-01
To facilitate stability analysis of discrete-time bidirectional associative memory (BAM) neural networks, they were converted into novel neural network models, termed standard neural network models (SNNMs), which interconnect linear dynamic systems and bounded static nonlinear operators. By combining a number of different Lyapunov functionals with S-procedure, some useful criteria of global asymptotic stability and global exponential stability of the equilibrium points of SNNMs were derived. These stability conditions were formulated as linear matrix inequalities (LMIs). So global stability of the discrete-time BAM neural networks could be analyzed by using the stability results of the SNNMs. Compared to the existing stability analysis methods, the proposed approach is easy to implement, less conservative, and is applicable to other recurrent neural networks.
Reliable gain-scheduled control of discrete-time systems and its application to CSTR model
Sakthivel, R.; Selvi, S.; Mathiyalagan, K.; Shi, Y.
2016-10-01
This paper is focused on reliable gain-scheduled controller design for a class of discrete-time systems with randomly occurring nonlinearities and actuator fault. Further, the nonlinearity in the system model is assumed to occur randomly according to a Bernoulli distribution with measurable time-varying probability in real time. The main purpose of this paper is to design a gain-scheduled controller by implementing a probability-dependent Lyapunov function and linear matrix inequality (LMI) approach such that the closed-loop discrete-time system is stochastically stable for all admissible randomly occurring nonlinearities. The existence conditions for the reliable controller is formulated in terms of LMI constraints. Finally, the proposed reliable gain-scheduled control scheme is applied on continuously stirred tank reactor model to demonstrate the effectiveness and applicability of the proposed design technique.
Bifurcation Analysis and Chaos Control in a Discrete-Time Parasite-Host Model
Directory of Open Access Journals (Sweden)
Xueli Chen
2017-01-01
Full Text Available A discrete-time parasite-host system with bifurcation is investigated in detail in this paper. The existence and stability of nonnegative fixed points are explored and the conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. And we also prove the chaos in the sense of Marotto. The numerical simulations not only illustrate the consistence with the theoretical analysis, but also exhibit other complex dynamical behaviors, such as bifurcation diagrams, Maximum Lyapunov exponents, and phase portraits. More specifically, when the integral step size is chosen as a bifurcation parameter, this paper presents the finding of period orbits, attracting invariant cycles and chaotic attractors of the discrete-time parasite-host system. Specifically, we have stabilized the chaotic orbits at an unstable fixed point by using the feedback control method.
A simple method of chaos control for a class of chaotic discrete-time systems
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Jiang Guoping E-mail: jianggp@njupt.edu.cn; Zheng Weixing E-mail: w.zheng@uws.edu.au
2005-02-01
In this paper, a simple method is proposed for chaos control for a class of discrete-time chaotic systems. The proposed method is built upon the state feedback control and the characteristic of ergodicity of chaos. The feedback gain matrix of the controller is designed using a simple criterion, so that control parameters can be selected via the pole placement technique of linear control theory. The new controller has a feature that it only uses the state variable for control and does not require the target equilibrium point in the feedback path. Moreover, the proposed control method cannot only overcome the so-called 'odd eigenvalues number limitation' of delayed feedback control, but also control the chaotic systems to the specified equilibrium points. The effectiveness of the proposed method is demonstrated by a two-dimensional discrete-time chaotic system.
Massambone de Oliveira, Rafael; Salomão Helou, Elias; Fontoura Costa, Eduardo
2016-11-01
We present a method for non-smooth convex minimization which is based on subgradient directions and string-averaging techniques. In this approach, the set of available data is split into sequences (strings) and a given iterate is processed independently along each string, possibly in parallel, by an incremental subgradient method (ISM). The end-points of all strings are averaged to form the next iterate. The method is useful to solve sparse and large-scale non-smooth convex optimization problems, such as those arising in tomographic imaging. A convergence analysis is provided under realistic, standard conditions. Numerical tests are performed in a tomographic image reconstruction application, showing good performance for the convergence speed when measured as the decrease ratio of the objective function, in comparison to classical ISM.
Institute of Scientific and Technical Information of China (English)
Zi-you Gao; Tian-de Guo; Guo-ping He; Fang Wu
2002-01-01
In this paper, a new superlinearly convergent algorithm of sequential systems of linear equations (SSLE) for nonlinear optimization problems with inequality constraints is proposed. Since the new algorithm only needs to solve several systems of linear equations having a same coefficient matrix per iteration, the computation amount of the algorithm is much less than that of the existing SQP algorithms per iteration. Moreover, for the SQPtype algorithms, there exist so-called inconsistent problems, i.e., quadratic programming subproblems of the SQP algorithms may not have a solution at some iterations, but this phenomenon will not occur with the SSLE algorithms because the related systems of linear equations always have solutions. Some numerical results are reported.
Lemanski, Natalie J; Fefferman, Nina H
2017-06-01
Honeybees are an excellent model system for examining how trade-offs shape reproductive timing in organisms with seasonal environments. Honeybee colonies reproduce two ways: producing swarms comprising a queen and thousands of workers or producing males (drones). There is an energetic trade-off between producing workers, which contribute to colony growth, and drones, which contribute only to reproduction. The timing of drone production therefore determines both the drones' likelihood of mating and when colonies reach sufficient size to swarm. Using a linear programming model, we ask when a colony should produce drones and swarms to maximize reproductive success. We find the optimal behavior for each colony is to produce all drones prior to swarming, an impossible solution on a population scale because queens and drones would never co-occur. Reproductive timing is therefore not solely determined by energetic trade-offs but by the game theoretic problem of coordinating the production of reproductives among colonies.
HR approximation of FIR filters via discrete-time hybrid-domain vector fitting
2009-01-01
We present a discrete-time hybrid-domain vector fitting algorithm, called HD-VFz, for the HR approximation of FIR filters with an arbitrary combination of time- and frequency-sampled responses. The core routine involves a two-step pole refinement process based on a linear least-squares solve and an eigenvalue problem. Through hybrid-domain data approximation and digital partial fraction basis with relative stability consideration, HD-VFz exhibits fast computation and remarkable fitting accura...
Discrete-Time Sliding Mode Control for Uncertain Networked System Subject to Time Delay
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Saulo C. Garcia
2015-01-01
Full Text Available We deal with uncertain systems with networked sliding mode control, subject to time delay. To minimize the degenerative effects of the time delay, a simpler format of state predictor is proposed in the control law. Some ultimate bounded stability analyses and stabilization conditions are provided for the uncertain time delay system with proposed discrete-time sliding mode control strategy. A numerical example is presented to corroborate the analyses.
A new approach to consensus problems in discrete-time multiagent systems with time-delays
Institute of Scientific and Technical Information of China (English)
WANG Long; XIAO Feng
2007-01-01
In this paper, consensus problems in discrete-time multiagent systems with timeinvariant delays are considered. In order to characterize the structures of communication topologies, the concept of "pre-leader-follower" decomposition is introduced.Then, a necessary and sufficient condition for state consensus is established. By this method, consensus problems in networks with a single time-delay, as well as with multiple time-delays, are studied, and some necessary and sufficient conditions for solvability of consensus problems are obtained.
Chaos communication based on synchronization of discrete-time chaotic systems
Institute of Scientific and Technical Information of China (English)
Lu Jun-Guo; Xi Yu-Geng
2005-01-01
A novel chaos communication method is proposed based on synchronization of discrete-time chaotic systems. This method uses a full-order state observer to achieve synchronization and secure communication between the transmitter and the receiver. Further, we present a multiple-access chaotic digital communication method by combining the observer with the on-line least square method. Simulation results are also given for illustration.
STABILITY OF DISCRETE-TIME COHEN-GROSSBERG BAM NEURAL NETWORKS WITH DELAYS
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this paper, we study the existence and stability of an equilibrium of discrete-time Cohen-Grossberg BAM Neural Networks with delays. We obtain several sufficient conditions ensuring the existence and stability of an equilibrium of such systems, using discrete Halanay-type inequality and vector Lyapunov methods. In addition, we show that the proposed sufficient condition is independent of the delay parameter. An example is given to demonstrate the effectiveness of the results obtained.
Stability Analysis of Uncertain Discrete-Time Piecewise Linear Systems with Time Delays
Institute of Scientific and Technical Information of China (English)
Ou Ou; Hong-Bin Zhang; Jue-Bang Yu
2009-01-01
This paper considers the stability analysis of uncertain discrete-time piecewise linear systems with time delays based on piecewise Lyapunov-Krasovskii functionals. It is shown that the stability can be established for the control systems if there is a piecewise Lyapunov-Krasovskii functional, and moreover, the functional can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. A numerical example is given to demonstrate the efficiency and advantage of the proposed method.
Observers design for one-sided Lipschitz discrete-time systems
Benallouch, Mohamed; Boutayeb, Mohamed; Zasadzinski, Michel
2012-01-01
International audience; This note focuses on state observer design for a general class of nonlinear discrete-time systems that satisfies the one-sided Lipschitz condition. It has been shown that this condition may encompass a large class of nonlinearities. However, challenging problems arise such as relevant choice of the Lyapunov function or non convexity of the obtained stability conditions. Both full-order and reduced-order observer design are considered. In this work, the main contributio...
Institute of Scientific and Technical Information of China (English)
Zhu Jin; Xi Hongsheng; Xiao Xiaobo; Ji Haibo
2007-01-01
Robust LQG problems of discrete-time Markovian jump systems with uncertain noises are investigated.The problem addressed is the construction of perturbation upper bounds on the uncertain noise covariances so as to guarantee that the deviation of the control performance remains within the precision prescribed in actual problems.Furthermore, this regulator is capable of minimizing the worst performance in an uncertain case. A numerical example is exploited to show the validity of the method.
Dynamic output feedback for discrete-time systems under amplitude and rate actuator constraints
Silva Junior, Joao Manoel Gomes da; Limon Marruedo, Daniel; Alamo Cantarero, Teodoro Rafael; Camacho, Eduardo F.
2008-01-01
This work proposes a technique for the design of stabilizing dynamic output feedback controllers for discrete-time linear systems with rate and amplitude saturating actuators. The nonlinear effects introduced by the saturations in the closed-loop system are taken into account by using a generalized sector condition, which leads to theoretical conditions for solving the problem directly in the form of linear matrix inequalities.
Global Exponential Stability of Discrete-Time Neural Networks with Time-Varying Delays
Directory of Open Access Journals (Sweden)
S. Udpin
2013-01-01
Full Text Available This paper presents some global stability criteria of discrete-time neural networks with time-varying delays. Based on a discrete-type inequality, a new global stability condition for nonlinear difference equation is derived. We consider nonlinear discrete systems with time-varying delays and independence of delay time. Numerical examples are given to illustrate the effectiveness of our theoretical results.
Tightened Exponential Bounds for Discrete-Time Conditionally Symmetric Martingales and Applications
Sason, Igal
2012-01-01
This paper revisits the derivation of some exponential bounds for discrete-time and real-valued martingales with bounded jumps in order to improve these bounds for conditionally symmetric martingales. The new bounds are extended to conditionally symmetric sub or super-martingales, and they are also considered in connection to some previously reported bounds in the literature. Two applications of these bounds are exemplified in the context of gambling, and the number of up-crossings of a super-martingale.
Control design for discrete-time state-multiplicative noise stochastic systems
Krokavec, Dušan; Filasová, Anna
2015-11-01
Design conditions for existence of the H∞ linear state feedback control for discretetime stochastic systems with state-multiplicative noise and polytopic uncertainties are presented in the paper. Using an enhanced form of the bounded real lemma for discrete-time stochastic systems with state-multiplicative noise, the LMI-based procedure is provided for computation of the gains of linear, as well as nonlinear, state control law. The approach is illustrated on an example demonstrating the validity of the proposed method.
Institute of Scientific and Technical Information of China (English)
Xianming ZHANG; Min WU; Jinhua SHE; Dongsheng HAN
2007-01-01
This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties.A new and simple method is presented to directly decouple the Lyapunov matrix and the system dynamic matrix.Combining this method with the parameter-dependent Lyapunov function approach yields new criteria that include some existing ones as special cases.A numerical example illustrates the improvement over the existing ones.
Introduction to fractional linear systems. Part 2: discrete-time case
Ortigueira, M.D.
2000-01-01
IEE Proceedings - Vision, Image, and Signal Processing, Vol. 147, nº 1 In the paper, the class of discrete linear systems is enlarged with the inclusion of discrete-time fractional linear systems. These are systems described by fractional difference equations and fractional frequency responses. It is shown how io compute the impulse response and transfer function. Fractal signals are introduced as output of special linear systems: fractional differaccumulators, systems that can be co...
Impulsive synchronization of discrete-time chaotic systems under communication constraints
Gao, Yanbo; Zhang, Xiaomei; Lu, Guoping; Zheng, Yufan
2011-03-01
This paper investigates the problem of impulsive synchronization of discrete-time chaotic systems subject to limited communication capacity. Control laws with impulses are derived by using measurement feedback, where the effect of quantization errors is considered. Sufficient conditions for asymptotic stability of synchronization error systems are given in terms of linear matrix inequalities and algebraic inequalities. Some numerical simulations are given to demonstrate the effectiveness of the method.
Stabilization of a class of discrete-time switched systems via observer-based output feedback
Institute of Scientific and Technical Information of China (English)
Jiao LI; Yuzhong LIU
2007-01-01
In this paper, observer-based static output feedback control problem for discrete-time uncertain switched systems is investigated under an arbitrary switching rule. The main method used in this note is combining switched. Lyapunov function (SLF) method with Finsler's Lemma. Based on linear matrix inequality (LMI) a less conservative stability condition is established and this condition allows extra degree of freedom for stability analysis. Finally, a simulation example is given to illustrate the efficiency of the result.
Discrete-Time Chaotic Circuits for Implementation of Tent Map and Bernoulli Map
Institute of Scientific and Technical Information of China (English)
LI Zhi-zhong; QIU Shui-sheng
2005-01-01
Discrete-time chaotic circuit implementations of a tent map and a Bernoulli map using switched-current (SI) techniques are presented. The two circuits can be constructed with 16MOSFET's and 2 capacitors. The simulations and experiments built with commercially available IC's for the circuits have demonstrated the validity of the circuit designs. The experiment results also indicate that the proposed circuits are integrable by a standard CMOS technology. The implementations are useful for studies and applications of chaos.
Asymptotic stability of monostable wavefronts in discrete-time integral recursions
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The aim of this work is to study the traveling wavefronts in a discrete-time integral recursion with a Gauss kernel in R2.We first establish the existence of traveling wavefronts as well as their precise asymptotic behavior.Then,by employing the comparison principle and upper and lower solutions technique,we prove the asymptotic stability and uniqueness of such monostable wavefronts in the sense of phase shift and circumnutation.We also obtain some similar results in R.
2000-01-01
We propose in this paper two methods to compute Markovian bounds for monotone functions of a discrete time homogeneous Markov chain evolving in a totally ordered state space. The main interest of such methods is to propose algorithms to simplify analysis of transient characteristics such as the output process of a queue, or sojourn time in a subset of states. Construction of bounds are based on two kinds of results: well-known results on stochastic comparison between Markov cha...
Anticontrol of chaos for discrete-time fuzzy hyperbolic model with uncertain parameters
Institute of Scientific and Technical Information of China (English)
Zhao Yan; Zhang Hua-Guang; Zheng Cheng-De
2008-01-01
This paper proposes a new method to chaotify the discrete-time fuzzy hyperbolic model (DFHM) with uncertain parameters.A simple nonlinear state feedback controller is designed for this purpose.By revised Marotto theorem,it is proven that the chaos generated by this controller satisfies the Li-Yorke definition.An example is presented to demonstrate the effectiveness of the approach.
Parametrization of Minimal Spectral Factors of Discrete-Time Rational Spectral Densities
Baggio, Giacomo; Ferrante, Augusto
2016-01-01
In this paper, the problem of providing a complete parametrization of the minimal spectral factors of a discrete-time rational spectral density is considered. The desired parametrization is given in terms of the all-pass divisors of an all-pass function, related to the so-called phase function, under very mild assumptions on the given spectral density. This result provides a partial answer to a conjecture raised in [3].
Restricted feedback control in discrete-time dynamical systems with memory
Workman, Kathryn G.; Zhao, Shuang; Cain, John W.
2014-04-01
When an equilibrium state of a physical or biological system suffers a loss of stability (e.g., via a bifurcation), it may be both possible and desirable to stabilize the equilibrium via closed-loop feedback control. Significant effort has been devoted towards using such control to prevent oscillatory or chaotic behavior in dynamical systems, both continuous-time and discrete-time. Regarding control in discrete-time systems, most prior attempts to stabilize unstable equilibria require that the system be perturbed once during each time step. However, there are examples of systems for which this is neither feasible nor possible. In this paper, we analyze a restricted feedback control method for discrete-time systems (restricted in the sense that the controller's perturbations may be applied only in every other time step). We apply our theoretical analysis to a specific example from cardiac electrophysiology in which this sort of restricted feedback control is especially relevant. The example is a useful test case for the theory, and one for which an experimental setup is rather straightforward.
Multilayer discrete-time neural-net controller with guaranteed performance.
Jagannathan, S; Lewis, F L
1996-01-01
A family of novel multilayer discrete-time neural-net (NN) controllers is presented for the control of a class of multi-input multi-output (MIMO) dynamical systems. The neural net controller includes modified delta rule weight tuning and exhibits a learning while-functioning-features. The structure of the NN controller is derived using a filtered error/passivity approach. Linearity in the parameters is not required and certainty equivalence is not used. This overcomes several limitations of standard adaptive control. The notion of persistency of excitation (PE) for multilayer NN is defined and explored. New online improved tuning algorithms for discrete-time systems are derived, which are similar to sigma or epsilon-modification for the case of continuous-time systems, that include a modification to the learning rate parameter plus a correction term. These algorithms guarantee tracking as well as bounded NN weights in nonideal situations so that PE is not needed. An extension of these novel weight tuning updates to NN with an arbitrary number of hidden layers is discussed. The notions of discrete-time passive NN, dissipative NN, and robust NN are introduced. The NN makes the closed-loop system passive.
Riccati discrete time transfer matrix method for elastic beam undergoing large overall motion
Energy Technology Data Exchange (ETDEWEB)
He Bin [Sun Yat-sen University, College of Engineering (China)], E-mail: njhebin@gmail.com; Rui Xiaoting, E-mail: ruixt@163.net; Wang Guoping [Nanjing University of Science and Technology, Institute of Power Engineering (China)
2007-11-15
An efficient method for dynamics simulation for elastic beam with large overall spatial motion and nonlinear deformation, namely, the Riccati discrete time transfer matrix method (Riccati-DT-TMM), is proposed in this investigation. With finite segments, continuous deformation field of a beam can be decomposed into many rigid bodies connected by rotational springs. Discrete time transfer matrices of rigid bodies and rotational springs are used to analyze the dynamic characteristic of the beam, and the Riccati transform is used to improve the numerical stability of discrete time transfer matrix method of multibody system dynamics. A predictor-corrector method is used to improve the numerical accuracy of the Riccati-DT-TMM. Using the Riccati-DT-TMM in dynamics analysis, the global dynamics equations of the system are not needed and the computation time required increases linearly with the system's number of degrees of freedom. Three numerical examples are given to validate the method for the dynamic simulation of a geometric nonlinear beam undergoing large overall motion.