Gearbox design for uncertain load requirements using active robust optimization
Salomon, Shaul; Avigad, Gideon; Purshouse, Robin C.; Fleming, Peter J.
2016-04-01
Design and optimization of gear transmissions have been intensively studied, but surprisingly the robustness of the resulting optimal design to uncertain loads has never been considered. Active Robust (AR) optimization is a methodology to design products that attain robustness to uncertain or changing environmental conditions through adaptation. In this study the AR methodology is utilized to optimize the number of transmissions, as well as their gearing ratios, for an uncertain load demand. The problem is formulated as a bi-objective optimization problem where the objectives are to satisfy the load demand in the most energy efficient manner and to minimize production cost. The results show that this approach can find a set of robust designs, revealing a trade-off between energy efficiency and production cost. This can serve as a useful decision-making tool for the gearbox design process, as well as for other applications.
Robust Solutions of Optimization Problems Affected by Uncertain Probabilities
Ben-Tal, A.; den Hertog, D.; De Waegenaere, A.M.B.; Melenberg, B.; Rennen, G.
2011-01-01
In this paper we focus on robust linear optimization problems with uncertainty regions defined by ø-divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on ø-divergences arise in a natural way as confidence sets if the uncertain parameters contai
Robust Solutions of Optimization Problems Affected by Uncertain Probabilities
Ben-Tal, A.; den Hertog, D.; De Waegenaere, A.M.B.; Melenberg, B.; Rennen, G.
2011-01-01
In this paper we focus on robust linear optimization problems with uncertainty regions defined by ø-divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on ø-divergences arise in a natural way as confidence sets if the uncertain parameters
Robust solutions of optimization problems affected by uncertain probabilities
Ben-Tal, A.; den Hertog, D.; De Waegenaere, A.M.B.; Melenberg, B.; Rennen, G.
2013-01-01
In this paper we focus on robust linear optimization problems with uncertainty regions defined by φ-divergences (for example, chi-squared, Hellinger, Kullback–Leibler). We show how uncertainty regions based on Φ-divergences arise in a natural way as confidence sets if the uncertain parameters
On the robust optimization to the uncertain vaccination strategy problem
Chaerani, D., E-mail: d.chaerani@unpad.ac.id; Anggriani, N., E-mail: d.chaerani@unpad.ac.id; Firdaniza, E-mail: d.chaerani@unpad.ac.id [Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Padjadjaran Indonesia, Jalan Raya Bandung Sumedang KM 21 Jatinangor Sumedang 45363 (Indonesia)
2014-02-21
In order to prevent an epidemic of infectious diseases, the vaccination coverage needs to be minimized and also the basic reproduction number needs to be maintained below 1. This means that as we get the vaccination coverage as minimum as possible, thus we need to prevent the epidemic to a small number of people who already get infected. In this paper, we discuss the case of vaccination strategy in term of minimizing vaccination coverage, when the basic reproduction number is assumed as an uncertain parameter that lies between 0 and 1. We refer to the linear optimization model for vaccination strategy that propose by Becker and Starrzak (see [2]). Assuming that there is parameter uncertainty involved, we can see Tanner et al (see [9]) who propose the optimal solution of the problem using stochastic programming. In this paper we discuss an alternative way of optimizing the uncertain vaccination strategy using Robust Optimization (see [3]). In this approach we assume that the parameter uncertainty lies within an ellipsoidal uncertainty set such that we can claim that the obtained result will be achieved in a polynomial time algorithm (as it is guaranteed by the RO methodology). The robust counterpart model is presented.
Optimally robust redundancy relations for failure detection in uncertain systems
Lou, X.-C.; Willsky, A. S.; Verghese, G. C.
1986-01-01
All failure detection methods are based, either explicitly or implicitly, on the use of redundancy, i.e. on (possibly dynamic) relations among the measured variables. The robustness of the failure detection process consequently depends to a great degree on the reliability of the redundancy relations, which in turn is affected by the inevitable presence of model uncertainties. In this paper the problem of determining redundancy relations that are optimally robust is addressed in a sense that includes several major issues of importance in practical failure detection and that provides a significant amount of intuition concerning the geometry of robust failure detection. A procedure is given involving the construction of a single matrix and its singular value decomposition for the determination of a complete sequence of redundancy relations, ordered in terms of their level of robustness. This procedure also provides the basis for comparing levels of robustness in redundancy provided by different sets of sensors.
Robust time-optimal control of uncertain structural dynamic systems
Wie, Bong; Sinha, Ravi; Liu, Qiang
1993-01-01
A time-optimal open-loop control problem of flexible spacecraft in the presence of modeling uncertainty has been investigated. The results indicate that the proposed approach significantly reduces the residual structural vibrations caused by modeling uncertainty. The results also indicate the importance of proper jet placement for practical tradeoffs among the maneuvering time, fuel consumption, and performance robustness.
Robust Solutions of Optimization Problems Affected by Uncertain Probabilities
A. Ben-Tal (Aharon); D. den Hertog; A.M.B. De Waegenaere; B. Melenberg; G. Rennen
2011-01-01
htmlabstract Samenvatting In this paper we focus on robust linear optimization problems with uncertainty regions defined by ø-divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on ø-divergences arise in a natural way as confidence sets if the
Robust controller design for fuzzy parametric uncertain systems: an optimal control approach.
Patre, Balasaheb M; Bhiwani, R J
2013-03-01
A new approach of designing a robust controller for fuzzy parametric uncertain systems is proposed. A linear time invariant (LTI) system with fuzzy coefficients is called as fuzzy parametric uncertain system (FPUS). The proposed method envisages conversion of the FPUS into an uncertain (interval) state space controllable canonical form system in terms of its alpha cut. Further, the problem of designing a robust controller is translated into an optimal control problem minimizing a cost function. For matched uncertainty, it is shown that the optimal control problem is a linear quadratic regulator (LQR) problem, which can be solved to obtain a robust controller for FPUS. The numerical examples and simulation results show the effectiveness of the proposed method in terms of robustness of the controller. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.
Xing-cai Liu
2014-01-01
Full Text Available Railway freight center location problem is an important issue in railway freight transport programming. This paper focuses on the railway freight center location problem in uncertain environment. Seeing that the expected value model ignores the negative influence of disadvantageous scenarios, a robust optimization model was proposed. The robust optimization model takes expected cost and deviation value of the scenarios as the objective. A cloud adaptive clonal selection algorithm (C-ACSA was presented. It combines adaptive clonal selection algorithm with Cloud Model which can improve the convergence rate. Design of the code and progress of the algorithm were proposed. Result of the example demonstrates the model and algorithm are effective. Compared with the expected value cases, the amount of disadvantageous scenarios in robust model reduces from 163 to 21, which prove the result of robust model is more reliable.
Robust Optimization-Based Generation Self-Scheduling under Uncertain Price
Xiao Luo
2011-01-01
Full Text Available This paper considers generation self-scheduling in electricity markets under uncertain price. Based on the robust optimization (denoted as RO methodology, a new self-scheduling model, which has a complicated max-min optimization structure, is set up. By using optimal dual theory, the proposed model is reformulated to an ordinary quadratic and quadratic cone programming problems in the cases of box and ellipsoidal uncertainty, respectively. IEEE 30-bus system is used to test the new model. Some comparisons with other methods are done, and the sensitivity with respect to the uncertain set is analyzed. Comparing with the existed uncertain self-scheduling approaches, the new method has twofold characteristics. First, it does not need a prediction of distribution of random variables and just requires an estimated value and the uncertain set of power price. Second, the counterpart of RO corresponding to the self-scheduling is a simple quadratic or quadratic cone programming. This indicates that the reformulated problem can be solved by many ordinary optimization algorithms.
Keyong Li; Seong-Cheol Kang; I. Ch. Paschalidis
2007-09-01
This paper investigates stochastic processes that are modeled by a finite number of states but whose transition probabilities are uncertain and possibly time-varying. The treatment of uncertain transition probabilities is important because there appears to be a disconnection between the practice and theory of stochastic processes due to the difficulty of assigning exact probabilities to real-world events. Also, when the finite-state process comes as a reduced model of one that is more complicated in nature (possibly in a continuous state space), existing results do not facilitate rigorous analysis. Two approaches are introduced here. The first focuses on processes with one terminal state and the properties that affect their convergence rates. When a process is on a complicated graph, the bound of the convergence rate is not trivially related to that of the probabilities of individual transitions. Discovering the connection between the two led us to define two concepts which we call 'progressivity' and 'sortedness', and to a new comparison theorem for stochastic processes. An optimality criterion for robust optimal control also derives from this comparison theorem. In addition, this result is applied to the case of mission-oriented autonomous robot control to produce performance estimate within a control framework that we propose. The second approach is in the MDP frame work. We will introduce our preliminary work on optimistic robust optimization, which aims at finding solutions that guarantee the upper bounds of the accumulative discounted cost with prescribed probabilities. The motivation here is to address the issue that the standard robust optimal solution tends to be overly conservative.
Robust Optimal Attitude Controller for MIMO Uncertain Hexarotor MAVs: Disturbance Observer-Based
Nurul Dayana Salim
2016-01-01
Full Text Available This paper proposes a robust optimal attitude control design for multiple-input, multiple-output (MIMO uncertain hexarotor micro aerial vehicles (MAVs in the presence of parametric uncertainties, external time-varying disturbances, nonlinear dynamics, and coupling. The parametric uncertainties, external time-varying disturbances, nonlinear dynamics, and coupling are treated as the total disturbance in the proposed design. The proposed controller is achieved in two simple steps. First, an optimal linear-quadratic regulator (LQR controller is designed to guarantee that the nominal closed-loop system is asymptotically stable without considering the total disturbance. After that, a disturbance observer is integrated into the closed-loop system to estimate the total disturbance acting on the system. The total disturbance is compensated by a compensation input based on the estimated total disturbance. Robust properties analysis is given to prove that the state is ultimately bounded in specified boundaries. Simulation results illustrate the robustness of the disturbance observer-based optimal attitude control design for hovering and aggressive flight missions in the presence of the total disturbance.
A mean–variance objective for robust production optimization in uncertain geological scenarios
Capolei, Andrea; Suwartadi, Eka; Foss, Bjarne
2014-01-01
directly. In the mean–variance bi-criterion objective function risk appears directly, it also considers an ensemble of reservoir models, and has robust optimization as a special extreme case. The mean–variance objective is common for portfolio optimization problems in finance. The Markowitz portfolio......In this paper, we introduce a mean–variance criterion for production optimization of oil reservoirs and suggest the Sharpe ratio as a systematic procedure to optimally trade-off risk and return. We demonstrate by open-loop simulations of a two-phase synthetic oil field that the mean......–variance criterion is able to mitigate the significant inherent geological uncertainties better than the alternative certainty equivalence and robust optimization strategies that have been suggested for production optimization. In production optimization, the optimal water injection profiles and the production...
Bingyong Yan
2015-01-01
Full Text Available A robust fault detection scheme for a class of nonlinear systems with uncertainty is proposed. The proposed approach utilizes robust control theory and parameter optimization algorithm to design the gain matrix of fault tracking approximator (FTA for fault detection. The gain matrix of FTA is designed to minimize the effects of system uncertainty on residual signals while maximizing the effects of system faults on residual signals. The design of the gain matrix of FTA takes into account the robustness of residual signals to system uncertainty and sensitivity of residual signals to system faults simultaneously, which leads to a multiobjective optimization problem. Then, the detectability of system faults is rigorously analyzed by investigating the threshold of residual signals. Finally, simulation results are provided to show the validity and applicability of the proposed approach.
Robust optimization of uncertain multistage inventory systems with inexact data in decision rules
de Ruiter, Frans; Ben-Tal, A.; Brekelmans, Ruud; den Hertog, Dick
2017-01-01
In production-inventory problems customer demand is often subject to uncertainty. Therefore, it is challenging to design production plans that satisfy both demand and a set of constraints on e.g. production capacity and required inventory levels. Adjustable robust optimization (ARO) is a technique t
Liu, Derong; Wang, Ding; Wang, Fei-Yue; Li, Hongliang; Yang, Xiong
2014-12-01
In this paper, the infinite horizon optimal robust guaranteed cost control of continuous-time uncertain nonlinear systems is investigated using neural-network-based online solution of Hamilton-Jacobi-Bellman (HJB) equation. By establishing an appropriate bounded function and defining a modified cost function, the optimal robust guaranteed cost control problem is transformed into an optimal control problem. It can be observed that the optimal cost function of the nominal system is nothing but the optimal guaranteed cost of the original uncertain system. A critic neural network is constructed to facilitate the solution of the modified HJB equation corresponding to the nominal system. More importantly, an additional stabilizing term is introduced for helping to verify the stability, which reinforces the updating process of the weight vector and reduces the requirement of an initial stabilizing control. The uniform ultimate boundedness of the closed-loop system is analyzed by using the Lyapunov approach as well. Two simulation examples are provided to verify the effectiveness of the present control approach.
Non-fragile robust optimal guaranteed cost control of uncertain 2-D discrete state-delayed systems
Tandon, Akshata; Dhawan, Amit
2016-10-01
This paper is concerned with the problem of non-fragile robust optimal guaranteed cost control for a class of uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model with norm-bounded uncertainties. Our attention is focused on the design of non-fragile state feedback controllers such that the resulting closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible parameter uncertainties and controller gain variations. A sufficient condition for the existence of such controllers is established under the linear matrix inequality framework. Moreover, a convex optimisation problem is proposed to select a non-fragile robust optimal guaranteed cost controller stabilising the 2-D discrete state-delayed system as well as achieving the least guaranteed cost for the resulting closed-loop system. The proposed method is compared with the previously reported criterion. Finally, illustrative examples are given to show the potential of the proposed technique.
Robust dissipativity for uncertain impulsive dynamical systems
Liu Bin
2003-01-01
Full Text Available We discuss the robust dissipativity with respect to the quadratic supply rate for uncertain impulsive dynamical systems. By employing the Hamilton-Jacobi inequality approach, some sufficient conditions of robust dissipativity for this kind of system are established. Finally, we specialize the obtained results to the case of uncertain linear impulsive dynamical systems.
Balandin, DV; Kogan, MM
2004-01-01
An algorithm for checking feasibility of the robust H-infinity-control problem for systems with time-varying norm bounded uncertainty is suggested. This algorithm is an iterative procedure on each step of which an optimization problem for a linear function under convex constraints determined by LMIs
μ Synthesis Method for Robust Control of Uncertain Nonlinear Systems
无
2000-01-01
μ synthesis method for robust control of uncertain nonlinear systems is propored, which is based on feedback linearization. First, nonlinear systems are linearized as controllable linear systems by I/O linearization,such that uncertain nonlinear systems are expressed as the linear fractional transformations (LFTs) on the generalized linearized plants and uncertainty.Then,linear robust controllers are obtained for the LFTs usingμsynthesis method based on H∞ optimization.Finally,the nonlinear robust controllers are constructed by combining the linear robust controllers and the nonlinear feedback.An example is given to illustrate the design.
Gorissen, B.L.; Ben-Tal, A.; Blanc, J.P.C.; den Hertog, D.
2012-01-01
Abstract: We propose a new way to derive tractable robust counterparts of a linear conic optimization problem by using the theory of Beck and Ben-Tal [2] on the duality between the robust (“pessimistic”) primal problem and its “optimistic” dual. First, we obtain a new convex reformulation of the
Robust Solutions of Uncertain Complex-valued Quadratically Constrained Programs
Da Chuan XU; Zheng Hai HUANG
2008-01-01
In this paper,we discuss complex convex quadratically constrained optimization with uncertain data.Using S-Lemma,we show that the robust counterpart of complex convex quadratically constrained optimization with ellipsoidal or intersection-of-two-ellipsoids uncertainty set leads to a complex semidefinite program.By exploring the approximate S-Lemma,we give a complex semidefinite program which approximates the NP-hard robust counterpart of complex convex quadratic optimization with intersection-of-ellipsoids uncertainty set.
Robust control synthesis for uncertain dynamical systems
Byun, Kuk-Whan; Wie, Bong; Sunkel, John
1989-01-01
This paper presents robust control synthesis techniques for uncertain dynamical systems subject to structured parameter perturbation. Both QFT (quantitative feedback theory) and H-infinity control synthesis techniques are investigated. Although most H-infinity-related control techniques are not concerned with the structured parameter perturbation, a new way of incorporating the parameter uncertainty in the robust H-infinity control design is presented. A generic model of uncertain dynamical systems is used to illustrate the design methodologies investigated in this paper. It is shown that, for a certain noncolocated structural control problem, use of both techniques results in nonminimum phase compensation.
Robust stabilization, robust performance, and disturbance attenuation for uncertain linear systems
Wang, Yeih J.; Shieh, Leang S.; Sunkel, John W.
1992-01-01
This paper presents a linear quadratic regulator approach to the robust stabilization, robust performance, and disturbance attenuation of uncertain linear systems. The state-feedback designed systems provide both the robust stability with optimal performance and the disturbance attenuation with H-infinity-norm bounds. The proposed approach can be applied to matched and/or mismatched uncertain linear systems. For a matched uncertain linear system, it is shown that the disturbance attenuation robust-stabilizing controllers with or without optimal performance always exist and can be easily determined without searching; whereas, for a mismatched uncertain linear system, the introduced tuning parameters greatly enhance the flexibility of finding the disturbance-attenuation robust-stabilizing controllers.
Robust lyapunov controller for uncertain systems
Laleg-Kirati, Taous-Meriem
2017-02-23
Various examples of systems and methods are provided for Lyapunov control for uncertain systems. In one example, a system includes a process plant and a robust Lyapunov controller configured to control an input of the process plant. The robust Lyapunov controller includes an inner closed loop Lyapunov controller and an outer closed loop error stabilizer. In another example, a method includes monitoring a system output of a process plant; generating an estimated system control input based upon a defined output reference; generating a system control input using the estimated system control input and a compensation term; and adjusting the process plant based upon the system control input to force the system output to track the defined output reference. An inner closed loop Lyapunov controller can generate the estimated system control input and an outer closed loop error stabilizer can generate the system control input.
Robust solutions of Uncertain Capacity inventory control
Yajing Li
2013-01-01
This paper analyzes the uncertainties of air cargo and applies revenue management to solve the problem of air cargo capacity control.A robust capacity al ocation model for a multiple-leg with multiple shipment types is established,which describe uncertainty of these parameters as a number of discrete scenarios,and obtain the optimal al ocation with Mutation Particle Swarm Optimization.Simulation experiments show that this method can balance uncertainty of the model effectively and accord with actual situation.
Robust synchronization of uncertain chaotic systems
Li Fang; Hu Ai-Hua; Xu Zheng-Yuan
2006-01-01
This paper investigates robust unified (lag, anticipated, and complete) synchronization of two coupled chaotic systems. By introducing the concepts of positive definite symmetrical matrix and Riccati inequality and the theory of robust stability, several criteria on robust synchronization are established. Extensive numerical simulations are also used to confirm the results.
Robust scheduling in an uncertain environment
Wilson, M.
2016-01-01
This thesis presents research on scheduling in an uncertain environment, which forms a part of the rolling stock life cycle logistics applied research and development program funded by Dutch railway industry companies. The focus therefore lies on scheduling of maintenance operations on rolling stock
Robust control for a class of uncertain switched fuzzy systems
Hong YANG; Jun ZHAO
2007-01-01
A model of uncertain switched fuzzy systems whose subsystems are uncertain fuzzy systems is presented.Robust controllers for a class of switched fuzzy systems are designed by using the Lyapunov function method. Stability conditions for global asymptotic stability are developed and a switching strategy is proposed. An example shows the effectiveness of the method.
Nonlinear robust hierarchical control for nonlinear uncertain systems
Leonessa Alexander
1999-01-01
Full Text Available A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.
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.
Robust H2 control for uncertain sampled-data systems
Xie Weinan; Ma Guangcheng; Li Qinghua; Wang Changhong
2009-01-01
A new approach is proposed for robust H2 problem of uncertain sampled-data systems. Through introducing a free variable, a new Lyapunov asymptotical stability criterion with less conservativeness is established. Based on this criterion, some sufficient conditions on two classes of robust H2 problems for uncertain sampled-data control systems are presented through a set of coupled linear matrix inequalities, Finally, the less conservatism and potential of the developed results are illustrated via a numerical example.
Robust sliding mode control for uncertain discrete time systems
QU Shaocheng; WANG Yongji
2003-01-01
A novel variable structure control (VSC) strategy with a dynamic disturbance compensator based on the reaching law for a class of uncertain discrete systems is presented. The robust stability to disturbance and the system dynamics in the vicinity of the switching plane are studied. A measure of the uncertain parameters and external disturbance is obtained through delaying every sampling time. Theoretical analysis and experimental simulation results demonstrate that the dynamic performance and robustness of the closed-loop system are improved effectively.
Identification of uncertain nonlinear systems for robust fuzzy control.
Senthilkumar, D; Mahanta, Chitralekha
2010-01-01
In this paper, we consider fuzzy identification of uncertain nonlinear systems in Takagi-Sugeno (T-S) form for the purpose of robust fuzzy control design. The uncertain nonlinear system is represented using a fuzzy function having constant matrices and time varying uncertain matrices that describe the nominal model and the uncertainty in the nonlinear system respectively. The suggested method is based on linear programming approach and it comprises the identification of the nominal model and the bounds of the uncertain matrices and then expressing the uncertain matrices into uncertain norm bounded matrices accompanied by constant matrices. It has been observed that our method yields less conservative results than the other existing method proposed by Skrjanc et al. (2005). With the obtained fuzzy model, we showed the robust stability condition which provides a basis for different robust fuzzy control design. Finally, different simulation examples are presented for identification and control of uncertain nonlinear systems to illustrate the utility of our proposed identification method for robust fuzzy control.
A robust test of uncertain linear systems
Yogesh V.HOTE; D.Roy CHOUDHURY; J.R.P.GUPTA
2009-01-01
In this paper,it is shown that for low-order uncertain systems,there is no need to calculate all the minimum and maximum values of the coefficients for a perturbed system which is expressed in terms of polynomials and hence no need to formulate and test all the four Kharitonov's polynomials.Furthermore,for higher-order systems such as n ≥ 5,the usual four Kharitonov's polynomials need not be tested initially for sufficient condition of perturbed systems; rather,the necessary condition can be checked before going for sufficient condition.In order to show the effectiveness of the proposed method,numerical examples are shown and computational efficiency is highlighted.
Robustified time-optimal control of uncertain structural dynamic systems
Liu, Qiang; Wie, Bong
1991-01-01
A new approach for computing open-loop time-optimal control inputs for uncertain linear dynamical systems is developed. In particular, the single-axis, rest-to-rest maneuvering problem of flexible spacecraft in the presence of uncertainty in model parameters is considered. Robustified time-optimal control inputs are obtained by solving a parameter optimization problem subject to robustness constraints. A simple dynamical system with a rigid-body mode and one flexible mode is used to illustrate the concept.
Robust Control of Urban Industrial Water Mismatching Uncertain System
LI Kebai
2013-02-01
Full Text Available Urban industrial water system parameter fluctuation producing uncertainty may not occur in a control input channel, can be applied mismatching uncertain system to describe. Based on Lyapunov direct method and linear matrix inequality, design the urban industrial water mismatching uncertain system feedback stabilization robust control scheme. Avoid the defects that the feedback stabilization control method based on the matrix Riccati equation need to preset equation parameters, easier to solve and can reduce the conservative.
Robust Optimization in Simulation : Taguchi and Response Surface Methodology
Dellino, G.; Kleijnen, J.P.C.; Meloni, C.
2008-01-01
Optimization of simulated systems is tackled by many methods, but most methods assume known environments. This article, however, develops a 'robust' methodology for uncertain environments. This methodology uses Taguchi's view of the uncertain world, but replaces his statistical techniques by
Robust controller for a class of uncertain switched fuzzy systems
YANG Hong; ZHAO Jun
2007-01-01
A robustness control of uncertain switched fuzzy systems is presented.Using the switching technique and the Lyapunov function method,a continuous state feedback controller is built to ensure that for all allowable uncertainties the relevant closed-loop system is asymptotically stable.Furthermore,a switching strategy that achieves system global asymptotic stability of the uncertain switched fuzzy system is given.In this model,each subsystem of the switched system is an uncertain fuzzy system,and a common parallel distributed compensation controller is presented.The main condition is given in the form of convex combinations which are more solvable.This method transforms a certain switched system and has strong robustness for various system parameters.Simulations show the feasibility and the effectiveness of this method.
Robust Synchronization of Uncertain Linear Multi-Agent Systems
Trentelman, Harry L.; Takaba, Kiyotsugu; Monshizadeh Naini, Nima
2013-01-01
This paper deals with robust synchronization of uncertain multi-agent networks. Given a network with for each of the agents identical nominal linear dynamics, we allow uncertainty in the form of additive perturbations of the transfer matrices of the nominal dynamics. The perturbations are assumed to
MULTIDISCIPLINARY ROBUST OPTIMIZATION DESIGN
Chen Jianjiang; Xiao Renbin; Zhong Yifang; Dou Gang
2005-01-01
Because uncertainty factors inevitably exist under multidisciplinary design environment, a hierarchical multidisciplinary robust optimization design based on response surface is proposed. The method constructs optimization model of subsystem level and system level to coordinate the coupling among subsystems, and also the response surface based on the artificial neural network is introduced to provide information for system level optimization tool to maintain the independence of subsystems,i.e. to realize multidisciplinary parallel design. The application case of electrical packaging demonstrates that reasonable robust optimum solution can be yielded and it is a potential and efficient multidisciplinary robust optimization approach.
Jiawang XU; Xiaoyuan HUANG; Nina YAN
2007-01-01
A multi-objective robust operation model is proposed in this paper for an electronic market enabled supply chain consisting of multi-supplier and multi-customer with uncertain demands.Suppliers in this supply chain provide many kinds of products to different customers directly or through electronic market.Uncertain demands are described as a scenario set with certain probability; the supply chain operation model is constructed by using the robust optimization method based on scenario analyses.The operation model we proposed is a multi-objective programming problem satisfying several conflict objectives,such as meeting the demands of all customers,minimizing the system cost,the availabilities of suppliers' capacities not below a certain level,and robustness of decision to uncertain demands.The results of numerical examples proved that the solution of the model is most conservative; however,it can ensure the robustness of the operation of the supply chain effectively.
Robust quadratic assignment problem with budgeted uncertain flows
Mohammad Javad Feizollahi
2015-12-01
Full Text Available We consider a generalization of the classical quadratic assignment problem, where material flows between facilities are uncertain, and belong to a budgeted uncertainty set. The objective is to find a robust solution under all possible scenarios in the given uncertainty set. We present an exact quadratic formulation as a robust counterpart and develop an equivalent mixed integer programming model for it. To solve the proposed model for large-scale instances, we also develop two different heuristics based on 2-Opt local search and tabu search algorithms. We discuss performance of these methods and the quality of robust solutions through extensive computational experiments.
Robust Stabilization of Nonlinear Systems with Uncertain Varying Control Coefficient
Zaiyue Yang
2014-01-01
Full Text Available This paper investigates the stabilization problem for a class of nonlinear systems, whose control coefficient is uncertain and varies continuously in value and sign. The study emphasizes the development of a robust control that consists of a modified Nussbaum function to tackle the uncertain varying control coefficient. By such a method, the finite-time escape phenomenon has been prevented when the control coefficient is crossing zero and varying its sign. The proposed control guarantees the asymptotic stabilization of the system and boundedness of all closed-loop signals. The control performance is illustrated by a numerical simulation.
Robust Input-Output Energy Decoupling for Uncertain Singular Systems
Xin-Zhuang Dong; Qing-Ling Zhang
2005-01-01
This paper addresses the robust input-output energy decoupling problem for uncertain singular systems in which all parameter matrices except E exist as time-varying uncertainties. By means of linear matrix inequalities (LMIs),sufficient conditions are derived for the existence of linear state feedback and input transformation control laws, such that the resulting closed-loop uncertain singular system is generalized quadratically stable and the energy of every input controls mainly the energy of a corresponding output, and influences the energy of other outputs as weakly as possible.
Robust Hierarchical Control for Uncertain Multivariable Hexarotor Systems
Wei Lin
2015-01-01
Full Text Available Multirotor helicopter attracts more attention due to its increased load capacity and being highly maneuverable. However, these helicopters are uncertain multivariable systems, which pose a challenge for their robust controller design. In this paper, a robust two-loop control scheme is proposed for a hexarotor system. The resulted controller consists of a nominal controller and a robust compensator. The robust compensators are added to restrain the influences of uncertainties such as nonlinear dynamics, coupling, parametric uncertainties, and external disturbances. It is proven that the tracking errors are ultimately bounded with specified boundaries by choosing the parameters of the robust compensators. Simulation results on the hexarotor demonstrate the effectiveness of the proposed control method.
SU Cheng-li; WANG Shu-qing
2006-01-01
An extended robust model predictive control approach for input constrained discrete uncertain nonlinear systems with time-delay based on a class of uncertain T-S fuzzy models that satisfy sector bound condition is presented. In this approach, the minimization problem of the "worst-case" objective function is converted into the linear objective minimization problem involving linear matrix inequalities (LMIs) constraints. The state feedback control law is obtained by solving convex optimization of a set of LMIs. Sufficient condition for stability and a new upper bound on robust performance index are given for these kinds of uncertain fuzzy systems with state time-delay. Simulation results of CSTR process show that the proposed robust predictive control approach is effective and feasible.
Dynamic compensator design for robust stability of linear uncertain systems
Yedavalli, R. K.
1986-01-01
This paper presents a robust linear dynamic compensator design algorithm for linear uncertain systems whose parameters vary within given bounded sets. The algorithm explicitly incorporates the structure of the uncertainty into the design procedure and utilizes the elemental perturbation bounds developed recently. The special cases of linear state feedback and measurement feedback controllers are considered and the relative trade offs are discussed. The design algorithm is illustrated with the help of a simple example.
Robust digital controllers for uncertain chaotic systems: A digital redesign approach
Ababneh, Mohammad [Department of Controls, FMC Kongsberg Subsea, FMC Energy Systems, Houston, TX 77067 (United States); Barajas-Ramirez, Juan-Gonzalo [CICESE, Depto. De Electronica y Telecomunicaciones, Ensenada, BC, 22860 (Mexico); Chen Guanrong [Centre for Chaos Control and Synchronization, Department of Electronic Engineering, City University of Hong Kong (China); Shieh, Leang S. [Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77204-4005 (United States)
2007-03-15
In this paper, a new and systematic method for designing robust digital controllers for uncertain nonlinear systems with structured uncertainties is presented. In the proposed method, a controller is designed in terms of the optimal linear model representation of the nominal system around each operating point of the trajectory, while the uncertainties are decomposed such that the uncertain nonlinear system can be rewritten as a set of local linear models with disturbed inputs. Applying conventional robust control techniques, continuous-time robust controllers are first designed to eliminate the effects of the uncertainties on the underlying system. Then, a robust digital controller is obtained as the result of a digital redesign of the designed continuous-time robust controller using the state-matching technique. The effectiveness of the proposed controller design method is illustrated through some numerical examples on complex nonlinear systems--chaotic systems.
Adaptive Fuzzy and Robust H∞ Compensation Control for Uncertain Robot
Yuan Chen
2013-06-01
Full Text Available In this paper, two types of robust adaptive compensation control schemes for the trajectory tracking control of robot manipulator with uncertain dynamics are proposed. The proposed controllers incorporate the computed-torque control scheme as a nominal portion of the controller; an adaptive fuzzy control algorithm to approximate the structured uncertainties; and a nonlinear H∞ tracking control model as a feedback portion to eliminate the effects of the unstructured uncertainties and approximation errors. The validity of the robust adaptive compensation control schemes is investigated by numerical simulations of a two-link rotary robot manipulator
A New Lyapunov Based Robust Control for Uncertain Mechanical Systems
ZHEN Sheng-Chao; ZHAO Han; CHEN Ye-Hwa; HUANG Kang
2014-01-01
We design a new robust controller for uncertain mechanical systems. The inertia matrix0s singularity and upper bound property are first analyzed. It is shown that the inertia matrix may be positive semi-definite due to over-simplified model. Further-more, the inertia matrix0s being uniformly bounded above is also limited. A robust controller is proposed to suppress the effect of uncertainty in mechanical systems with the assumption of uniform positive definiteness and upper bound of the inertia matrix. We theoretically prove that the robust control renders uniform boundedness and uniform ultimate boundedness. The size of the ultimate boundedness ball can be made arbitrarily small by the designer. Simulation results are presented and discussed.
Distributed Robustness Analysis of Interconnected Uncertain Systems Using Chordal Decomposition
Pakazad, Sina Khoshfetrat; Hansson, Anders; Andersen, Martin Skovgaard
2014-01-01
Large-scale interconnected uncertain systems commonly have large state and uncertainty dimensions. Aside from the heavy computational cost of performing robust stability analysis in a centralized manner, privacy requirements in the network can also introduce further issues. In this paper, we...... utilize IQC analysis for analyzing large-scale interconnected uncertain systems and we evade these issues by describing a decomposition scheme that is based on the interconnection structure of the system. This scheme is based on the so-called chordal decomposition and does not add any conservativeness...... to the analysis approach. The decomposed problem can be solved using distributed computational algorithms without the need for a centralized computational unit. We further discuss the merits of the proposed analysis approach using a numerical experiment....
Simultaneous Robust Fault and State Estimation for Linear Discrete-Time Uncertain Systems
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.
Robust Stabilization of Uncertain Systems Based on Energy Dissipation Concepts
Gupta, Sandeep
1996-01-01
Robust stability conditions obtained through generalization of the notion of energy dissipation in physical systems are discussed in this report. Linear time-invariant (LTI) systems which dissipate energy corresponding to quadratic power functions are characterized in the time-domain and the frequency-domain, in terms of linear matrix inequalities (LMls) and algebraic Riccati equations (ARE's). A novel characterization of strictly dissipative LTI systems is introduced in this report. Sufficient conditions in terms of dissipativity and strict dissipativity are presented for (1) stability of the feedback interconnection of dissipative LTI systems, (2) stability of dissipative LTI systems with memoryless feedback nonlinearities, and (3) quadratic stability of uncertain linear systems. It is demonstrated that the framework of dissipative LTI systems investigated in this report unifies and extends small gain, passivity, and sector conditions for stability. Techniques for selecting power functions for characterization of uncertain plants and robust controller synthesis based on these stability results are introduced. A spring-mass-damper example is used to illustrate the application of these methods for robust controller synthesis.
Acikmese, Ahmet Behcet; Carson, John M., III
2006-01-01
A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees resolvability. With resolvability, initial feasibility of the finite-horizon optimal control problem implies future feasibility in a receding-horizon framework. The control consists of two components; (i) feed-forward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives and derivatives in polytopes. An illustrative numerical example is also provided.
Robust Stability Criterion for Uncertain Neural Networks with Time Delays
LIN Zhi-wei; ZHANG Ning; YANG Hong-jiu
2010-01-01
The robust stability of uncertain neural network with time-varying delay was investigated. The norm-bounded un-certainties are included in the system matrices. The constraint on time-varying delays is removed, which means that a fast time-varying delay is admissible. Some new delay-dependent stability criteria were presented by using Lyapunov-Krasovskii functional and linear matrix inequalities (LMIs) approaches. Finally, a numerical example was given to illustrate the effec-tiveness and innovation nature of the developed techniques.
Uncertain Dynamics, Correlation Effects, and Robust Investment Decisions
Flor, Christian Riis; Hesel, Søren
2015-01-01
We analyze a firm's investment problem when the dynamics of project value and investment cost are uncertain. We provide an explicit solution using a robust method for an ambiguity averse firm taking this into account. Ambiguity aversion regarding a common risk factor impacts differently than...... ambiguity aversion regarding investment cost residual risk. Correlation between project value and investment cost matters; ambiguity aversion regarding common risk can decrease the investment probability only if correlation is positive. Ambiguity aversion regarding residual risk always increases...... the investment probability. When only project value is risky, volatility can monotonically decrease the investment threshold; this does not hold with the multiple prior method....
Robust guaranteed cost observer design for linear uncertain jump systems with state delays
FU Yan-ming; ZHANG Bo; DUAN Guang-ren
2008-01-01
This paper deals with the robust guaranteed cost observer with guaranteed cost performance for a class of linear uncertain jump systems with state delay. The transition of the jumping parameters in systems is governed by a finite-state Markov process. Based on the stability theory in stochastic differential equations, a sufficient condition on the existence of the proposed robust guaranteed cost observer is derived. Robust guaran-teed cost observers are designed in terms of a set of linear coupled matrix inequalities. A convex optimization problem with LMI constraints is formulated to design the suboptimal guaranteed cost observers.
Robust Control for Uncertain Linear System Subject to Input Saturation
Qingyun Yang
2014-01-01
Full Text Available A robust control scheme using composite nonlinear feedback (CNF technology is proposed to improve tracking control performance for the uncertain linear system with input saturation and unknown external disturbances. A disturbance observer is presented to estimate the unknown disturbance generated by a linear exogenous system. The designed gain matrix of the disturbance observer is determined by solving linear matrix inequalities (LMIs. Based on the output of the designed disturbance observer, a robust CNF controller including a linear feedback control item and a nonlinear item is developed to follow the desired tracking signals. The linear feedback controller is designed using LMIs and the stability of the closed-loop system is proved via rigorous Lyapunov analysis. Finally, the extensive simulation results are presented to illustrate the effectiveness of the proposed control scheme.
Design for robust stabilization of nonlinear systems with uncertain parameters
赖旭芝; 文静; 吴敏
2004-01-01
Based on Lyapunov stability theory, a design method for the robust stabilization problem of a class of nonlinear systems with uncertain parameters is presented. The design procedure is divided into two steps: the first is to design controllers for the nominal system and make the system asymptotically stabilize at the expected equilibrium point; the second is to construct closed-loop nominal system based on the first step, then design robust controller to make the error of state between the original system and the nominal system converge to zero, thereby a dynamic controller with the constructed closed-loop nominal system served as interior dynamic is obtained. A numerical simulation verifies the correctness of the design method.
Robust H {sub {infinity}} output dynamic observer-based control of uncertain time-delay systems
Chen, J.-D. [Department of Electronic Engineering, National Kinmen Institute of Technology, Jinning, Kinmen 892, Taiwan (China)]. E-mail: tdchen@mail.kmit.edu.tw
2007-01-15
In this paper, the robustness and H {sub {infinity}} control problems of output dynamic observer-based control for a class of uncertain linear systems with time delay are considered. Under no disturbance input, the asymptotic stabilization for uncertain time-delay systems will be guaranteed. Linear matrix inequality (LMI) optimization approach is used to design three classes of the H {sub {infinity}} output dynamic controls. Based on the results of this paper, the constraint of matrix equality is not necessary for designing the observer-based controls.
Non-probabilistic Robust Optimal Design Method
SUN Wei; XU Huanwei; ZHANG Xu
2009-01-01
For the purpose of dealing with uncertainty factors in engineering optimization problems, this paper presents a new non-probabilistic robust optimal design method based on maximum variation estimation. The method analyzes the effect of uncertain factors to objective and constraints functions, and then the maximal variations to a solution are calculated. In order to guarantee robust feasibility the maximal variations of constraints are added to original constraints as penalty term; the maximal variation of objective function is taken as a robust index to a solution; linear physical programming is used to adjust the values of quality characteristic and quality variation, and then a bi-level mathematical robust optimal model is coustructed. The method does not require presumed probability distribution of uncertain factors or continuous and differentiable of objective and constraints functions. To demonstrate the proposed method, the design of the two-bar structure acted by concentrated load is presented. In the example the robustness of the normal stress, feasibility of the total volume and the buckling stress are studied. The robust optimal design results show that in the condition of maintaining feasibility robustness, the proposed approach can obtain a robust solution which the designer is satisfied with the value of objective function and its variation.
A Robust Service Selection Method Based on Uncertain QoS
Yanping Chen
2016-01-01
Full Text Available Nowadays, the number of Web services on the Internet is quickly increasing. Meanwhile, different service providers offer numerous services with the similar functions. Quality of Service (QoS has become an important factor used to select the most appropriate service for users. The most prominent QoS-based service selection models only take the certain attributes into account, which is an ideal assumption. In the real world, there are a large number of uncertain factors. In particular, at the runtime, QoS may become very poor or unacceptable. In order to solve the problem, a global service selection model based on uncertain QoS was proposed, including the corresponding normalization and aggregation functions, and then a robust optimization model adopted to transform the model. Experiment results show that the proposed method can effectively select services with high robustness and optimality.
A nonlinear robust PI controller for an uncertain system
Aguilar-Ibañez, Carlos; Mendoza-Mendoza, Julio A.; Suarez-Castanon, Miguel S.; Davila, Jorge
2014-05-01
This paper presents a smooth control strategy for the regulation problem of an uncertain system, which assures uniform ultimate boundedness of the closed-loop system inside of the zero-state neighbourhood. This neighbourhood can be made arbitrarily small. To this end, a class of nonlinear proportional integral controllers or PI controllers was designed. The behaviour of this controller emulates very close a sliding mode controller. To accomplish this behaviour saturation functions were combined with traditional PI controller. The controller did not need a high-gain controller or a sliding mode controller to accomplish robustness against unmodelled persistent perturbations. The obtained closed-solution has a finite time of convergence in a small vicinity. The corresponding stability convergence analysis was done applying the traditional Lyapunov method. Numerical simulations were carried out to assess the effectiveness of the obtained controller.
Optimal second order sliding mode control for linear uncertain systems.
Das, Madhulika; Mahanta, Chitralekha
2014-11-01
In this paper an optimal second order sliding mode controller (OSOSMC) is proposed to track a linear uncertain system. The optimal controller based on the linear quadratic regulator method is designed for the nominal system. An integral sliding mode controller is combined with the optimal controller to ensure robustness of the linear system which is affected by parametric uncertainties and external disturbances. To achieve finite time convergence of the sliding mode, a nonsingular terminal sliding surface is added with the integral sliding surface giving rise to a second order sliding mode controller. The main advantage of the proposed OSOSMC is that the control input is substantially reduced and it becomes chattering free. Simulation results confirm superiority of the proposed OSOSMC over some existing.
Structured controllers for uncertain systems a stochastic optimization approach
Toscano, Rosario
2013-01-01
Structured Controllers for Uncertain Systems focuses on the development of easy-to-use design strategies for robust low-order or fixed-structure controllers (particularly the industrially ubiquitous PID controller). These strategies are based on a recently-developed stochastic optimization method termed the "Heuristic Kalman Algorithm" (HKA) the use of which results in a simplified methodology that enables the solution of the structured control problem without a profusion of user-defined parameters. An overview of the main stochastic methods employable in the context of continuous non-convex optimization problems is also provided and various optimization criteria for the design of a structured controller are considered; H∞, H2, and mixed H2/H∞ each merits a chapter to itself. Time-domain-performance specifications can be easily incorporated in the design. Advances in Industrial Control aims to report and encourage the transfer of technology in control engineering. The rapid development of control technolo...
Robust Control of Uncertain Systems via Dissipative LQG-Type Controllers
Joshi, Suresh M.
2000-01-01
Optimal controller design is addressed for a class of linear, time-invariant systems which are dissipative with respect to a quadratic power function. The system matrices are assumed to be affine functions of uncertain parameters confined to a convex polytopic region in the parameter space. For such systems, a method is developed for designing a controller which is dissipative with respect to a given power function, and is simultaneously optimal in the linear-quadratic-Gaussian (LQG) sense. The resulting controller provides robust stability as well as optimal performance. Three important special cases, namely, passive, norm-bounded, and sector-bounded controllers, which are also LQG-optimal, are presented. The results give new methods for robust controller design in the presence of parametric uncertainties.
Improved Robustness of Generalized Predictive Control for Uncertain Systems
Khelifa, Khelifi Otmane; Noureddine, Bali; Lazhari, Nezli
2015-01-01
An off-line methodology has been developed to improve the robustness of an initial generalized predictive control (GPC) through convex optimization of the Youla parameter. However, this method is restricted with the case of the systems affected only by unstructured uncertainties. This paper proposes an extension of this method to the systems subjected to both unstructured and polytopic uncertainties. The basic idea consists in adding supplementary constraints to the optimization problem which validates the Lipatov stability condition at each vertex of the polytope. These polytopic uncertainties impose a non convex quadratically constrained quadratic programming (QCQP) problem. Based on semidefinite programming (SDP), this problem is relaxed and solved. Therefore, the robustification provides stability robustness towards unstructured uncertainties for the nominal system, while guaranteeing stability properties over a specified polytopic domain of uncertainties. Finally, we present a numerical example to demonstrate the proposed method.
Robust guaranteed cost filtering for uncertain time-delay systems with Markovian jumping parameters
Fu Yanming; Zhang Ying; Duan Guangren; Chai Qingxuan
2005-01-01
The robust guaranteed cost filtering problem for a class of linear uncertain stochastic systems with time delays is investigated. The system under study involves time delays, jumping parameters and Brownian motions. The transition of the jumping parameters in systems is governed by a finite-state Markov process. The objective is to design linear memoryless filters such that for all uncertainties, the resulting augmented system is robust stochastically stable independent of delays and satisfies the proposed guaranteed cost performance. Based on stability theory in stochastic differential equations, a sufficient condition on the existence of robust guaranteed cost filters is derived. Robust guaranteed cost filters are designed in terms of linear matrix inequalities. A convex optimization problem with LMI constraints is formulated to design the suboptimal guaranteed cost filters.
Robust Optimization in Simulation : Taguchi and Response Surface Methodology
Dellino, G.; Kleijnen, J.P.C.; Meloni, C.
2008-01-01
Optimization of simulated systems is tackled by many methods, but most methods assume known environments. This article, however, develops a 'robust' methodology for uncertain environments. This methodology uses Taguchi's view of the uncertain world, but replaces his statistical techniques by Respons
Robust Optimization in Simulation : Taguchi and Krige Combined
Dellino, G.; Kleijnen, Jack P.C.; Meloni, C.
2009-01-01
Optimization of simulated systems is the goal of many methods, but most methods as- sume known environments. We, however, develop a `robust' methodology that accounts for uncertain environments. Our methodology uses Taguchi's view of the uncertain world, but replaces his statistical techniques by Kr
Event-Based Robust Control for Uncertain Nonlinear Systems Using Adaptive Dynamic Programming.
Zhang, Qichao; Zhao, Dongbin; Wang, Ding
2016-10-18
In this paper, the robust control problem for a class of continuous-time nonlinear system with unmatched uncertainties is investigated using an event-based control method. First, the robust control problem is transformed into a corresponding optimal control problem with an augmented control and an appropriate cost function. Under the event-based mechanism, we prove that the solution of the optimal control problem can asymptotically stabilize the uncertain system with an adaptive triggering condition. That is, the designed event-based controller is robust to the original uncertain system. Note that the event-based controller is updated only when the triggering condition is satisfied, which can save the communication resources between the plant and the controller. Then, a single network adaptive dynamic programming structure with experience replay technique is constructed to approach the optimal control policies. The stability of the closed-loop system with the event-based control policy and the augmented control policy is analyzed using the Lyapunov approach. Furthermore, we prove that the minimal intersample time is bounded by a nonzero positive constant, which excludes Zeno behavior during the learning process. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed control scheme.
Robust Portfolio Optimization using CAPM Approach
mohsen gharakhani
2013-08-01
Full Text Available In this paper, a new robust model of multi-period portfolio problem has been developed. One of the key concerns in any asset allocation problem is how to cope with uncertainty about future returns. There are some approaches in the literature for this purpose including stochastic programming and robust optimization. Applying these techniques to multi-period portfolio problem may increase the problem size in a way that the resulting model is intractable. In this paper, a novel approach has been proposed to formulate multi-period portfolio problem as an uncertain linear program assuming that asset return follows the single-index factor model. Robust optimization technique has been also used to solve the problem. In order to evaluate the performance of the proposed model, a numerical example has been applied using simulated data.
向月; 刘俊勇; 魏震波; 曹银利; 江东林; 冯艾
2014-01-01
为了实现含可再生能源的并网微电网经济运行，提出了出力不确定集，并综合考虑“源储荷”协调调控，构建了广义能量优化鲁棒模型。模型采用多阶段求解策略，其中端点场景根据设计的生成规则产生，而二层规划问题则转化为单层非线性数学结构进行求解，得到使交互成本最大端点场景下社会效益成本最小的经济运行调度方案。算例验证了模型和算法的可行性，可为调度提供决策参考。此外，仿真结果还表明：微电网向主网购电价格大小会影响交互功率传输量；而售电价格与其比值的增加在一定程度上会减少系统总的社会效益成本。%To realize economic operation of grid-connected microgrid with intermitted renewable energy, uncertain set was proposed and robust model of general energy optimization was built considering coordination of“source-storage-load”. The model could be solved by multi-stage strategy with endpoint scenarios produced by the proposed rules, and the two-level programming problem was transformed into single layer nonlinear mathematical structure. Thus, the economy operation result with the minimum social benefit cost and the maximum interactive cost was obtained. The feasibility of the proposed model and algorithm was verified by test cases. In addition, the results also indicated that the size of electricity purchasing price would affect the amount of interactive power and the increase of the proportion between the purchasing price and selling price would reduce social benefit cost to some extent.
Minimax robust power split in AF relays based on uncertain long-term CSI
Nisar, Muhammad Danish
2011-09-01
An optimal power control among source and relay nodes in presence of channel state information (CSI) is vital for an efficient amplify and forward (AF) based cooperative communication system. In this work, we study the optimal power split (power control) between the source and relay node in presence of an uncertainty in the CSI. The prime contribution is to solve the problem based on an uncertain long-term knowledge of both the first and second hop CSI (requiring less frequent updates), and under an aggregate network-level power constraint. We employ the minimax optimization methodology to arrive at the minimax robust optimal power split, that offers the best possible guarantee on the end-to-end signal to noise ratio (SNR). The derived closed form analytical expressions admit simple intuitive interpretations and are easy to implement in real-world AF relaying systems. Numerical results confirm the advantages of incorporating the presence of uncertainty into the optimization problem, and demonstrate the usefulness of the proposed minimax robust optimal power split. © 2011 IEEE.
Robust H∞ control of uncertain systems with two additive time-varying delays
Syed, Ali M.; Saravanakumar, R.
2015-09-01
This paper is concerned with the problem of delay-dependent robust H∞ control for a class of uncertain systems with two additive time-varying delays. A new suitable Lyapunov-Krasovskii functional (LKF) with triple integral terms is constructed and a tighter upper bound of the derivative of the LKF is derived. By applying a convex optimization technique, new delay-dependent robust H∞ stability criteria are derived in terms of linear matrix inequalities (LMI). Based on the stability criteria, a state feedback controller is designed such that the closed-loop system is asymptotically stable. Finally, numerical examples are given to illustrate the effectiveness of the proposed method. Comparison results show that our results are less conservative than the existing methods. Project supported by the Fund from the Department of Science and Technology of India (Grant No. SR/FTP/MS-039/2011).
Robust output feedback H-infinity control and filtering for uncertain linear systems
Chang, Xiao-Heng
2014-01-01
"Robust Output Feedback H-infinity Control and Filtering for Uncertain Linear Systems" discusses new and meaningful findings on robust output feedback H-infinity control and filtering for uncertain linear systems, presenting a number of useful and less conservative design results based on the linear matrix inequality (LMI) technique. Though primarily intended for graduate students in control and filtering, the book can also serve as a valuable reference work for researchers wishing to explore the area of robust H-infinity control and filtering of uncertain systems. Dr. Xiao-Heng Chang is a Professor at the College of Engineering, Bohai University, China.
Robust stability of uncertain neutral linear stochastic differential delay system
JIANG Ming-hui; SHEN Yi; LIAO Xiao-xin
2007-01-01
The LaSalle-type theorem for the neutral stochastic differential equations with delay is established for the first time and then applied to propose algebraic criteria of the stochastically asymptotic stability and almost exponential stability for the uncertain neutral stochastic differential systems with delay. An example is given to verify the effectiveness of obtained results.
Robust Solutions for Systems of Uncertain Linear Equations
Zhen, Jianzhe; den Hertog, Dick
2015-01-01
Our contribution is twofold. Firstly, for a system of uncertain linear equations where the uncertainties are column-wise and reside in general convex sets, we show that the intersection of the set of possible solutions and any orthant is convex. We derive a convex representation of this intersection
Robust decentralized output regulation for uncertain heterogeneous systems
Persis, Claudio De; Liu, Hui; Cao, Ming
2012-01-01
We consider the problem in which N heterogeneous uncertain linear systems aim at tracking a reference signal generated by a given exosystem under the restriction that not all the systems are directly connected to the exosystem. To tackle this problem, the reference signal is reconstructed via local
Performance-Driven Robust Identification and Control of Uncertain Dynamical Systems
Basar, Tamer
2001-10-29
The grant DEFG02-97ER13939 from the Department of Energy has supported our research program on robust identification and control of uncertain dynamical systems, initially for the three-year period June 15, 1997-June 14, 2000, which was then extended on a no-cost basis for another year until June 14, 2001. This final report provides an overview of our research conducted during this period, along with a complete list of publications supported by the Grant. Within the scope of this project, we have studied fundamental issues that arise in modeling, identification, filtering, control, stabilization, control-based model reduction, decomposition and aggregation, and optimization of uncertain systems. The mathematical framework we have worked in has allowed the system dynamics to be only partially known (with the uncertainties being of both parametric or structural nature), and further the dynamics to be perturbed by unknown dynamic disturbances. Our research over these four years has generated a substantial body of new knowledge, and has led to new major developments in theory, applications, and computational algorithms. These have all been documented in various journal articles and book chapters, and have been presented at leading conferences, as to be described. A brief description of the results we have obtained within the scope of this project can be found in Section 3. To set the stage for the material of that section, we first provide in the next section (Section 2) a brief description of the issues that arise in the control of uncertain systems, and introduce several criteria under which optimality will lead to robustness and stability. Section 4 contains a list of references cited in these two sections. A list of our publications supported by the DOE Grant (covering the period June 15, 1997-June 14, 2001) comprises Section 5 of the report.
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.
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.
Robust filtering for uncertain systems a parameter-dependent approach
Gao, Huijun
2014-01-01
This monograph provides the reader with a systematic treatment of robust filter design, a key issue in systems, control and signal processing, because of the fact that the inevitable presence of uncertainty in system and signal models often degrades the filtering performance and may even cause instability. The methods described are therefore not subject to the rigorous assumptions of traditional Kalman filtering. The monograph is concerned with robust filtering for various dynamical systems with parametric uncertainties, and focuses on parameter-dependent approaches to filter design. Classical filtering schemes, like H2 filtering and H¥ filtering, are addressed, and emerging issues such as robust filtering with constraints on communication channels and signal frequency characteristics are discussed. The text features: · design approaches to robust filters arranged according to varying complexity level, and emphasizing robust filtering in the parameter-dependent framework for the first time; ·...
Robust stability of time-varying uncertain systems with rational dependence on the uncertainty
2010-01-01
Robust stability of time-varying uncertain systems is a key problem in automatic control. This note considers the case of linear systems with rational dependence on an uncertain time-varying vector constrained in a polytope, which is typically addressed in the literature by using the linear fractional representation (LFR). A novel sufficient condition for robust stability is derived in terms of a linear matrix inequality (LMI) feasibility test by exploiting homogeneous polynomial Lyapunov fun...
Design and Analysis of Robust Kanban System in an Uncertain Environment
Li, Zhe
2013-01-01
Kanban is a representative control policy pursuing cost-efficient features for the material flow system. However, the Kanban mechanism increases the system vulnerability especially when the environment is uncertain. Therefore, we proposed a robust Kanban system model for the supply chain system based on the Kanban mechanism. The model can use robust approaches from strategic, tactical, and operational levels to deal with the risks in an uncertain environment.
Robust Admissible Analyse of Uncertain Singular Systems via Delta Operator Method
WANG Wen; WANG Hui
2016-01-01
This paper investigates the problem of robust admissible analysis for uncertain singular delta operator systems(SDOSs). Firstly, we introduce the definition of generalized quadratic admissibility to ensure robust admissibility. Then, by means of LMI, a necessary and sufficient condition is given to prove a uncertain SDOS is generalized quadratic admissible. Finally, a numerical example is provided to demonstrate the effectiveness of the results in this paper.
Delay-dependent state feedback robust stabilization for uncertain singular time-delay systems
Gao Huanli; Xu Bugong
2008-01-01
The problem of robust stabilization for uncertain singular time-delay systems is studied.First,a new delay-dependent asymptotic stability criteria for normal singular time-delay systems is given,which is less conservative.Using this result,the problem of state feedback robust stabilization for uncertain singular time-delay systems is discussed.Finally,two examples are given to illustrate the effectiveness of the results.
Goberna, Miguel A.; Jeyakumar, Vaithilingam; Li, Guoyin; Linh, Nguyen
2016-01-01
The radius of robust feasibility of a convex program with uncertain constraints gives a value for the maximal ‘size’ of an uncertainty set under which robust feasibility can be guaranteed. This paper provides an upper bound for the radius for convex programs with uncertain convex polynomial constraints and exact formulas for convex programs with SOS-convex polynomial constraints (or convex quadratic constraints) under affine data uncertainty. These exact formulas allow the radius to be comput...
An uncertain multidisciplinary design optimization method using interval convex models
Li, Fangyi; Luo, Zhen; Sun, Guangyong; Zhang, Nong
2013-06-01
This article proposes an uncertain multi-objective multidisciplinary design optimization methodology, which employs the interval model to represent the uncertainties of uncertain-but-bounded parameters. The interval number programming method is applied to transform each uncertain objective function into two deterministic objective functions, and a satisfaction degree of intervals is used to convert both the uncertain inequality and equality constraints to deterministic inequality constraints. In doing so, an unconstrained deterministic optimization problem will be constructed in association with the penalty function method. The design will be finally formulated as a nested three-loop optimization, a class of highly challenging problems in the area of engineering design optimization. An advanced hierarchical optimization scheme is developed to solve the proposed optimization problem based on the multidisciplinary feasible strategy, which is a well-studied method able to reduce the dimensions of multidisciplinary design optimization problems by using the design variables as independent optimization variables. In the hierarchical optimization system, the non-dominated sorting genetic algorithm II, sequential quadratic programming method and Gauss-Seidel iterative approach are applied to the outer, middle and inner loops of the optimization problem, respectively. Typical numerical examples are used to demonstrate the effectiveness of the proposed methodology.
Robust H∞ control for uncertain descriptor systems with state and control delay
Piao Fengxian; Zhang Qingling; Ma Xiuzhen
2006-01-01
The problem of robust stabilization for uncertain continuous descriptor system with state and control delay is considered. The time-varying parametric uncertainty is assumed to be norm-bounded. The purpose of the robust stabilization is to design a memoryless state feedback law such that the resulting closed-loop system is robustly stable. A sufficient condition that uncertain continuous descriptor system is robustly stabilizabled by state feedback law is derived in terms of linear matrix inequality (LMI). Finally, a numerical example is provided to demonstrate the application of the proposed method.
Fault-tolerant control of linear uncertain systems using H∞ robust predictive control
Chen Xueqin; Geng Yunhai; Zhang Yingchun; Wang Feng
2008-01-01
The robust fault-tolerant control problem of linear uncertain systems is studied. It is shown that a solution for this problem can be obtained from a H∞ robust predictive controller (RMPC) by the method of linear matrix inequality (LMI). This approach has the advantages of both H∞ control and MPC: the robustness and ability to handle constraints explicitly. The robust closed-loop stability of the linear uncertain system with input and output constraints is proven under an actuator and sensor faults condition. Finally, satisfactory results of simulation experiments verify the validity of this algorithm.
Robust Portfolio Optimization Using Pseudodistances.
Toma, Aida; Leoni-Aubin, Samuela
2015-01-01
The presence of outliers in financial asset returns is a frequently occurring phenomenon which may lead to unreliable mean-variance optimized portfolios. This fact is due to the unbounded influence that outliers can have on the mean returns and covariance estimators that are inputs in the optimization procedure. In this paper we present robust estimators of mean and covariance matrix obtained by minimizing an empirical version of a pseudodistance between the assumed model and the true model underlying the data. We prove and discuss theoretical properties of these estimators, such as affine equivariance, B-robustness, asymptotic normality and asymptotic relative efficiency. These estimators can be easily used in place of the classical estimators, thereby providing robust optimized portfolios. A Monte Carlo simulation study and applications to real data show the advantages of the proposed approach. We study both in-sample and out-of-sample performance of the proposed robust portfolios comparing them with some other portfolios known in literature.
Robust stabilization of uncertain nonholonomic systems with strong nonlinear drifts
Yuqiang WU; Xiuyun ZHENG
2008-01-01
This paper investigates the robust stabilization of the nonholonomic control systems with strongly nonlinear uncertainties.In order to make the state scaling effective and to prevent the fiflite time escape phenomenon from happening.the switching control strategy based on the state measurement of the first subsystem is employed to achieve the asymptotic stabilization.The recurslve integrator backstepping technique is applied to the design of the robust controller.The simulation example demonstrates the efficiency and robust features of the proposed method.
Robust Stabilization for Uncertain Linear Delay Markow Jump System
钟麦英; 汤兵勇; 黄小原
2001-01-01
Markov jump linear systems are defined as a family of linear systems with randomly Markov jumping parameters and are used to model systems subject to failures or changes in structure. The robust stabilization problem of jump linear delay system with umcerratnty was studied. By using of linear matrix inequalities, the existence conditions of robust stabilizing and the state feedback controller designing methods are also presented and proved. Finally, an illustrated example shows the effectiveness of this approach.
Robust dual-response optimization
Yanikoglu, Ihsan; den Hertog, Dick; Kleijnen, J.P.C.
2016-01-01
This article presents a robust optimization reformulation of the dual-response problem developed in response surface methodology. The dual-response approach fits separate models for the mean and the variance and analyzes these two models in a mathematical optimization setting. We use metamodels esti
QI Wen-Juan; ZHANG Peng; DENG Zi-Li
2014-01-01
This paper deals with the problem of designing robust sequential covariance intersection (SCI) fusion Kalman filter for the clustering multi-agent sensor network system with measurement delays and uncertain noise variances. The sensor network is partitioned into clusters by the nearest neighbor rule. Using the minimax robust estimation principle, based on the worst-case conservative sensor network system with conservative upper bounds of noise variances, and applying the unbiased linear minimum variance (ULMV) optimal estimation rule, we present the two-layer SCI fusion robust steady-state Kalman filter which can reduce communication and computation burdens and save energy sources, and guarantee that the actual filtering error variances have a less-conservative upper-bound. A Lyapunov equation method for robustness analysis is proposed, by which the robustness of the local and fused Kalman filters is proved. The concept of the robust accuracy is presented and the robust accuracy relations of the local and fused robust Kalman filters are proved. It is proved that the robust accuracy of the global SCI fuser is higher than those of the local SCI fusers and the robust accuracies of all SCI fusers are higher than that of each local robust Kalman filter. A simulation example for a tracking system verifies the robustness and robust accuracy relations.
Waterflooding optimization in uncertain geological scenarios
Capolei, Andrea; Suwartadi, Eka; Foss, Bjarne;
2013-01-01
In conventional waterflooding of an oil field, feedback based optimal control technologies may enable higher oil recovery than with a conventional reactive strategy in which producers are closed based on water breakthrough. To compensate for the inherent geological uncertainties in an oil field, ...
Robust Control Design for Uncertain Nonlinear Dynamic Systems
Kenny, Sean P.; Crespo, Luis G.; Andrews, Lindsey; Giesy, Daniel P.
2012-01-01
Robustness to parametric uncertainty is fundamental to successful control system design and as such it has been at the core of many design methods developed over the decades. Despite its prominence, most of the work on robust control design has focused on linear models and uncertainties that are non-probabilistic in nature. Recently, researchers have acknowledged this disparity and have been developing theory to address a broader class of uncertainties. This paper presents an experimental application of robust control design for a hybrid class of probabilistic and non-probabilistic parametric uncertainties. The experimental apparatus is based upon the classic inverted pendulum on a cart. The physical uncertainty is realized by a known additional lumped mass at an unknown location on the pendulum. This unknown location has the effect of substantially altering the nominal frequency and controllability of the nonlinear system, and in the limit has the capability to make the system neutrally stable and uncontrollable. Another uncertainty to be considered is a direct current motor parameter. The control design objective is to design a controller that satisfies stability, tracking error, control power, and transient behavior requirements for the largest range of parametric uncertainties. This paper presents an overview of the theory behind the robust control design methodology and the experimental results.
Fault detection and optimization for networked control systems with uncertain time-varying delay
Qing Wang; Zhaolei Wang; Chaoyang Dong; Erzhuo Niu
2015-01-01
The observer-based robust fault detection filter design and optimization for networked control systems (NCSs) with uncer-tain time-varying delays are addressed. The NCSs with uncertain time-varying delays are modeled as parameter-uncertain systems by the matrix theory. Based on the model, an observer-based residual generator is constructed and the sufficient condition for the existence of the desired fault detection filter is derived in terms of the linear matrix inequality. Furthermore, a time domain opti-mization approach is proposed to improve the performance of the fault detection system. To prevent the false alarms, a new thresh-old function is established, and the solution of the optimization problem is given by using the singular value decomposition (SVD) of the matrix. A numerical example is provided to il ustrate the effectiveness of the proposed approach.
A New Robust Stabilization Analysis Result for Uncertain Systems with Time-Varying Delay
WANG Zhong-sheng; WANG Dong-yun; LIAO Xiao-xin
2005-01-01
The robust stabilization problem for uncertain systems with time-varying delay has been discussed. A new sufficient criterion is obtained to guarantee the closed-loop system robust stabilizable. The controller gain matrix is included in a Hamiltonian matrix. The Hamiltonian matrix can be constructed by the boundedness of the uncertainties. Some examples are given to illustrate the feasibility of the criterion.
Pakazad, Sina Khoshfetrat; Hansson, Anders; Andersen, Martin Skovgaard;
2013-01-01
We consider a class of convex feasibility problems where the constraints that describe the feasible set are loosely coupled. These problems arise in robust stability analysis of large, weakly interconnected uncertain systems. To facilitate distributed implementation of robust stability analysis o...
Evaluation of Ares-I Control System Robustness to Uncertain Aerodynamics and Flex Dynamics
Jang, Jiann-Woei; VanTassel, Chris; Bedrossian, Nazareth; Hall, Charles; Spanos, Pol
2008-01-01
This paper discusses the application of robust control theory to evaluate robustness of the Ares-I control systems. Three techniques for estimating upper and lower bounds of uncertain parameters which yield stable closed-loop response are used here: (1) Monte Carlo analysis, (2) mu analysis, and (3) characteristic frequency response analysis. All three methods are used to evaluate stability envelopes of the Ares-I control systems with uncertain aerodynamics and flex dynamics. The results show that characteristic frequency response analysis is the most effective of these methods for assessing robustness.
On delay-dependent robust stability for uncertain neutral systems
He Yong; Wu Min
2005-01-01
The problem of delay-dependent criteria for the robust stability of neutral systems with time-varying structured uncertainties and identi-eal neutral-delay and discrete-delay is concerned. A criterion for nominal systems is presented by taking the relationship between the terms in the Leibniz-Newton formula into account, which is described by some freeweighting matrices. In addition, this criterion is extended to robust stability of the systems with time-varying structured uncertainties. All of the criteria are based on linear matrix inequality such that it is easy to calculate the upper bound of the time-delay and the free-weighting matrices. Numerical examples illustrate the effectiveness and the improvement over the existing results.
Hints for practical robust optimization
Gorissen, B.L.; Yanikoglu, I.; den Hertog, D.
2013-01-01
Robust optimization (RO) is a young and active research field that has been mainly developed in the last 15 years. RO techniques are very useful for practice and not difficult to understand for practitioners. It is therefore remarkable that real-life applications of RO are still lagging behind; ther
Liu, Derong; Yang, Xiong; Wang, Ding; Wei, Qinglai
2015-07-01
The design of stabilizing controller for uncertain nonlinear systems with control constraints is a challenging problem. The constrained-input coupled with the inability to identify accurately the uncertainties motivates the design of stabilizing controller based on reinforcement-learning (RL) methods. In this paper, a novel RL-based robust adaptive control algorithm is developed for a class of continuous-time uncertain nonlinear systems subject to input constraints. The robust control problem is converted to the constrained optimal control problem with appropriately selecting value functions for the nominal system. Distinct from typical action-critic dual networks employed in RL, only one critic neural network (NN) is constructed to derive the approximate optimal control. Meanwhile, unlike initial stabilizing control often indispensable in RL, there is no special requirement imposed on the initial control. By utilizing Lyapunov's direct method, the closed-loop optimal control system and the estimated weights of the critic NN are proved to be uniformly ultimately bounded. In addition, the derived approximate optimal control is verified to guarantee the uncertain nonlinear system to be stable in the sense of uniform ultimate boundedness. Two simulation examples are provided to illustrate the effectiveness and applicability of the present approach.
Liu, Ping
2013-07-01
This paper deals with the finite-time stabilization of unified chaotic complex systems with known and unknown parameters. Based on the finite-time stability theory, nonlinear control laws are presented to achieve finite-time chaos control of the determined and uncertain unified chaotic complex systems, respectively. The two controllers are simple, and one of the uncertain unified chaotic complex systems is robust. For the design of a finite-time controller on uncertain unified chaotic complex systems, only some of the unknown parameters need to be bounded. Simulation results for the chaotic complex Lorenz, Lü and Chen systems are presented to validate the design and analysis.
Robust Portfolio Optimization Using Pseudodistances
2015-01-01
The presence of outliers in financial asset returns is a frequently occurring phenomenon which may lead to unreliable mean-variance optimized portfolios. This fact is due to the unbounded influence that outliers can have on the mean returns and covariance estimators that are inputs in the optimization procedure. In this paper we present robust estimators of mean and covariance matrix obtained by minimizing an empirical version of a pseudodistance between the assumed model and the true model underlying the data. We prove and discuss theoretical properties of these estimators, such as affine equivariance, B-robustness, asymptotic normality and asymptotic relative efficiency. These estimators can be easily used in place of the classical estimators, thereby providing robust optimized portfolios. A Monte Carlo simulation study and applications to real data show the advantages of the proposed approach. We study both in-sample and out-of-sample performance of the proposed robust portfolios comparing them with some other portfolios known in literature. PMID:26468948
Delay-dependent robust H∞ control of convex polyhedral uncertain fuzzy systems
无
2008-01-01
The robust H∞ control problem for a class of uncertain Takagi-Sugeno fuzzy systems with time-varying state delays is studied. The uncertain parameters are supposed to reside in a polytope. Based on the delay-dependent Lyapunov functional method, a new delay-dependent robust H∞ fuzzy controller, which depends on the size of the delays and the derivative of the delays, is presented in term of linear matrix inequalities (LMIs). For all admissible uncertainties and delays, the controller guarantees not only the asymptotic stability of the system but also the prescribed H∞ attenuation level. In addition, the effectiveness of the proposed design method is demonstrated by a numerical example.
Fengjiao Wu
2016-01-01
Full Text Available The robust fuzzy control for fractional-order hydroturbine regulating system is studied in this paper. First, the more practical fractional-order hydroturbine regulating system with uncertain parameters and random disturbances is presented. Then, on the basis of interval matrix theory and fractional-order stability theorem, a fuzzy control method is proposed for fractional-order hydroturbine regulating system, and the stability condition is expressed as a group of linear matrix inequalities. Furthermore, the proposed method has good robustness which can process external random disturbances and uncertain parameters. Finally, the validity and superiority are proved by the numerical simulations.
Hitoshi FURUTA; Ken ISHIBASHI; Koichiro NAKATSU; Shun HOTTA
2008-01-01
The purpose of this research is to propose an early restoration for lifeline systems after earthquake disasters. The previous researches show that the optimization of the restoration schedule by using genetic algorithm (GA) is powerful. However, those are not considering the uncertain environment after earthquake disasters. The circumstances of the damage at devastated areas are very changeable due to the aftershock,fire disaster and bad weather. In addition, the restoring works may delay by unexpected accidents. Therefore,it is necessary to obtain the restoration schedule which has robustness, because the actual restoring works could not progress smoothly under the uncertain environment. GA considering uncertainty (GACU) can treat various uncertainties involved, but it is difficult to obtain the robust schedule. In this study, an attempt is made to develop a decision support system of the optimal restoration scheduling by using the improved GACU.
Group Elevator Peak Scheduling Based on Robust Optimization Model
ZHANG, J.
2013-08-01
Full Text Available Scheduling of Elevator Group Control System (EGCS is a typical combinatorial optimization problem. Uncertain group scheduling under peak traffic flows has become a research focus and difficulty recently. RO (Robust Optimization method is a novel and effective way to deal with uncertain scheduling problem. In this paper, a peak scheduling method based on RO model for multi-elevator system is proposed. The method is immune to the uncertainty of peak traffic flows, optimal scheduling is realized without getting exact numbers of each calling floor's waiting passengers. Specifically, energy-saving oriented multi-objective scheduling price is proposed, RO uncertain peak scheduling model is built to minimize the price. Because RO uncertain model could not be solved directly, RO uncertain model is transformed to RO certain model by elevator scheduling robust counterparts. Because solution space of elevator scheduling is enormous, to solve RO certain model in short time, ant colony solving algorithm for elevator scheduling is proposed. Based on the algorithm, optimal scheduling solutions are found quickly, and group elevators are scheduled according to the solutions. Simulation results show the method could improve scheduling performances effectively in peak pattern. Group elevators' efficient operation is realized by the RO scheduling method.
Robust H∞ control for uncertain stochastic saturating systems with time delays
谢立; 何星; 张卫东; 许晓鹏
2004-01-01
The robust H∞ control problem for uncertain stochastic time-delay systems containing nonlinear actuators is considered. The uncertainties in the systems are assumed to satisfy specific match condition. The time delays exitst in state as well as control input. The new stochastic robust stabilization criterion and a sufficient condition for the existence of stochastic robust stabilizing control law are derived. The delay-independent memoryless robust H∞ controllers are constructed to stabilize the given systems in terms of a group of linear matrix inequalities. A numerical simulation example is presented to show that the proposed approach is valid.
Delay-dependent robust H∞ control for uncertain discrete time-delay fuzzy systems
Gong Cheng; Su Baoku
2009-01-01
The robust H∞ control problem of norm bounded uncertain discrete Takagi-Sugeno (T-S) fuzzy tems with state delay is addressed. First, by constructing an appropriate basis-dependent Lyapunov-Krasovskii function, a new delay-dependent sufficient condition on robust H∞-disturbance attenuation is presented, in which both robust stability and prescribed H∞ performance are guaranteed to be achieved. Then based on the condition, a delay-dependent robust H∞ controller design scheme is developed in term of a convex algorithm. Finally, examples are given to illustrate the effectiveness of the proposed method.
Delay-dependent robust passivity control for uncertain time-delay systems
Li Guifang; Li Huiying; Yang Chengwu
2007-01-01
The robust passivity control problem is addressed for a class of uncertain delayed systems with timevarying delay. The parameter uncertainties are norm-bounded. First, the delay-dependent stability sufficient condition is obtained for the nominal system, and then, based-on the former, the delay-dependent robust passivity criteria is provided and the corresponding controller is designed in terms of linear matrix inequalities. Finally, a numerical example is given to demonstrate the validity of the proposed approach.
Robust predictive control of uncertain intergrating linear systems with input constraints
张良军; 李江; 宋执环; 李平
2002-01-01
This paper presents a two-stage robust model predictive control (RMPC) algorithm named as IRMPC for uncertain linear integrating plants described by a state-space model with input constraints. The global convergence of the result e d closed loop system is guaranteed under mild assumption. The simulation example shows its validity and better performance than conventional Min-Max RMPC strat egies.
Robust Stabilization for Uncertain Control Systems Using Piecewise Quadratic Lyapunov Functions
无
2002-01-01
The sufficient condition based on piecewise quadratic simultaneous Lyapunov functions for robust stabilizationof uncertain control systems via a constant linear state feedback control law is obtained. The objective is to use a robuststability criterion that is less conservative than the usual quadratic stability criterion. Numerical example is given, show-ing the advanteges of the proposed method.
Gorissen, B.L.; Blanc, J.P.C.; den Hertog, D.; Ben-Tal, A.
We propose a new way to derive tractable robust counterparts of a linear program based on the duality between the robust (“pessimistic”) primal problem and its “optimistic” dual. First we obtain a new convex reformulation of the dual problem of a robust linear program, and then show how to construct
Reliable grading robust stabilization for uncertain time-varying systems via dynamic compensator
无
2002-01-01
A new general model for uncertain time-varying parameters and a new measure sensor failure model are presented, and the problems of both grading robust stabilization and reliable grading robust stabilization for such systems are studied. By the Lyapunov stability theory and matrix algebra method, some sufficient criteria for the above two control problems are established in quasi-linear matrix inequalities (Q-LMIS) forms. In view of linear matrix inequality (LMI) approach, a solving procedure for the Q-LMIS problem is proposed. The solvability of the Q-LMIS problem can be improved obviously by adding some LMI constraints to the Q-LMIS. Based on the two Q-LMIS criteria, a grading robust stable control strategy, namely, the controller with different energy is acted on the system with different uncertain parameter range, is presented. The numerical simulating results show that the grading robust stable control strategy for the robust stabilization of uncertain systems has important theoretical and practical significance.
Robust passive filtering for continuous-time polytopic uncertain time-delay systems
LU Ling-ling; DUAN Guang-ren; WU Ai-guo
2008-01-01
To obtain a stable and proper linear filter to make the filtering error system robustly and strictly passive,the problem of full-order robust passive filtering for continuous-time polytopie uncertain time-delay systems was investigated.A criterion for the passivity of time-delay systems was firstly provided in terms of linear matrix inequalities(LMI).Then an LMI sufficient condition for the existence of a robust filter was established and a design procedure was proposed for this type of systems.A numerical example demonstrated the feasibility of the filtering design procedure.
Mohammed Tawfik Hussein
2015-04-01
Full Text Available Uncertainty is inherent property of all real life control systems, and this is due to that there is nothing constant practically; all parameters are going to change under some environmental circumstances, therefore control engineers must not ignore this changing since it can affect the behavior and the performance of the system. In this paper a critical research method for modeling uncertain systems is demonstrated with the utilization of built in robust control Matlab Toolbox®3 functions. Good results were obtained for testing the stability of interval linear time invariant systems. Finally mechanical and electrical uncertain systems were implemented as practical example to validate the uncertainty.
On Robust Stability of a Class of Uncertain Nonlinear Systems with Time-Varying Delay
NIAN Xiao-hong
2002-01-01
The problem of robust stability of a class of uncertain nonlinear dynamical systems with time-delay is considered. Based on the assumption that the nominal system is stable, some sufficient conditions onrobust stability of uncertain nonlinear dynamical systems with time-delay are derived. Some analytical methods and a type of Lyapunov functional are used to investigate such sufficient conditions. The results obtained in this paper are applicable to perturbed time-delay systems with unbounded time-varying delay.Some previous results are improved and a numerical example is given to demonstrate the validity of our results.
Dynamic neural network-based robust observers for uncertain nonlinear systems.
Dinh, H T; Kamalapurkar, R; Bhasin, S; Dixon, W E
2014-12-01
A dynamic neural network (DNN) based robust observer for uncertain nonlinear systems is developed. The observer structure consists of a DNN to estimate the system dynamics on-line, a dynamic filter to estimate the unmeasurable state and a sliding mode feedback term to account for modeling errors and exogenous disturbances. The observed states are proven to asymptotically converge to the system states of high-order uncertain nonlinear systems through Lyapunov-based analysis. Simulations and experiments on a two-link robot manipulator are performed to show the effectiveness of the proposed method in comparison to several other state estimation methods.
Study on Robust Uniform Asymptotical Stability for Uncertain Linear Impulsive Delay Systems
刘斌; 刘新芝; 廖晓昕
2003-01-01
In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in control theory. As a result, many criteria for testing the stability of linear time-delay systems have been proposed. Significant progress has been made in the theory of impulsive systems and impulsive delay systems in recent years. However, the corresponding theory for uncertain impulsive systems and uncertain impulsive delay systems has not been fully developed. In this paper, robust stability criteria are established for uncertain linear delay impulsive systems by using Lyapunov function, Razumikhin techniques and the results obtained. Some examples are given to illustrate our theory.
Robust H∞ control for discrete-time polytopic uncertain systems with linear fractional vertices
Shaosheng ZHOU; James LAM; Shengyuan XU
2004-01-01
The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear matrix inequality (LMI) characterization of the H∞ performance for discrete systems is given by introducing a matrix slack variable which decouples the matrix of a Lyapunov function candidate and the parametric matrices of the system. This feature enables one to derive sufficient conditions for discrete uncertain systems by using parameter-dependent Lyapunov functions with less conservativeness. Based on the result, H∞ performance analysis and controller design are carried out. A numerical example is included to demonstrate the effectiveness of the proposed results.
Liu Ping
2013-01-01
This paper deals with the finite-time stabilization of unified chaotic complex systems with known and unknown parameters.Based on the finite-time stability theory,nonlinear control laws are presented to achieve finite-time chaos control of the determined and uncertain unified chaotic complex systems,respectively.The two controllers are simple,and one of the uncertain unified chaotic complex systems is robust.For the design of a finite-time controller on uncertain unified chaotic complex systems,only some of the unknown parameters need to be bounded.Simulation results for the chaotic complex Lorenz,Lü and Chen systems are presented to validate the design and analysis.
Adaptive robust stabilisation for a class of uncertain nonlinear time-delay dynamical systems
Wu, Hansheng
2013-02-01
The problem of adaptive robust stabilisation is considered for a class of uncertain nonlinear dynamical systems with multiple time-varying delays. It is assumed that the upper bounds of the nonlinear delayed state perturbations are unknown and that the time-varying delays are any non-negative continuous and bounded functions which do not require that their derivatives have to be less than one. In particular, it is only required that the nonlinear uncertainties, which can also include time-varying delays, are bounded in any non-negative nonlinear functions which are not required to be known for the system designer. For such a class of uncertain nonlinear time-delay systems, a new method is presented whereby a class of continuous memoryless adaptive robust state feedback controllers with a rather simpler structure is proposed. It is also shown that the solutions of uncertain nonlinear time-delay systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. Finally, as an application, an uncertain nonlinear time-delay ecosystem with two competing species is given to demonstrate the validity of the results.
Robust control of uncertain dynamic systems a linear state space approach
Yedavalli, Rama K
2014-01-01
This textbook aims to provide a clear understanding of the various tools of analysis and design for robust stability and performance of uncertain dynamic systems. In model-based control design and analysis, mathematical models can never completely represent the “real world” system that is being modeled, and thus it is imperative to incorporate and accommodate a level of uncertainty into the models. This book directly addresses these issues from a deterministic uncertainty viewpoint and focuses on the interval parameter characterization of uncertain systems. Various tools of analysis and design are presented in a consolidated manner. This volume fills a current gap in published works by explicitly addressing the subject of control of dynamic systems from linear state space framework, namely using a time-domain, matrix-theory based approach. This book also: Presents and formulates the robustness problem in a linear state space model framework Illustrates various systems level methodologies with examples and...
Robust admissibility and admissibilisation of uncertain discrete singular time-delay systems
Cui, Yukang; Lam, James; Feng, Zhiguang; Shen, Jun
2016-11-01
This paper is concerned with the characterisation of robust admissibility and admissibilisation for uncertain discrete-time singular system with interval time-varying delay. Considering the norm-bounded uncertainty and the interval time-varying delay, a new comparison model is introduced to transform the original singular system into two connected subsystems. After this transformation, a singular system without uncertainty and delay can be handled by the Lyapunov-Krasovskii functional method. By virtue of the scaled small gain theorem, an admissibility condition of the original singular system is proposed in terms of linear matrix inequalities. Moreover, the problem of robust admissibilisation of uncertain discrete singular time-varying system is also studied by iterative linear matrix inequality algorithm with initial condition optimisation. Several numerical examples are used to illustrate that the results are less conservative than existing ones.
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.
Optimal second order sliding mode control for nonlinear uncertain systems.
Das, Madhulika; Mahanta, Chitralekha
2014-07-01
In this paper, a chattering free optimal second order sliding mode control (OSOSMC) method is proposed to stabilize nonlinear systems affected by uncertainties. The nonlinear optimal control strategy is based on the control Lyapunov function (CLF). For ensuring robustness of the optimal controller in the presence of parametric uncertainty and external disturbances, a sliding mode control scheme is realized by combining an integral and a terminal sliding surface. The resulting second order sliding mode can effectively reduce chattering in the control input. Simulation results confirm the supremacy of the proposed optimal second order sliding mode control over some existing sliding mode controllers in controlling nonlinear systems affected by uncertainty.
CONTINUOUS ROBUST TRACKING CONTROLLERS FOR A CLASS OF UNCERTAIN NONLINEAR DYNAMICAL SYSTEMS
胡剑波; 苏宏业; 柯挺; 褚健; 陈新海
2001-01-01
Robust tracking controller for a class of uncertain nonlinear dynamical systems, which are linearizable by input-output feedback with matching uncertainties, was investigated. In this study, uniform ultimate bound or uniformly asymptotic stability of tracking errors were obtained by different choice of the control gain. A simulation to determine the effectiveness of the proposed approach showed that the control performance was better than that of VSC (Variable Structure Control).
Robust and Active Fault-tolerant Control for a Class of Nonlinear Uncertain Systems
You-Qing Wang; Dong-Hua Zhou; Li-Heng Liu
2006-01-01
A novel integrated design strategy for robust fault diagnosis and fault-tolerant control (FTC) of a class of nonlinear uncertain systems is proposed. The uncertainties considered in this paper are more general than those in other existing works, and faults are described in a new formulation. It is proven that the states of a closed-loop system converge asymptotically to zero even if there are uncertainties and faults in a system. Simulation results on a simple pendulum are presented for illustration.
Robust adaptive control for uncertain systems with discrete and distributed delays
Qing ZHU; Shumin FEI; Tao Li; Tianping ZHANG
2008-01-01
In this paper,a robust adaptive control scheme is proposed for the stabilization of uncertain linear systems with discrete and distributed delays and bounded peturbaturbations.The uncertainty is assumed to be an unknown continuous function with norm-bounded restriction.The perturbation is sector-bounded.Combining with the liner matrix inequality method,neural networks and adaptive control,the control scheme ensures the exponential stability of the closed-loop system for any admissible uncertainty.
Zhengguang WU; Wuneng ZHOU
2008-01-01
This paper investigates the problem of delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays in terms of linear matrix inequality(LMI)approach.Based on a delay-dependent stability condition for the nominal system,a state feedback controller is designed,which guarantees the resultant closedloop system to be robustly stable.An explicit expression for the desired controller is also given by solving a set of matrix inequalities.Some numerical examples are provided to illustrate the less conservativeness of the proposed methods.
A Robust Filter Design for Uncertain Singular Systems with Unreliable Channels
Ching-Min Lee
2011-06-01
Full Text Available This paper considers the problem of robust H_∞ filter design in uncertain discrete-time singular systems with possible missing measurements due to unreliable network transmission channels. The stochastic variable satisfying Bernoulli random binary distribution is introduced to model the missing phenomena and the corresponding filtering error dynamics with delay is then induced. We provide a set of sufficient conditions for the existence of the desired filter, and propose a robust filter design method under a strict linear matrix inequality framework. A numerical example is given to illustrate the effectiveness of the proposed method
Yajun Li
2015-01-01
Full Text Available This paper deals with the robust H∞ filter design problem for a class of uncertain neutral stochastic systems with Markovian jumping parameters and time delay. Based on the Lyapunov-Krasovskii theory and generalized Finsler Lemma, a delay-dependent stability condition is proposed to ensure not only that the filter error system is robustly stochastically stable but also that a prescribed H∞ performance level is satisfied for all admissible uncertainties. All obtained results are expressed in terms of linear matrix inequalities which can be easily solved by MATLAB LMI toolbox. Numerical examples are given to show that the results obtained are both less conservative and less complicated in computation.
无
2011-01-01
In this paper,the robust stability issue of switched uncertain multidelay systems resulting from actuator failures is considered.Based on the average dwell time approach,a set of suitable switching signals is designed by using the total activation time ratio between the stable subsystem and the unstable one.It is first proven that the resulting closed-loop system is robustly exponentially stable for some allowable upper bound of delays if the nominal system with zero delay is exponentially stable under thes...
Robust dissipative filtering for continuous-time polytopic uncertain neutral systems
Duan Guangren; L(u) Lingling; Wu Aiguo
2009-01-01
This article is concerned with the problem of robust dissipative filtering for continuous-time polytopic uncertain neutral systems. The main purpose is to obtain a stable and proper linear filter such that the filtering error system is strictly dissipative. A new criterion for the dissipativity of neutral systems is first provided in terms of linear matrix inequalities (LMI). Then, an LMI sufficient condition for the existence of a robust filter is established and a design procedure is proposed for this type of systems. Two numerical examples are given. One illustrates the less conservativeness of the proposed criterion; the other demonstrates the validity of the filtering design procedure.
Alignment Condition-Based Robust Adaptive Iterative Learning Control of Uncertain Robot System
Guofeng Tong
2014-04-01
Full Text Available This paper proposes an adaptive iterative learning control strategy integrated with saturation-based robust control for uncertain robot system in presence of modelling uncertainties, unknown parameter, and external disturbance under alignment condition. An important merit is that it achieves adaptive switching of gain matrix both in conventional PD-type feedforward control and robust adaptive control in the iteration domain simultaneously. The analysis of convergence of proposed control law is based on Lyapunov's direct method under alignment initial condition. Simulation results demonstrate the faster learning rate and better robust performance with proposed algorithm by comparing with other existing robust controllers. The actual experiment on three-DOF robot manipulator shows its better practical effectiveness.
Robust Stabilization, Robust Performance, and Disturbance Attenuation for Uncertain Linear Systems
1992-01-01
the following Riccati equation: [ - ] B Tp+!I+ 1 CTC+Q=O. (7) Then, a disturbance-attenuation robust- stabilizing control law is given by u(t) = K z(t...disturbance-attenuation robust- stabilizing control law with the attenuation constant 6 is given by u(t) = K x(t), where K = -- BT P with 7> 1/2... stabilizing control law with the attenuation constant 6 is given by u(t) = K z(t), where K = -7 BT P with 7> - 1/2. Furthermore, the state-feedback
Optimal Order Strategy in Uncertain Demands with Free Shipping Option
Qing-Chun Meng
2014-01-01
Full Text Available Free shipping with conditions has become one of the most effective marketing tools; more and more companies especially e-business companies prefer to offer free shipping to buyers whenever their orders exceed the minimum quantity specified by them. But in practice, the demands of buyers are uncertain, which are affected by weather, season, and many other factors. Firstly, we model the centralization ordering problem of retailers who face stochastic demands when suppliers offer free shipping, in which limited distributional information such as known mean, support, and some deviation measures of the random data is needed only. Then, based on the linear decision rule mainly for stochastic programming, we analyze the optimal order strategies of retailers and discuss the approximate solution. Further, we present the core allocation between all retailers via dual and cooperative game theory. The existence of core shows that each retailer is pleased to cooperate with others in the centralization problem. Finally, a numerical example is implemented to discuss how uncertain data and parameters affect the optimal solution.
Ma, Yuechao; Yang, Pingjing; Yan, Yifang; Zhang, Qingling
2017-01-10
This paper investigates the problem of robust observer-based passive control for uncertain singular time-delay system subject to actuator saturation. A polytopic approach is used to describe the saturation behavior. First, by constructing Lyapunov-Krasovskii functional, a less conservative sufficient condition is obtained which guarantees that the closed-loop system is regular, impulse free, stable and robust strictly passive. Then, with this condition, the design method of state feedback controller and the observer are given by solving linear matrix inequalities. In addition, a domain of attraction in which the admissible initial states are ensured to converge asymptotically to the origin is solved as a convex optimization problem. Finally, some simulations are provided to demonstrate the effectiveness and superiority of the proposed method.
Uncertain information fusion with robust adaptive neural networks-fuzzy reasoning
Zhang Yinan; Sun Qingwei; Quan He; Jin Yonggao; Quan Taifan
2006-01-01
In practical multi-sensor information fusion systems,there exists uncertainty about the network structure,active state of sensors,and information itself (including fuzziness,randomness,incompleteness as well as roughness,etc). Hence it requires investigating the problem of uncertain information fusion. Robust learning algorithm which adapts to complex environment and the fuzzy inference algorithm which disposes fuzzy information are explored to solve the problem. Based on the fusion technology of neural networks and fuzzy inference algorithm, a multi-sensor uncertain information fusion system is modeled. Also RANFIS learning algorithm and fusing weight synthesized inference algorithm are developed from the ANFIS algorithm according to the concept of robust neural networks. This fusion system mainly consists of RANFIS confidence estimator, fusing weight synthesized inference knowledge base and weighted fusion section. The simulation result demonstrates that the proposed fusion model and algorithm have the capability of uncertain information fusion, thus is obviously advantageous compared with the conventional Kalman weighted fusion algorithm.
Robust H ∞ control for uncertain Markovian jump systems with mixed delays
R, Saravanakumar; M Syed, Ali
2016-07-01
We scrutinize the problem of robust H ∞ control for a class of Markovian jump uncertain systems with interval time-varying and distributed delays. The Markovian jumping parameters are modeled as a continuous-time finite-state Markov chain. The main aim is to design a delay-dependent robust H ∞ control synthesis which ensures the mean-square asymptotic stability of the equilibrium point. By constructing a suitable Lyapunov-Krasovskii functional (LKF), sufficient conditions for delay-dependent robust H ∞ control criteria are obtained in terms of linear matrix inequalities (LMIs). The advantage of the proposed method is illustrated by numerical examples. The results are also compared with the existing results to show the less conservativeness. Project supported by Department of Science and Technology (DST) under research project No. SR/FTP/MS-039/2011.
Robust Distributed Kalman Filter for Wireless Sensor Networks with Uncertain Communication Channels
Du Yong Kim
2012-01-01
Full Text Available We address a state estimation problem over a large-scale sensor network with uncertain communication channel. Consensus protocol is usually used to adapt a large-scale sensor network. However, when certain parts of communication channels are broken down, the accuracy performance is seriously degraded. Specifically, outliers in the channel or temporal disconnection are avoided via proposed method for the practical implementation of the distributed estimation over large-scale sensor networks. We handle this practical challenge by using adaptive channel status estimator and robust L1-norm Kalman filter in design of the processor of the individual sensor node. Then, they are incorporated into the consensus algorithm in order to achieve the robust distributed state estimation. The robust property of the proposed algorithm enables the sensor network to selectively weight sensors of normal conditions so that the filter can be practically useful.
IMPROVED ROBUST H-INFINITY ESTIMATION FOR UNCERTAIN CONTINUOUS-TIME SYSTEMS
Aiguo WU; Huafeng DONG; Guangren DUAN
2007-01-01
The design of full-order robust estimators is investigated for continuous-time polytopic uncertain systems. The main purpose is to obtain a stable linear estimator such that the estimation error system remains robustly stable with a prescribed H∞ attenuation level. Firstly, a simple alterna- tive proof is given for an improved LMI representation of H∞ performance proposed recently. Based on the performance criterion which keeps the Lyapunov matrix out of the product of the system dynamic matrices, a sufficient condition for the existence of the robust estimator is provided in terms oflinear matrix inequalities. It is shown that the proposed design strategy allows the use of parameter-dependent Lyapunov functions and hence it is less conservative than the earlier results. A numericalexample is employed to illustrate the feasibility and advantage of the proposed design.
Robust H-infinity estimation for continuous-time polytopic uncertain systems
Aiguo WU; Guangren DUAN
2005-01-01
The design of full-order robust H-infinity estimators is investigated for continuous-time polytopic uncertain systems. The main purpose is to obtain a stable and proper linear estimator such that the estimation error system remains robustly stable with a prescribed H-infinity attenuation level. Based on a recently proposed H-infinity performance criterion which exhibits a kind of decoupling between the Lyapunov matrix and the system dynamic matrices, a sufficient condition for the existence of the robust estimator is provided in terms of linear matrix inequalities. It is shown that the proposed design strategy allows the use of parameter-dependent Lyapunov functions and hence it is less conservative than earlier results. A numerical example is employed to illustrate the feasibility and advantage of the proposed design.
Robust Fusion Filtering for Multisensor Time-Varying Uncertain Systems: The Finite Horizon Case
Xiaoliang Feng
2016-01-01
Full Text Available The robust H∞ fusion filtering problem is considered for linear time-varying uncertain systems observed by multiple sensors. A performance index function for this problem is defined as an indefinite quadratic inequality which is solved by the projection method in Krein space. On this basis, a robust centralized finite horizon H∞ fusion filtering algorithm is proposed. However, this centralized fusion method is with poor real time property, as the number of sensors increases. To resolve this difficulty, within the sequential fusion framework, the performance index function is described as a set of quadratic inequalities including an indefinite quadratic inequality. And a sequential robust finite horizon H∞ fusion filtering algorithm is given by solving this quadratic inequality group. Finally, two simulation examples for time-varying/time-invariant multisensor systems are exploited to demonstrate the effectiveness of the proposed methods in the respect of the real time property and filtering accuracy.
Robust reliable control for a class of time-varying uncertain impulsive systems
CHENG Xin-ming; GUI Wei-hua; GAN Zheng-jia
2005-01-01
The problem of robust and reliable control design for linear uncertain impulsive systems with both timevarying norm-bounded parameter uncertainty and actuator failures was studied. The actuators are classified into two groups. One set of actuators susceptible to failures is possible to fail, the other set of actuators robust to failures is assumed never to fail. The outputs of the actuator failures are regarded as zero. The purpose is to design the state feedback controller such that, for all admissible uncertainties as well as actuator failures occurring among a prespecified subset of actuators, the plant remains asymptotically stable. A modified algebraic Riccati equation approach was developed to solve the problem addressed and a robust reliable control law was obtained. An numerical example was also offered to prove the effectiveness of the proposed method.
Robust H∞control for uncertain Markovian jump systems with mixed delays
R Saravanakumar; M Syed Ali‡
2016-01-01
We scrutinize the problem of robust H∞control for a class of Markovian jump uncertain systems with interval time-varying and distributed delays. The Markovian jumping parameters are modeled as a continuous-time finite-state Markov chain. The main aim is to design a delay-dependent robust H∞control synthesis which ensures the mean-square asymptotic stability of the equilibrium point. By constructing a suitable Lyapunov–Krasovskii functional (LKF), sufficient conditions for delay-dependent robust H∞control criteria are obtained in terms of linear matrix inequalities (LMIs). The advantage of the proposed method is illustrated by numerical examples. The results are also compared with the existing results to show the less conservativeness.
Robust state estimation for uncertain linear systems with deterministic input signals
Huabo LIU; Tong ZHOU
2014-01-01
In this paper, we investigate state estimations of a dynamical system in which not only process and measurement noise, but also parameter uncertainties and deterministic input signals are involved. The sensitivity penalization based robust state estimation is extended to uncertain linear systems with deterministic input signals and parametric uncertainties which may nonlinearly affect a state-space plant model. The form of the derived robust estimator is similar to that of the well-known Kalman filter with a comparable computational complexity. Under a few weak assumptions, it is proved that though the derived state estimator is biased, the bound of estimation errors is finite and the covariance matrix of estimation errors is bounded. Numerical simulations show that the obtained robust filter has relatively nice estimation performances.
Robust stability analysis of uncertain discrete-time systems with state delay
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.
Wu, Wei; Jayasuriya, Suhada
2013-03-01
In this article, a control system design methodology for neutrally stable, uncertain, single-input single-output plants under input amplitude saturation is presented. Based on Horowitz's original three degree of freedom design and extensions developed afterwards, this approach concentrates on neutrally stable, higher type, uncertain plants. A three degree of freedom non-interfering loop structure is used for the synthesis, along with the structure of the additional, independent loop transmission around the saturating element proposed for designing the third degree of freedom H(s). Robust stability and performance are established. The circle criterion, the describing function and non-overshooting conditions are utilised to obtain design constraints. Finally, all these design constraints are expressed in frequency domain bounds and synthesis follows from loop shaping methods such as quantitative feedback theory.
A new smooth robust control design for uncertain nonlinear systems with non-vanishing disturbances
Xian, Bin; Zhang, Yao
2016-06-01
In this paper, we consider the control problem for a general class of nonlinear system subjected to uncertain dynamics and non-varnishing disturbances. A smooth nonlinear control algorithm is presented to tackle these uncertainties and disturbances. The proposed control design employs the integral of a nonlinear sigmoid function to compensate the uncertain dynamics, and achieve a uniformly semi-global practical asymptotic stable tracking control of the system outputs. A novel Lyapunov-based stability analysis is employed to prove the convergence of the tracking errors and the stability of the closed-loop system. Numerical simulation results on a two-link robot manipulator are presented to illustrate the performance of the proposed control algorithm comparing with the layer-boundary sliding mode controller and the robust of integration of sign of error control design. Furthermore, real-time experiment results for the attitude control of a quadrotor helicopter are also included to confirm the effectiveness of the proposed algorithm.
Robust Fault Detection of Linear Uncertain Time-Delay Systems Using Unknown Input Observers
Saeed Ahmadizadeh
2013-01-01
Full Text Available This paper deals with the problem of fault detection for linear uncertain time-delay systems. The proposed method for Luenberger observers is developed for unknown input observers (UIOs, and a novel procedure for the design of residual based on UIOs is presented. The design procedure is carried out based on the model matching approach which minimizes the difference between generated residuals by the optimal observer and those by the designed observer in the presence of uncertainties. The optimal observer is designed for the ideal system and works so that the fault effect is maximized while the exogenous disturbances and noise effects are minimized. This observer can give disturbance decoupling in the presence of noise and uncertainties for linear uncertain time-delay systems. The developed method is applied to a numerical example, and the simulation results show that the proposed approach is able to detect faults reliably in the presence of modeling errors, disturbances, and noise.
Robust control of uncertain time delay system: a novel sliding mode control design via LMI
Qu Shaocheng; Wang Yongji
2006-01-01
The sliding mode control problem (SMC) is studied for a class of uncertain delay system in the presence of both parameter uncertainties and external disturbances. A novel virtual feedback control method is presented. Based on Lyapunov theory, sufficient conditions for design of the robust sliding mode plane are derived. Sliding mode controller based on reaching law concept is developed, which is to ensure system trajectories from any initial conditions asymptotically convergent to sliding mode plane. The global asymptotically stability of the closed-loop system is guaranteed. A numerical example with simulation results is given to illustrate the effectiveness of the methodology.
Wang, Tianbo; Zhou, Wuneng; Zhao, Shouwei; Yu, Weiqin
2014-03-01
In this paper, the robust exponential synchronization problem for a class of uncertain delayed master-slave dynamical system is investigated by using the adaptive control method. Different from some existing master-slave models, the considered master-slave system includes bounded unmodeled dynamics. In order to compensate the effect of unmodeled dynamics and effectively achieve synchronization, a novel adaptive controller with simple updated laws is proposed. Moreover, the results are given in terms of LMIs, which can be easily solved by LMI Toolbox in Matlab. A numerical example is given to illustrate the effectiveness of the method.
Ahmadi, Mohamadreza; Mojallali, Hamed; Wisniewski, Rafal
2012-01-01
This paper addresses the robust stability and control problem of uncertain piecewise linear switched systems where, instead of the conventional Carathe ́odory solutions, we allow for Filippov solutions. In other words, in contrast to the previous studies, solutions with infinite switching in finite...... time along the facets and on faces of arbitrary dimensions are also taken into account. Firstly, based on earlier results, the stability problem of piecewise linear systems with Filippov solutions is translated into a number of linear matrix inequality feasibility tests. Subsequently, a set of matrix...
Robust reliable H∞ control for a class of uncertain time-delay systems
FU Yan-ming; ZHANG Bo; DUAN Guang-ren
2009-01-01
This paper deals with the problem of robust reliable H∞ control for a class of uncertain nonlinear systems with time-varying delays and actuator failures. The uncertainties in the system are norm-bounded and time varying. Based on Lyapunov methods, a sufficient condition on quadratic stabilization independent of delay is obtained. With the help of LMIs (linear matrix inequalities) approaches, a hnear state feedback controller is designed to quadratically stabilize the given systems with a H∞ performance constraint of disturbance attenuation for all admissible uncertainties and all actuator failures occurred within the prespecified subset. A numerical example is given to demonstrate the effect of the proposed design approach.
Globally robust nonlinear PID controllers for robot manipulators with an uncertain Jacobian matrix
Chunqing HUANG; Songjiao SHI
2004-01-01
Based on a continuous piecewise-differentiable increasing functions vector, a class of robust nonlinear PID(RN-PID) controllers is proposed for setpoint control with uncertain Jacobian matrix. Globally asymptotic stability is guaranteed and only position and joint velocity measurements are required. And stability problem arising from integral action and integrator windup, are consequendy resolved. Furthermore, RN-PID controllers can be of effective alternative for anti-integrator-wind-up,the control performance would not be very bad in the presence of rough parameter tuning.
Design of H(infinity) robust fault detection filter for linear uncertain time-delay systems.
Bai, Leishi; Tian, Zuohua; Shi, Songjiao
2006-10-01
In this paper, the robust fault detection filter design problem for linear time-delay systems with both unknown inputs and parameter uncertainties is studied. Using a multiobjective optimization technique, a new performance index is introduced, which takes into account the robustness of the fault detection filter against disturbances and sensitivity to faults simultaneously. The reference residual model is then designed based on this performance index to formulate the robust fault detection filter design problem as an H(infinity) model-matching problem. By applying robust H(infinity) optimization control technique, the existence condition of the robust fault detection filter for linear time-delay systems with both unknown inputs and parameter uncertainties is presented in terms of linear matrix inequality formulation, independently of time delay. In order to detect the fault, an adaptive threshold which depends on the inputs is finally determined. An illustrative design example is used to demonstrate the validity of the proposed approach.
Robust H∞ Control of Uncertain T-S Fuzzy Time-Delay System: A Delay Decomposition Approach
Cheng Gong; Chunsong Han
2013-01-01
This paper is concerned with the problem of robust H∞ control for a class of uncertain time-delay fuzzy systems with norm-bounded parameter uncertainties. By utilizing the instrumental idea of delay decomposition, the decomposed Lyapunov-Krasovskii functional is introduced to uncertain T-S fuzzy system, and some delay-dependent conditions for the existence of robust controller are formulated in the form of linear matrix inequalities (LMIs). When these LMIs are feasible, a controller is presen...
Robust, Optimal Water Infrastructure Planning Under Deep Uncertainty Using Metamodels
Maier, H. R.; Beh, E. H. Y.; Zheng, F.; Dandy, G. C.; Kapelan, Z.
2015-12-01
Optimal long-term planning plays an important role in many water infrastructure problems. However, this task is complicated by deep uncertainty about future conditions, such as the impact of population dynamics and climate change. One way to deal with this uncertainty is by means of robustness, which aims to ensure that water infrastructure performs adequately under a range of plausible future conditions. However, as robustness calculations require computationally expensive system models to be run for a large number of scenarios, it is generally computationally intractable to include robustness as an objective in the development of optimal long-term infrastructure plans. In order to overcome this shortcoming, an approach is developed that uses metamodels instead of computationally expensive simulation models in robustness calculations. The approach is demonstrated for the optimal sequencing of water supply augmentation options for the southern portion of the water supply for Adelaide, South Australia. A 100-year planning horizon is subdivided into ten equal decision stages for the purpose of sequencing various water supply augmentation options, including desalination, stormwater harvesting and household rainwater tanks. The objectives include the minimization of average present value of supply augmentation costs, the minimization of average present value of greenhouse gas emissions and the maximization of supply robustness. The uncertain variables are rainfall, per capita water consumption and population. Decision variables are the implementation stages of the different water supply augmentation options. Artificial neural networks are used as metamodels to enable all objectives to be calculated in a computationally efficient manner at each of the decision stages. The results illustrate the importance of identifying optimal staged solutions to ensure robustness and sustainability of water supply into an uncertain long-term future.
Modelling Robust Design Problems via Conic Optimization
Chaerani, D.
2006-01-01
This thesis deals with optimization problems with uncertain data. Uncertainty here means that the data is not known exactly at the time when its solution has to be determined. In many models the uncertainty is ignored and a representative nominal value of the data is used. The uncertainty may be due
Robust H-infinity filtering on uncertain systems under sampled measurements
Ping SUN; Yuanwei JING
2006-01-01
This paper is concerned with the problem of robust H-infinity filtering on uncertain systems under sampled measurements, both continuous disturbance and discrete disturbance are considered in the systems. The parameter uncertainty is assumed to be time-varying norm-bounded. The aim is to design an asymptotically stable filter, using the locally sampled measurements, which ensures both the robust asymptotic stability and a prescribed level of H-infinity performance for the filtering error dynamics for all admissible uncertainties. The derivation process is simplified by introducing auxiliary systems and the sufficient condition for the existence of such a filter is proposed. During the study, the main results were expressed as LMIs by employing various matrix techniques. Using LMI toolbox of Matlab software, it is very convenient to obtain the appropriate filter. Finally, a numerical example shows that the method is effective and feasible.
Robust H∞ Filtering for a Class of Uncertain Markovian Jump Systems with Time Delays
Yi Yang
2013-01-01
Full Text Available This paper studies the problem of robust H∞ filtering for a class of uncertain time-delay systems with Markovian jumping parameters. The system under consideration is subject to norm-bounded time-varying parameter uncertainties. The problem to be addressed is the design of a Markovian jump filter such that the filter error dynamics are stochastically stable and a prescribed bound on the ℒ2-induced gain from the noise signals to the filter error is guaranteed for all admissible uncertainties. A sufficient condition for the existence of the desired robust H∞ filter is given in terms of two sets of coupled algebraic Riccati inequalities. When these algebraic Riccati inequalities are feasible, the expression of a desired H∞ filter is also presented. Finally, an illustrative numerical example is provided.
An LMI approach to robust H-infinity control for uncertain singular time-delay systems
Xiaofu JI; Hongye SU; Jian CHU
2006-01-01
The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time-delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities (LMIs) involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method,
Yuefei Wu
2014-01-01
Full Text Available An adaptive robust fault tolerant control approach is proposed for a class of uncertain nonlinear systems with unknown signs of high-frequency gain and unmeasured states. In the recursive design, neural networks are employed to approximate the unknown nonlinear functions, K-filters are designed to estimate the unmeasured states, and a dynamical signal and Nussbaum gain functions are introduced to handle the unknown sign of the virtual control direction. By incorporating the switching function σ algorithm, the adaptive backstepping scheme developed in this paper does not require the real value of the actuator failure. It is mathematically proved that the proposed adaptive robust fault tolerant control approach can guarantee that all the signals of the closed-loop system are bounded, and the output converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by the simulation examples.
Robust PID tuning strategy for uncertain plants based on the Kharitonov theorem
Huang; Wang
2000-01-01
In this paper, the Kharitonov theorem for interval plants is exploited for the purpose of synthesizing a stabilizing controller. The aim here is to develop a controller to simultaneously stabilize the four Kharitonov-defined vortex polynomials. Different from the prevailing works, the controller is designed systematically and graphically through the search of a non-conservative Kharitonov region in the controller coefficient parameter plane. The region characterizes all stabilizing PID controllers that stabilize an uncertain plant. Thus the relationship between the Kharitonov region and the stabilizing controller parameters is manifest. Extensively, to further guarantee the system with certain robust safety margins, a virtual gain phase margin tester compensator is added. Stability analysis is carried out. The control system is proved to maintain robustness at least to the pre-specified margins. The synthesized controller with coefficients selected from the obtained non-conservative Kharitonov region can stabilize the concerned uncertain plants and fulfill system specifications in terms of gain margins and phase margins.
Efficient reanalysis techniques for robust topology optimization
Amir, Oded; Sigmund, Ole; Lazarov, Boyan Stefanov
2012-01-01
efficient robust topology optimization procedures based on reanalysis techniques. The approach is demonstrated on two compliant mechanism design problems where robust design is achieved by employing either a worst case formulation or a stochastic formulation. It is shown that the time spent on finite......The article focuses on the reduction of the computational effort involved in robust topology optimization procedures. The performance of structures designed by means of topology optimization may be seriously degraded due to fabrication errors. Robust formulations of the optimization problem were...... shown to yield optimized designs that are tolerant with respect to such manufacturing uncertainties. The main drawback of such procedures is the added computational cost associated with the need to evaluate a set of designs by performing multiple finite element analyses. In this article, we propose...
Nguyen, Nhan
2013-01-01
This paper presents the optimal control modification for linear uncertain plants. The Lyapunov analysis shows that the modification parameter has a limiting value depending on the nature of the uncertainty. The optimal control modification exhibits a linear asymptotic property that enables it to be analyzed in a linear time invariant framework for linear uncertain plants. The linear asymptotic property shows that the closed-loop plants in the limit possess a scaled input-output mapping. Using this property, we can derive an analytical closed-loop transfer function in the limit as the adaptive gain tends to infinity. The paper revisits the Rohrs counterexample problem that illustrates the nature of non-robustness of model-reference adaptive control in the presence of unmodeled dynamics. An analytical approach is developed to compute exactly the modification parameter for the optimal control modification that stabilizes the plant in the Rohrs counterexample. The linear asymptotic property is also used to address output feedback adaptive control for non-minimum phase plants with a relative degree 1.
Dayan Sun
2017-01-01
Full Text Available Because wind power spillage is barely considered, the existing robust unit commitment cannot accurately analyze the impacts of wind power accommodation on on/off schedules and spinning reserve requirements of conventional generators and cannot consider the network security limits. In this regard, a novel double-level robust security-constrained unit commitment formulation with optimizable interval of uncertain wind power output is firstly proposed in this paper to obtain allowable interval solutions for wind power generation and provide the optimal schedules for conventional generators to cope with the uncertainty in wind power generation. The proposed double-level model is difficult to be solved because of the invalid dual transform in solution process caused by the coupling relation between the discrete and continuous variables. Therefore, a two-stage iterative solution method based on Benders Decomposition is also presented. The proposed double-level model is transformed into a single-level and two-stage robust interval unit commitment model by eliminating the coupling relation, and then this two-stage model can be solved by Benders Decomposition iteratively. Simulation studies on a modified IEEE 26-generator reliability test system connected to a wind farm are conducted to verify the effectiveness and advantages of the proposed model and solution method.
Robust Collaborative Optimization Method Based on Dual-response Surface
WANG Wei; FAN Wenhui; CHANG Tianqing; YUAN Yuming
2009-01-01
A novel method for robust collaborative design of complex products based on dual-response surface (DRS-RCO) is proposed to solve multidisciplinary design optimization (MDO) problems under uncertainty. Collaborative optimization (CO) which decomposes the whole system into a double-level nonlinear optimization problem is widely Accepted as an efficient method to solve MDO problems. In order to improve the quality of complex product in design process, robust collaborative optimization (RCO) is developed to solve those problems under uncertain conditions. RCO does opfmiTation on the linear sum of mean and standard deviation of objective function and gets an optimal solution with high robustnmess. Response surfaces method is an important way to do approximation in robust design. DRS-RCO is an improved RCO method in which dual-response surface replaces system uncertainty analysis module of CO. The dual-response surface is the approximate model of mean and standard deviation of objective function respectively. In DRS-RCO, All the information of subsystems is included in dual-response surfaces. As an additional item, the standard deviation of objective function is added to the subsystem optimization. This item guarantee both the mean and standard deviation of this subsystem is reaching the minima at the same time. Finally, a test problem with two coupled subsystems is conducted to verify the feasibility and effectiveness of DRS-RCO.
Less Conservative Optimal Robust Control of a 3-DOF Helicopter
L. F. S. Buzachero
2015-01-01
Full Text Available This work proposes an improved technique for design and optimization of robust controllers norm for uncertain linear systems, with state feedback, including the possibility of time-varying the uncertainty. The synthesis techniques used are based on LMIs (linear matrix inequalities formulated on the basis of Lyapunov’s stability theory, using Finsler’s lemma. The design has used the addition of the decay rate restriction, including a parameter γ in the LMIs, responsible for decreasing the settling time of the feedback system. Qualitative and quantitative comparisons were made between methods of synthesis and optimization of the robust controllers norm, seeking alternatives with lower cost and better performance that meet the design restrictions. A practical application illustrates the efficiency of the proposed method with a failure purposely inserted in the system.
A first-order Lyapunov robustness method for linear systems with uncertain parameters
Leal, M. A.; Gibson, J. S.
1990-01-01
A method for stability-robustness analysis based on a quadratic Liapunov function that varies linearly with uncertainty parameters is derived. Linear time-invariant systems with structured uncertainties are discussed. The Liapunov function is optimized numerically to maximize the robustness region in parameter space. Numerical results are given for four examples in which the first-order method is compared to previous Liapunov methods. While the zero-order method is slightly better than the first-order method for one example, the first-order method is clearly superior in the other three (more realistic) examples. The first-order method is especially superior for the active control of flexible structures, where robustness with respect to (1) unmodeled coupling between modeled modes and (2) unmodeled modes is important. For such applications, the first-order method is much better at detecting the increased robustness associated with increased separation between frequencies.
A first-order Lyapunov robustness method for linear systems with uncertain parameters
Leal, M. A.; Gibson, J. S.
1990-01-01
A method for stability-robustness analysis based on a quadratic Liapunov function that varies linearly with uncertainty parameters is derived. Linear time-invariant systems with structured uncertainties are discussed. The Liapunov function is optimized numerically to maximize the robustness region in parameter space. Numerical results are given for four examples in which the first-order method is compared to previous Liapunov methods. While the zero-order method is slightly better than the first-order method for one example, the first-order method is clearly superior in the other three (more realistic) examples. The first-order method is especially superior for the active control of flexible structures, where robustness with respect to (1) unmodeled coupling between modeled modes and (2) unmodeled modes is important. For such applications, the first-order method is much better at detecting the increased robustness associated with increased separation between frequencies.
Huaicheng YAN; Xinhan HUANG; Min WANG
2007-01-01
In this paper, delay-dependent robust stability for a class of uncertain networked control systems (NCSs)with multiple state time-delays is investigated. Modeling of multi-input and multi-output (MIMO) NCSs with networkinduced delays and uncertainties through new methods are proposed. Some new stability criteria in terms of LMIs are derived by using Lyapunov stability theory combined with linear matrix inequalities (LMIs) techniques. We analyze the delay-dependent asymptotic stability and obtain maximum allowable delay bound (MADB) for the NCSs with the proposed methods. Compared with the reported results, the proposed results obtain a much less conservative MADB which are more general. Numerical example and simulation is used to illustrate the effectiveness of the proposed methods.
A Robust Output-Feedback Controller for a Class of Uncertain Nonlinear Systems
LIU Xiao-hua; WANG Xiu-hong; FEN En-min
2002-01-01
A robust output-feedback controller is designed by using observer plus backstepping procedure to solve the tracking problems of a class of nonlinear uncertain systems. To make the design procedure and to generate the normalization signal and a group of positive nonlinear functions used in the nonlinear damping terms are all chosen properly. The assumption made on the reference signals is much weaker than existing schemes, therefore the designed controller can be applied to track much broader classes of reference signals.The global boundness of all closed-loop signals can be guaranteed and the output tracking error can be made as small as possible if the design constants are chosen large enough.
Robust passive control for a class of uncertain neutral systems based on sliding mode observer.
Liu, Zhen; Zhao, Lin; Kao, Yonggui; Gao, Cunchen
2017-01-01
The passivity-based sliding mode control (SMC) problem for a class of uncertain neutral systems with unmeasured states is investigated. Firstly, a particular non-fragile state observer is designed to generate the estimations of the system states, based upon which a novel integral-type sliding surface function is established for the control process. Secondly, a new sufficient condition for robust asymptotic stability and passivity of the resultant sliding mode dynamics (SMDs) is obtained in terms of linear matrix inequalities (LMIs). Thirdly, the finite-time reachability of the predesigned sliding surface is ensured by resorting to a novel adaptive SMC law. Finally, the validity and superiority of the scheme are justified via several examples.
Observer-based robust stabilization for uncertain systems with unknown time-varying delay
Peigang JIANG; Chunwen LI
2004-01-01
This paper focuses on the problem of robust stabiiization for a class of linear systems with uncertain parameters and time varying delays in states. The parameter uncertainty is continuous, time varying, and norm-bounded. The state delay is unknown and time varying. The states of the system are not all measurable and an observer is constructed to estimate the states. If a linear matrix inequality (LMI) is solvable, the gains of the controller and observer can be obtained from the solution of the LMI.The observer and controller are dependent on the size of time delay and on the size of delay derivative. Finally, an example is given to illustrate the effectiveness of the proposed control method.
Robust dissipative filtering for continuous-time polytopic uncertain time-delay systems
LV Ling-ling; DUAN Guang-ren; WU Ai-guo
2010-01-01
This paper focuses on the problem of dissipative filtering for linear continuous-time polytopic uncertain time-delay systems.To obtain a stable and proper linear filter such that the filtering error system is strictly dissipative for all admissible uncertainties,a new dissipativity criterion which realizes separation between the Lyapunov matrices and the system dynamic matrices is firstly provided in terms of linear matrix inequalities (LMI).Then an LMI sufficient condition for the existence of a robust filter is established and a design procedure is proposed for this type of systems.One numerical example demonstrates less conservativeness of the proposed criterion,the other numerical example illustrates the validity of the proposed filter design.
Robust Hinf control of uncertain switched systems defined on polyhedral sets with Filippov solutions
Ahmadi, Mohamadreza; Mojallali, Hamed; Wisniewski, Rafal
2012-01-01
This paper considers the control problem of a class of uncertain switched systems defined on polyhedral sets known as piecewise linear systems where, instead of the conventional Carathe ́odory solutions, Filippov solutions are studied. In other words, in contrast to the previous studies, solutions...... with infinite switching in finite time along the facets and on faces of arbitrary dimensions are also taken into account. Firstly, established upon previous studies, a set of linear matrix inequalities are brought forward which determines the asymptotic stability of piecewise linear systems with Filippov...... solutions. Subsequently, bilinear matrix inequality conditions for synthesizing a robust controller with a guaranteed Hinf performance are presented. Furthermore, these results has been generalized to the case of piecewise affine systems. Finally, a V–K iteration algorithm is proposed to deal...
Robust H-infinity fault-tolerant control for uncertain descriptor systems by dynamical compensators
Bing LIANG; Guangren DUAN
2004-01-01
The problem of robust H-infinity fault-tolerant control against sensor failures for a class of uncertain descriptor systems via dynamical compensators is considered.Based on H-infinity theory in descriptor systems,a sufficient condition for the existence of dynamical compensators with H-infinity fault-tolerant function is derived and expressions for the gain matrices in the compensators are presented.The dynamical compensator guarantees that the resultant colsed-loop system is admissible;furthermore,it maintains certain H-infinity norm performance in the normal condition as well as in the event of sensor failures and parameter uncertainties.A numerical example shows the effect of the proposed method.
Finite-Time Control for Robust Tracking Consensus in MASs With an Uncertain Leader.
Lu, Xiaoqing; Wang, Yaonan; Yu, Xinghuo; Lai, Jingang
2016-03-31
This paper investigates the finite-time control for robust tracking consensus problems of multiagent systems with an uncertain leader for situations where the state of the considered active leader may not be measured and the directed network topology is time-varying. Based on the neighbor-based state-estimation rule and a new Lyapunov stability analysis method, a continuous and nonlinear distributed tracking protocol using only relative position information is designed, under which each agent can follow the leader in finite time if the input (acceleration) of the leader is known, and the tracking errors can converge to a bounded region in finite time if the input of the leader is unknown. In particular, a special continuous distributed tracking protocol with bounded control inputs is introduced to track the active leader in finite time. Numerical simulations are also given to illustrate the effectiveness of the theoretic results.
Robust adaptive neural control of uncertain pure-feedback nonlinear systems
Sun, Gang; Wang, Dan; Peng, Zhouhua; Wang, Hao; Lan, Weiyao; Wang, Mingxin
2013-05-01
In this paper, a robust adaptive neural control design approach is presented for a class of uncertain pure-feedback nonlinear systems. To reduce the complexity of the both controller structure and computation, only one neural network is used to approximate the lumped unknown function of the system at the last step of the recursive design process. By this approach, the complexity growing problem existing in conventional methods can be eliminated completely. Stability analysis shows that all the closed-loop system signals are uniformly ultimately bounded, and the steady state tracking error can be made arbitrarily small by appropriately choosing control parameters. Simulation results demonstrate the effectiveness and merits of the proposed approach.
Wang Jun-Wei; Zeng Cai-Bin
2012-01-01
This paper is concerned with the problem of robust H∞ control for a novel class of uncertain linear continuous-time systems with heterogeneous time-varying state/input delays and norm-bounded parameter uncertainties.The objective is to design a static output feedback controller such that the closed-loop system is asymptotically stable while satisfying a prescribed H∞ performance level for all admissible uncertainties.By constructing an appropriate Lyapunov-Krasvskii functional,a delay-dependent stability criterion of the closed-loop system is presented with the help of the Jensen integral inequality.From the derived criterion,the solutions to the problem are formulated in terms of linear matrix inequalities and hence are tractable numerically.A simulation example is given to illustrate the effectiveness of the proposed design method.
Riddhi Singh
2015-09-01
Full Text Available Managing ecosystems with deeply uncertain threshold responses and multiple decision makers poses nontrivial decision analytical challenges. The problem is imbued with deep uncertainties because decision makers do not know or cannot converge on a single probability density function for each key parameter, a perfect model structure, or a single adequate objective. The existing literature on managing multistate ecosystems has generally followed a normative decision-making approach based on expected utility maximization (MEU. This approach has simple and intuitive axiomatic foundations, but faces at least two limitations. First, a prespecified utility function is often unable to capture the preferences of diverse decision makers. Second, decision makers' preferences depart from MEU in the presence of deep uncertainty. Here, we introduce a framework that allows decision makers to pose multiple objectives, explore the trade-offs between potentially conflicting preferences of diverse decision makers, and to identify strategies that are robust to deep uncertainties. The framework, referred to as many-objective robust decision making (MORDM, employs multiobjective evolutionary search to identify trade-offs between strategies, re-evaluates their performance under deep uncertainty, and uses interactive visual analytics to support the selection of robust management strategies. We demonstrate MORDM on a stylized decision problem posed by the management of a lake in which surpassing a pollution threshold causes eutrophication. Our results illustrate how framing the lake problem in terms of MEU can fail to represent key trade-offs between phosphorus levels in the lake and expected economic benefits. Moreover, the MEU strategy deteriorates severely in performance for all objectives under deep uncertainties. Alternatively, the MORDM framework enables the discovery of strategies that balance multiple preferences and perform well under deep uncertainty. This
Mirzaei, Mahmood; Poulsen, Niels Kjølstad; Niemann, Hans Henrik
2012-01-01
Robust model predictive control (RMPC) of a class of nonlinear systems is considered in this paper. We will use Linear Parameter Varying (LPV) model of the nonlinear system. By taking the advantage of having future values of the scheduling variable, we will simplify state prediction. Because...... of the special structure of the problem, uncertainty is only in the B matrix (gain) of the state space model. Therefore by taking advantage of this structure, we formulate a tractable minimax optimization problem to solve robust model predictive control problem. Wind turbine is chosen as the case study and we...
Robust topology optimization accounting for geometric imperfections
Schevenels, M.; Jansen, M.; Lombaert, Geert
2013-01-01
performance. As a consequence, the actual structure may be far from optimal. In this paper, a robust approach to topology optimization is presented, taking into account two types of geometric imperfections: variations of (1) the crosssections and (2) the locations of structural elements. The first type...... of imperfections) and a vertical load carrying system (for the second type). © 2013 Taylor & Francis Group, London....
Reed, P. M.
2013-12-01
Water resources planning and management has always required the consideration of uncertainties and the associated system vulnerabilities that they may cause. Despite the long legacy of these issues, our decision support frameworks that have dominated the literature over the past 50 years have struggled with the strongly multiobjective and deeply uncertain nature of water resources systems. The term deep uncertainty (or Knightian uncertainty) refers to factors in planning that strongly shape system risks that maybe unknown and even if known there is a strong lack of consensus on their likelihoods over decadal planning horizons (population growth, financial stability, valuation of resources, ecosystem requirements, evolving water institutions, regulations, etc). In this presentation, I will propose and demonstrate the many-objective robust decision making (MORDM) framework for water resources management under deep uncertainty. The MORDM framework will be demonstrated using an urban water portfolio management test case. In the test case, a city in the Lower Rio Grande Valley managing population and drought pressures must cost effectively maintain the reliability of its water supply by blending permanent rights to reservoir inflows with alternative strategies for purchasing water within the region's water market. The case study illustrates the significant potential pitfalls in the classic Cost-Reliability conception of the problem. Moreover, the proposed MORDM framework exploits recent advances in multiobjective search, visualization, and sensitivity analysis to better expose these pitfalls en route to identifying highly robust water planning alternatives.
LMI-based robust iterative learning controller design for discrete linear uncertain systems
Jianming XU; Mingxuan SUN; Li YU
2005-01-01
This paper addresses the design problem of robust iterative learning controllers for a class of linear discrete-time systems with norm-bounded parameter uncertainties.An iterative learning algorithm with current cycle feedback is proposed to achieve both robust convergence and robust stability.The synthesis problem of the proposed iterative learning control (ILC) system is reformulated as a γ-suboptimal H-infinity control problem via the linear fractional transformation (LFT).A sufficient condition for the convergence of the ILC algorithm is presented in terms of linear matrix inequalities (LMIs).Furthermore,the linear transfer operators of the ILC algorithm with high convergence speed are obtained by using existing convex optimization techniques.The simulation results demonstrate the effectiveness of the proposed method.
Simplex sliding mode control for nonlinear uncertain systems via chaos optimization
Lu, Zhao; Shieh, Leang-San; Chen, Guanrong; Coleman, Norman P
2005-02-01
As an emerging effective approach to nonlinear robust control, simplex sliding mode control demonstrates some attractive features not possessed by the conventional sliding mode control method, from both theoretical and practical points of view. However, no systematic approach is currently available for computing the simplex control vectors in nonlinear sliding mode control. In this paper, chaos-based optimization is exploited so as to develop a systematic approach to seeking the simplex control vectors; particularly, the flexibility of simplex control is enhanced by making the simplex control vectors dependent on the Euclidean norm of the sliding vector rather than being constant, which result in both reduction of the chattering and speedup of the convergence. Computer simulation on a nonlinear uncertain system is given to illustrate the effectiveness of the proposed control method.
Robust Quantum Error Correction via Convex Optimization
Kosut, R L; Lidar, D A
2007-01-01
Quantum error correction procedures have traditionally been developed for specific error models, and are not robust against uncertainty in the errors. Using a semidefinite program optimization approach we find high fidelity quantum error correction procedures which present robust encoding and recovery effective against significant uncertainty in the error system. We present numerical examples for 3, 5, and 7-qubit codes. Our approach requires as input a description of the error channel, which can be provided via quantum process tomography.
Robust Structured Control Design via LMI Optimization
Adegas, Fabiano Daher; Stoustrup, Jakob
2011-01-01
This paper presents a new procedure for discrete-time robust structured control design. Parameter-dependent nonconvex conditions for stabilizable and induced L2-norm performance controllers are solved by an iterative linear matrix inequalities (LMI) optimization. A wide class of controller...... structures including decentralized of any order, ﬁxed-order dynamic output feedback, static output feedback can be designed robust to polytopic uncertainties. Stability is proven by a parameter-dependent Lyapunov function. Numerical examples on robust stability margins shows that the proposed procedure can...
Wu, Hansheng
2016-09-01
The problem of decentralised robust stabilisation is considered for a class of uncertain large-scale time-delay interconnected dynamical systems. In the paper, the upper bounds of delayed state perturbations, uncertainties, interconnection terms, and external disturbances are assumed to be completely unknown, and the delays are assumed to be any non-negative constants. For such a class of uncertain large-scale time-delay interconnected systems, a new method is presented whereby a class of adaptation-free decentralised local robust state feedback controllers can be constructed. In addition, it is also shown that the solutions of uncertain large-scale time-delay interconnected systems can be guaranteed to be uniformly ultimately bounded. Finally, as an application to the practical mechanical systems, some simulations of a numerical example are provided to demonstrate the validity of the theoretical results.
Robustizing Circuit Optimization using Huber Functions
Bandler, John W.; Biernacki, Radek M.; Chen, Steve H.
1993-01-01
The authors introduce a novel approach to 'robustizing' microwave circuit optimization using Huber functions, both two-sided and one-sided. They compare Huber optimization with l/sub 1/, l/sub 2/, and minimax methods in the presence of faults, large and small measurement errors, bad starting points......, and statistical uncertainties. They demonstrate FET statistical modeling, multiplexer optimization, analog fault location, and data fitting. They extend the Huber concept by introducing a 'one-sided' Huber function for large-scale optimization. For large-scale problems, the designer often attempts, by intuition...
Huber Optimization of Circuits: A Robust Approach
Bandler, J. W.; Biernacki, R.; Chen, S.
1993-01-01
The authors introduce an approach to robust circuit optimization using Huber functions, both two-sided and one-sided. They compare Huber optimization with l/sub 1/, l/sub 2/, and minimax methods in the presence of faults, large and small measurement errors, bad starting points, and statistical...... uncertainties. They demonstrate FET statistical modeling, multiplexer optimization, analog fault location, and data fitting. They extend the Huber concept by introducing a one-sided Huber function for large-scale optimization. For large-scale problems, the designer often attempts, by intuition, a preliminary...
Huber Optimization of Circuits: A Robust Approach
Bandler, J. W.; Biernacki, R.; Chen, S.;
1993-01-01
The authors introduce an approach to robust circuit optimization using Huber functions, both two-sided and one-sided. They compare Huber optimization with l/sub 1/, l/sub 2/, and minimax methods in the presence of faults, large and small measurement errors, bad starting points, and statistical...... uncertainties. They demonstrate FET statistical modeling, multiplexer optimization, analog fault location, and data fitting. They extend the Huber concept by introducing a one-sided Huber function for large-scale optimization. For large-scale problems, the designer often attempts, by intuition, a preliminary...
Hao, Li-Ying; Yang, Guang-Hong
2013-09-01
This paper is concerned with the problem of robust fault-tolerant compensation control problem for uncertain linear systems subject to both state and input signal quantization. By incorporating novel matrix full-rank factorization technique with sliding surface design successfully, the total failure of certain actuators can be coped with, under a special actuator redundancy assumption. In order to compensate for quantization errors, an adjustment range of quantization sensitivity for a dynamic uniform quantizer is given through the flexible choices of design parameters. Comparing with the existing results, the derived inequality condition leads to the fault tolerance ability stronger and much wider scope of applicability. With a static adjustment policy of quantization sensitivity, an adaptive sliding mode controller is then designed to maintain the sliding mode, where the gain of the nonlinear unit vector term is updated automatically to compensate for the effects of actuator faults, quantization errors, exogenous disturbances and parameter uncertainties without the need for a fault detection and isolation (FDI) mechanism. Finally, the effectiveness of the proposed design method is illustrated via a model of a rocket fairing structural-acoustic.
Robust Metric Learning by Smooth Optimization
Huang, Kaizhu; Xu, Zenglin; Liu, Cheng-Lin
2012-01-01
Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as users' implicit feedbacks and citations among articles. As a result, these constraints are usually noisy and contain many mistakes. In this work, we aim to learn a distance metric from noisy constraints by robust optimization in a worst-case scenario, to which we refer as robust metric learning. We formulate the learning task initially as a combinatorial optimization problem, and show that it can be elegantly transformed to a convex programming problem. We present an efficient learning algorithm based on smooth optimization [7]. It has a worst-case convergence rate of O(1/{\\surd}{\\varepsilon}) for smooth optimization problems, where {\\varepsilon} is the desired error of the approximate solution. Finally, our empirical study with UCI data sets demonstrate the effectiveness of ...
Renji Han; Wei Jiang
2009-01-01
The problem of delay-dependent robust stability for uncertain linear singular neu-tral systems with time-varying and distributed delays is investigated. The uncertain-ties under consideration are norm bounded, and possibly time varying. Some new stability criteria, which are simpler and less conservative than existing results, are derived based on a new class of Lyapunov-Krasovskii functionals combined with the descriptor model transformation and the decomposition technique of coefficient matrix and formulated in the form of a linear matrix inequalitys (LMIs). Also, the criteria can be easily checked by the Matlab LMI toolbox.
Robust topology optimization accounting for geometric imperfections
Schevenels, M.; Jansen, M.; Lombaert, Geert
2013-01-01
performance. As a consequence, the actual structure may be far from optimal. In this paper, a robust approach to topology optimization is presented, taking into account two types of geometric imperfections: variations of (1) the crosssections and (2) the locations of structural elements. The first type...... is modeled by means of a scalar non-Gaussian random field, which is represented as a translation process. The underlying Gaussian field is simulated by means of the EOLE method. The second type of imperfections is modeled as a Gaussian vector-valued random field, which is simulated directly by means...
Experiments with ROPAR, an approach for probabilistic analysis of the optimal solutions' robustness
Marquez, Oscar; Solomatine, Dimitri
2016-04-01
Robust optimization is defined as the search for solutions and performance results which remain reasonably unchanged when exposed to uncertain conditions such as natural variability in input variables, parameter drifts during operation time, model sensitivities and others [1]. In the present study we follow the approach named ROPAR (multi-objective robust optimization allowing for explicit analysis of robustness (see online publication [2]). Its main idea is in: a) sampling the vectors of uncertain factors; b) solving MOO problem for each of them obtaining multiple Pareto sets; c) analysing the statistical properties (distributions) of the subsets of these Pareto sets corresponding to different conditions (e.g. based on constraints formulated for the objective functions values of other system variables); d) selecting the robust solutions. The paper presents the results of experiments with the two case studies: 1) a benchmark function ZDT1 (with an uncertain factor) often used in algorithms comparisons, and 2) a problem of drainage network rehabilitation that uses SWMM hydrodynamic model (the rainfall is assumed to be an uncertain factor). This study is partly supported by the FP7 European Project WeSenseIt Citizen Water Observatory (www.http://wesenseit.eu/) and the CONACYT (Mexico's National Council of Science and Technology) supporting the PhD study of the first author. References [1] H.G.Beyer and B. Sendhoff. "Robust optimization - A comprehensive survey." Comput. Methods Appl. Mech. Engrg., 2007: 3190-3218. [2] D.P. Solomatine (2012). An approach to multi-objective robust optimization allowing for explicit analysis of robustness (ROPAR). UNESCO-IHE. Online publication. Web: https://www.unesco-ihe.org/sites/default/files/solomatine-ropar.pdf
New approaches to robust l2-l∞ and H∞ filtering for uncertain discrete-time systems
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.
Minimax robust relay selection based on uncertain long-term CSI
Nisar, Muhammad Danish
2014-02-01
Cooperative communications via multiple relay nodes is known to provide the benefits of increase diversity and coverage. Simultaneous transmission via multiple relays, however, requires strong coordination between nodes either in terms of slot-based transmission or distributed space-time (ST) code implementation. Dynamically selecting a single best relay out of multiple relays and then using it alone for cooperative transmission alleviates the need for this strong coordination while still reaping the benefits of increased diversity and coverage. In this paper, we consider the design of relay selection (RS) under an imperfect knowledge of long-term channel state information (CSI) at the relay nodes, and we pursue minimax optimization to arrive at a robust RS approach that promises the best guarantee on the worst-case end-to-end signal-to-noise ratio (SNR). We provide some intuitive examples and extensive simulation results, not only in terms of worst-case SNR performance but also in terms of average bit-error-rate (BER) performance, to demonstrate the benefits of the proposed minimax robust RS scheme. © 2013 IEEE.
Sreekanth, J.; Moore, Catherine; Wolf, Leif
2016-02-01
Simulation-optimization methods are used to develop optimal solutions for a variety of groundwater management problems. The true optimality of these solutions is often dependent on the reliability of the simulation model. Therefore, where model predictions are uncertain due to parameter uncertainty, this should be accounted for within the optimization formulation to ensure that solutions are robust and reliable. In this study, we present a stochastic multi-objective formulation of the otherwise single objective groundwater optimization problem by considering minimization of prediction uncertainty as an additional objective. The proposed method is illustrated by applying to an injection bore field design problem. The primary objective of optimization is maximization of the total volume of water injected into a confined aquifer, subject to the constraints that the resulting increases in hydraulic head in a set of control bores are below specified target levels. Both bore locations and injection rates were considered as optimization variables. Prediction uncertainty is estimated using stacks of uncertain parameters and is explicitly minimized to produce robust and reliable solutions. Reliability analysis using post-optimization Monte Carlo analysis proved that while a stochastic single objective optimization failed to provide reliable solutions with a stack size of 50, the proposed method resulted in many robust solutions with high reliability close to 1.0. Results of the comparison indicate potential gains in efficiency of the stochastic multi-objective formulation to identify robust and reliable groundwater management strategies.
DYNAMIC OPTIMIZATION FOR UNCERTAIN STRUCTURES USING INTERVAL METHOD
ChertSub-A-; WuJie; LiuChun
2003-01-01
An interval optimization method for the dynamic response of structures with interval parameters is presented. The matrices of structures with interval parameters are given. Combining the interval extension with the perturbation, the method for interval dynamic response analysis is derived. The interval optimization problem is transformed into a corresponding deterministic one. Because the mean values and the uncertainties of the interval parameters can be elected design variables, more information of the optimization results can be obtained by the present method than that obtained by the deterministic one. The present method is implemented for a truss structure. The numerical results show that the method is effective.
Li, Zhifu; Hu, Yueming; Li, Di
2016-08-01
For a class of linear discrete-time uncertain systems, a feedback feed-forward iterative learning control (ILC) scheme is proposed, which is comprised of an iterative learning controller and two current iteration feedback controllers. The iterative learning controller is used to improve the performance along the iteration direction and the feedback controllers are used to improve the performance along the time direction. First of all, the uncertain feedback feed-forward ILC system is presented by an uncertain two-dimensional Roesser model system. Then, two robust control schemes are proposed. One can ensure that the feedback feed-forward ILC system is bounded-input bounded-output stable along time direction, and the other can ensure that the feedback feed-forward ILC system is asymptotically stable along time direction. Both schemes can guarantee the system is robust monotonically convergent along the iteration direction. Third, the robust convergent sufficient conditions are given, which contains a linear matrix inequality (LMI). Moreover, the LMI can be used to determine the gain matrix of the feedback feed-forward iterative learning controller. Finally, the simulation results are presented to demonstrate the effectiveness of the proposed schemes.
Robust control methods for nonlinear systems with uncertain dynamics and unknown control direction
Ton, Chau T.
consideration is required in control design for systems that also include unknown bounded disturbances. To cope with these challenges, a robust continuous controller is developed using an ISMC technique, which achieves asymptotic trajectory tracking for systems with unknown bounded disturbances, while simultaneously compensating for parametric uncertainty in the input gain matrix. The ISMC design is rigorously proven to achieve asymptotic trajectory tracking for a quadrotor system and a synthetic jet actuator (SJA)-based aircraft system. In the ISMC designs, it is assumed that the signs in the uncertain input-multiplicative gain matrix (i.e., the actuator control directions) are known. A much more challenging scenario is encountered in designing controllers for classes of systems, where the uncertainty in the input gain matrix is extreme enough to result in an a priori-unknown control direction. Such a scenario can result when dealing with highly inaccurate dynamic models, unmodeled parameter variations, actuator anomalies, unknown external or internal disturbances, and/or other adversarial operating conditions. To address this challenge, a SMCbased self-recongurable control algorithm is presented, which automatically adjusts for unknown control direction via periodic switching between sliding manifolds that ultimately forces the state to a converging manifold. Rigorous mathematical analyses are presented to prove the theoretical results, and simulation results are provided to demonstrate the effectiveness of the three proposed control algorithms.
Optimal Power Flow for Distribution Systems under Uncertain Forecasts: Preprint
Dall' Anese, Emiliano; Baker, Kyri; Summers, Tyler
2016-12-01
The paper focuses on distribution systems featuring renewable energy sources and energy storage devices, and develops an optimal power flow (OPF) approach to optimize the system operation in spite of forecasting errors. The proposed method builds on a chance-constrained multi-period AC OPF formulation, where probabilistic constraints are utilized to enforce voltage regulation with a prescribed probability. To enable a computationally affordable solution approach, a convex reformulation of the OPF task is obtained by resorting to i) pertinent linear approximations of the power flow equations, and ii) convex approximations of the chance constraints. Particularly, the approximate chance constraints provide conservative bounds that hold for arbitrary distributions of the forecasting errors. An adaptive optimization strategy is then obtained by embedding the proposed OPF task into a model predictive control framework.
Optimal Power Flow for Distribution Systems under Uncertain Forecasts
Dall' Anese, Emiliano; Baker, Kyri; Summers, Tyler
2016-12-29
The paper focuses on distribution systems featuring renewable energy sources and energy storage devices, and develops an optimal power flow (OPF) approach to optimize the system operation in spite of forecasting errors. The proposed method builds on a chance-constrained multi-period AC OPF formulation, where probabilistic constraints are utilized to enforce voltage regulation with a prescribed probability. To enable a computationally affordable solution approach, a convex reformulation of the OPF task is obtained by resorting to i) pertinent linear approximations of the power flow equations, and ii) convex approximations of the chance constraints. Particularly, the approximate chance constraints provide conservative bounds that hold for arbitrary distributions of the forecasting errors. An adaptive optimization strategy is then obtained by embedding the proposed OPF task into a model predictive control framework.
Wu, Huai-Ning; Li, Mao-Mao; Guo, Lei
2015-07-01
This paper studies the finite-horizon optimal guaranteed cost control (GCC) problem for a class of time-varying uncertain nonlinear systems. The aim of this problem is to find a robust state feedback controller such that the closed-loop system has not only a bounded response in a finite duration of time for all admissible uncertainties but also a minimal guaranteed cost. A neural network (NN) based approximate optimal GCC design is developed. Initially, by modifying the cost function to account for the nonlinear perturbation of system, the optimal GCC problem is transformed into a finite-horizon optimal control problem of the nominal system. Subsequently, with the help of the modified cost function together with a parametrized bounding function for all admissible uncertainties, the solution to the optimal GCC problem is given in terms of a parametrized Hamilton-Jacobi-Bellman (PHJB) equation. Then, a NN method is developed to solve offline the PHJB equation approximately and thus obtain the nearly optimal GCC policy. Furthermore, the convergence of approximate PHJB equation and the robust admissibility of nearly optimal GCC policy are also analyzed. Finally, by applying the proposed design method to the entry guidance problem of the Mars lander, the achieved simulation results show the effectiveness of the proposed controller.
A numerical investigation for robust stability of fractional-order uncertain systems.
Senol, Bilal; Ates, Abdullah; Alagoz, B Baykant; Yeroglu, Celaleddin
2014-03-01
This study presents numerical methods for robust stability analysis of closed loop control systems with parameter uncertainty. Methods are based on scan sampling of interval characteristic polynomials from the hypercube of parameter space. Exposed-edge polynomial sampling is used to reduce the computational complexity of robust stability analysis. Computer experiments are used for demonstration of the proposed robust stability test procedures.
OPTIMAL LAND CONVERSION AND GROWTH WITH UNCERTAIN BIODIVERSITY COSTS
Anke Leroux; John Creedy
2005-01-01
An important characteristic defining the threat of environmental crises is the uncertainty about their consequences for future welfare. Random processes governing ecosystem dynamics and adaptation to anthropogenic change are important sources of prevailing ecological uncertainty and contribute to the problem of how to balance economic development against natural resource conservation. The aim of this study is to examine optimal growth subject to non-linear dynamic environmental constraints. I...
Automatic Synthesis of Robust and Optimal Controllers
Cassez, Franck; Jessen, Jan Jacob; Larsen, Kim Guldstrand;
2009-01-01
In this paper, we show how to apply recent tools for the automatic synthesis of robust and near-optimal controllers for a real industrial case study. We show how to use three different classes of models and their supporting existing tools, Uppaal-TiGA for synthesis, phaver for verification......, and Simulink for simulation, in a complementary way. We believe that this case study shows that our tools have reached a level of maturity that allows us to tackle interesting and relevant industrial control problems....
Robust H∞ Control for a Class of Uncertain Switched Fuzzy Time-Delay Systems Based on T-S Models
Yang Cui
2013-01-01
Full Text Available The problem of robust H∞ control for a class of uncertain switched fuzzy time-delay systems is discussed for system described by T-S fuzzy model with Lyapunov stable theory and linear matrix inequality approach. A sufficient condition in terms of the LMI is derived such that the stability of the closed-loop systems is guaranteed. The continuous state feedback controller is built to ensure the asymptotically stable closed-loop system for all allowable uncertainties, with the switching law designed to implement the global asymptotic stability of uncertain switched fuzzy time-delay systems. In this model, each and every subsystem of the switched systems is an uncertain fuzzy one to which the parallel distributed compensation (PDC controller of each sub fuzzy system system is proposed with its main condition given in a more solvable form of convex combinations. Such a switched control system is highly robust to varying parameters. A simulation shows the feasibility and effectiveness of the design method.
Vliet, van M.; Kok, K.
2015-01-01
Water management strategies in times of global change need to be developed within a complex and uncertain environment. Scenarios are often used to deal with uncertainty. A novel backcasting methodology has been tested in which a normative objective (e.g. adaptive water management) is backcasted with
Robust Stabilization Analysis for Uncertain Systems with Time-Varying Delays
WANG Zhong-sheng; WANG Dong-yun; SHEN Yi
2004-01-01
In this paper, the stabilization problem for uncertain systems with time-varying delays both in state and control are discussed. A stabilization criterion is obtained to guarantee the quadratic stability of the closed-loop system. The controller gain matrix is included in an Hamiltonian matrix, which is easily constructed by the boundedness of the uncertainties.
2013-01-01
A new paradigm for planning under conditions of deep uncertainty has emerged in the literature. According to this paradigm, a planner should create a strategic vision of the future, commit to short-term actions, and establish a framework to guide future actions. A plan that embodies these ideas allows for its dynamic adaptation over time to meet changing circumstances. We propose a method for decisionmaking under uncertain global and regional changes called ‘Dynamic Adaptive Policy Pathways’....
Yedavalli, R. K.
1992-01-01
The aspect of controller design for improving the ride quality of aircraft in terms of damping ratio and natural frequency specifications on the short period dynamics is addressed. The controller is designed to be robust with respect to uncertainties in the real parameters of the control design model such as uncertainties in the dimensional stability derivatives, imperfections in actuator/sensor locations and possibly variations in flight conditions, etc. The design is based on a new robust root clustering theory developed by the author by extending the nominal root clustering theory of Gutman and Jury to perturbed matrices. The proposed methodology allows to get an explicit relationship between the parameters of the root clustering region and the uncertainty radius of the parameter space. The current literature available for robust stability becomes a special case of this unified theory. The bounds derived on the parameter perturbation for robust root clustering are then used in selecting the robust controller.
Optimal core acquisition and remanufacturing policies under uncertain core quality fractions
Teunter, Ruud H.; Flapper, Simme Douwe P.
2011-01-01
Cores acquired by a remanufacturer are typically highly variable in quality. Even if the expected fractions of the various quality levels are known, then the exact fractions when acquiring cores are still uncertain. Our model incorporates this uncertainty in determining optimal acquisition decisions
A robust optimization model for agile and build-to-order supply chain planning under uncertainties
Lalmazloumian, Morteza; Wong, Kuan Yew; Govindan, Kannan
2015-01-01
Supply chain planning as one of the most important processes within the supply chain management concept, has a great impact on firms' success or failure. This paper considers a supply chain planning problem of an agile manufacturing company operating in a build-to-order environment under various...... kinds of uncertainty. An integrated optimization approach of procurement, production and distribution costs associated with the supply chain members has been taken into account. A robust optimization scenario-based approach is used to absorb the influence of uncertain parameters and variables....... The formulation is a robust optimization model with the objective of minimizing the expected total supply chain cost while maintaining customer service level. The developed multi-product, multi-period, multi-echelon robust mixed-integer linear programming model is then solved using the CPLEX optimization studio...
Yazdani, Sahar; Haeri, Mohammad
2017-08-11
In this work, we study the flocking problem of multi-agent systems with uncertain dynamics subject to actuator failure and external disturbances. By considering some standard assumptions, we propose a robust adaptive fault tolerant protocol for compensating of the actuator bias fault, the partial loss of actuator effectiveness fault, the model uncertainties, and external disturbances. Under the designed protocol, velocity convergence of agents to that of virtual leader is guaranteed while the connectivity preservation of network and collision avoidance among agents are ensured as well. Copyright © 2017. Published by Elsevier Ltd.
Weihua Mao
2012-01-01
Full Text Available This paper discusses the mean-square exponential stability of uncertain neutral linear stochastic systems with interval time-varying delays. A new augmented Lyapunov-Krasovskii functional (LKF has been constructed to derive improved delay-dependent robust mean-square exponential stability criteria, which are forms of linear matrix inequalities (LMIs. By free-weight matrices method, the usual restriction that the stability conditions only bear slow-varying derivative of the delay is removed. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.
Robust optimization based energy dispatch in smart grids considering demand uncertainty
Nassourou, M.; Puig, V.; Blesa, J.
2017-01-01
In this study we discuss the application of robust optimization to the problem of economic energy dispatch in smart grids. Robust optimization based MPC strategies for tackling uncertain load demands are developed. Unexpected additive disturbances are modelled by defining an affine dependence between the control inputs and the uncertain load demands. The developed strategies were applied to a hybrid power system connected to an electrical power grid. Furthermore, to demonstrate the superiority of the standard Economic MPC over the MPC tracking, a comparison (e.g average daily cost) between the standard MPC tracking, the standard Economic MPC, and the integration of both in one-layer and two-layer approaches was carried out. The goal of this research is to design a controller based on Economic MPC strategies, that tackles uncertainties, in order to minimise economic costs and guarantee service reliability of the system.
Robust H∞ Control for Uncertain Markovian Jump Linear Time-Delay Systems
无
2002-01-01
This paper studies the robust stochastic stabilization and robust H∞ control for linear time-delay systems with both Markovian jump parameters and unknown norm-bounded parameter uncertainties. This problem can be solved on the basis of stochastic Lyapunov approach and linear matrix inequality (LMI) technique. Sufficient conditions for the existence of stochastic stabilization and robust H∞ state feedback controller are presented in terms of a set of solutions of coupled LMIs. Finally, a numerical example is included to demonstrate the practicability of the proposed methods.
Athans, M.; Ku, R.; Gershwin, S. B.
1977-01-01
This note shows that the optimal control of dynamic systems with uncertain parameters has certain limitations. In particular, by means of a simple scalar linear-quadratic optimal control example, it is shown that the infinite horizon solution does not exist if the parameter uncertainty exceeds a certain quantifiable threshold; we call this the uncertainty threshold principle. The philosophical and design implications of this result are discussed.
Robust optimization based upon statistical theory.
Sobotta, B; Söhn, M; Alber, M
2010-08-01
Organ movement is still the biggest challenge in cancer treatment despite advances in online imaging. Due to the resulting geometric uncertainties, the delivered dose cannot be predicted precisely at treatment planning time. Consequently, all associated dose metrics (e.g., EUD and maxDose) are random variables with a patient-specific probability distribution. The method that the authors propose makes these distributions the basis of the optimization and evaluation process. The authors start from a model of motion derived from patient-specific imaging. On a multitude of geometry instances sampled from this model, a dose metric is evaluated. The resulting pdf of this dose metric is termed outcome distribution. The approach optimizes the shape of the outcome distribution based on its mean and variance. This is in contrast to the conventional optimization of a nominal value (e.g., PTV EUD) computed on a single geometry instance. The mean and variance allow for an estimate of the expected treatment outcome along with the residual uncertainty. Besides being applicable to the target, the proposed method also seamlessly includes the organs at risk (OARs). The likelihood that a given value of a metric is reached in the treatment is predicted quantitatively. This information reveals potential hazards that may occur during the course of the treatment, thus helping the expert to find the right balance between the risk of insufficient normal tissue sparing and the risk of insufficient tumor control. By feeding this information to the optimizer, outcome distributions can be obtained where the probability of exceeding a given OAR maximum and that of falling short of a given target goal can be minimized simultaneously. The method is applicable to any source of residual motion uncertainty in treatment delivery. Any model that quantifies organ movement and deformation in terms of probability distributions can be used as basis for the algorithm. Thus, it can generate dose
A robust optimization model for blood supply chain in emergency situations
Meysam Fereiduni; Kamran Shahanaghi
2016-01-01
In this paper, a multi-period model for blood supply chain in emergency situation is presented to optimize decisions related to locate blood facilities and distribute blood products after natural disasters. In disastrous situations, uncertainty is an inseparable part of humanitarian logistics and blood supply chain as well. This paper proposes a robust network to capture the uncertain nature of blood supply chain during and after disasters. This study considers donor points, blood facilities,...
Observer-based robust H-infinity control for uncertain switched systems
Zhengyi SONG; Jun ZHAO
2007-01-01
The problem of observer-based robust H-infinity control is addressed for a class of linear discrete-time switched systems with time-varying norm-bounded uncertainties by using switched Lyapunov function method. None of the individual subsystems is assumed to be robustly H-infinity solvable. A novel switched Lypunov function matrix with diagonal-block form is devised to overcome the difficulties in designing switching laws. For robust H-infinity stability analysis, two linear-matrix-inequality-based sufficient conditions are derived by only using the smallest region function strategy if some parameters are preselected. Then, the robust H-infinity control synthesis is studied using a switching state feedback and an observer-based switching dynamical output feedback. All the switching laws are simultaneously constructively designed. Finally, a simulation example is given to illustrate the validity of the results.
Robust H-infinity reliable control for a class of nonlinear uncertain neutral delay systems
Ximing SUN; Jun ZHAO; Bing CHEN
2004-01-01
This paper focuses on the robust H-infinity reliable control for a class of nonlinear neutral delay systems with uncertainties and actuator failures.We design a state feedback controller in terms of linear matrix inequality(LMI)such that the plant satisfies robust H-infinity performance for all admissible uncertainties,and actuator failures among a prespecified subset of actuators.An example is also given to illustrate the effectiveness of the proposed approach.
Robust exponential stability and stabilization of linear uncertain polytopic time-delay systems
Nam PHAN T.; Phat VU N.
2008-01-01
This paper proposes new sufficient conditions for the exponential stability and stabilization.of linear uncertain polytopic time-delay systems.The conditions for exponential stability are expressed in terms of Kharitonov-type linear matrix inequalities(LMIs)and we develop control design methods based on UMIs for solving stabilization problem.Our method consists of a combination of the LMI approach and the use of parameter-dependent Lyapunov funcfionals,which allows to compute simultaneously the two bounds that characterize the exponetial stability rate of the solution.Numerical examples illustrating the conditions are given.
Robust Stability of a Class of Uncertain Lur'e Systems of Neutral Type
W. Weera
2012-01-01
Full Text Available This paper deals with the problem of stability for a class of Lur’e systems with interval time-varying delay and sector-bounded nonlinearity. The interval time-varying delay function is not assumed to be differentiable. We analyze the global exponential stability for uncertain neutral and Lur’e dynamical systems with some sector conditions. By constructing a set of improved Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, we establish some stability criteria in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the results.
Fuzzy robust sliding mode control of a class of uncertain systems
任立通; 谢寿生; 苗卓广; 田虎森; 彭靖波
2016-01-01
Aiming at a class of systems under parameter perturbations and unknown external disturbances, a method of fuzzy robust sliding mode control was proposed. Firstly, an integral sliding mode surface containing state feedback item was designed based on robustH∞control theory. The robust state feedback control was utilized to substitute for the equivalent control of the traditional sliding mode control. Thus the robustness of systems sliding mode motion was improved even the initial states were unknown. Furthermore, when the upper bound of disturbance was unknown, the switching control logic was difficult to design, and the drawbacks of chattering in sliding mode control should also be considered simultaneously. To solve the above-mentioned problems, the fuzzy nonlinear method was applied to approximate the switching control term. Based on the Lyapunov stability theory, the parameter adaptive law which could guarantee the system stability was devised. The proposed control strategy could reduce the system chattering effectively. And the control input would not switch sharply, which improved the practicality of the sliding mode controller. Finally, simulation was conducted on system with parameter perturbations and unknown external disturbances. The result shows that the proposed method could enhance the approaching motion performance effectively. The chattering phenomenon is weakened, and the system possesses stronger robustness against parameter perturbations and external disturbances.
Mean-Variance portfolio optimization when each asset has individual uncertain exit-time
Reza Keykhaei
2016-12-01
Full Text Available The standard Markowitz Mean-Variance optimization model is a single-period portfolio selection approach where the exit-time (or the time-horizon is deterministic. In this paper we study the Mean-Variance portfolio selection problem with uncertain exit-time when each has individual uncertain xit-time, which generalizes the Markowitz's model. We provide some conditions under which the optimal portfolio of the generalized problem is independent of the exit-times distributions. Also, it is shown that under some general circumstances, the sets of optimal portfolios in the generalized model and the standard model are the same.
Lü, Hui; Yu, Dejie
2014-12-01
An uncertain optimization method for brake squeal reduction of vehicle disc brake system with interval parameters is presented in this paper. In the proposed method, the parameters of frictional coefficient, material properties and the thicknesses of wearing components are treated as uncertain parameters, which are described as interval variables. Attention is focused on the stability analysis of a brake system in squeal, and the stability of brake system is investigated via the complex eigenvalue analysis (CEA) method. The dominant unstable mode is extracted by performing CEA based on a linear finite element (FE) model, and the negative damping ratio corresponding to the dominant unstable mode is selected as the indicator of instability. The response surface method (RSM) is applied to approximate the implicit relationship between the unstable mode and the system parameters. A reliability-based optimization model for improving the stability of the vehicle disc brake system with interval parameters is constructed based on RSM, interval analysis and reliability analysis. The Genetic Algorithm is used to get the optimal values of design parameters from the optimization model. The stability analysis and optimization of a disc brake system are carried out, and the results show that brake squeal propensity can be reduced by using stiffer back plates. The proposed approach can be used to improve the stability of the vehicle disc brake system with uncertain parameters effectively.
Delay-dependent robust H∞ control for uncertain fuzzy hyperbolic systems with multiple delays
无
2008-01-01
The robust H∞ control problem was considered for a class of fuzzy hyperbolic model (FHM) systems with parametric uncertainties and multiple delays. First, FHM modeling method was presented for time-delay nonlinear systems. Then, by using Lyapunov-Krasovskii approaches, delay-dependent sufficient condition for the existence of a kind of state feedback controller was proposed, which was expressed as linear matrix inequalities (LMIs). The controller can guarantee that the resulting closed-loop system is robustly asymptotically stable with a prescribed H∞ performance level for all admissible uncertainties and time-delay. Finally, a simulation example was provided to illustrate the effectiveness of the proposed approach.
Robust Regulation and Tracking Control of a Class of Uncertain 2DOF Underactuated Mechanical Systems
David I. Rosas Almeida
2015-01-01
Full Text Available A strategy to design and implement a robust controller for a class of underactuated mechanical systems, with two degrees of freedom, which solves the problems of regulation and trajectory tracking, is proposed. This control strategy considers the partial measurement of the state vector and the presence of parametric uncertainties in the plant; these conditions are common in the implementation of a control system. The strategy is based on the use of robust finite time convergence observers to estimate the unmeasured state variables, unknown disturbances, and other signals needed for the control system implementation. The performance of the control strategy is illustrated numerically and experimentally.
Oracle-based online robust optimization via online learning
Ben-Tal, A.; Hazan, E.; Koren, T.; Shie, M.
2015-01-01
Robust optimization is a common optimization framework under uncertainty when problem parameters are unknown, but it is known that they belong to some given uncertainty set. In the robust optimization framework, a min-max problem is solved wherein a solution is evaluated according to its performance
Design of Robust AMB Controllers for Rotors Subjected to Varying and Uncertain Seal Forces
Lauridsen, Jonas Skjødt; Santos, Ilmar
2017-01-01
, and experimental results. Three controllers are synthesized: I) AnH∞ controller based on nominal plant representation, II) A µ controller, designed to be robust against uncertaintiesin the dynamic seal model and III) a Linear Parameter Varying (LPV) controller, designed to provide a unifiedperformance over a large...
Robust optimization of a MEMS accelerometer considering temperature variations.
Liu, Guangjun; Yang, Feng; Bao, Xiaofan; Jiang, Tao
2015-03-16
A robust optimization approach for a MEMS accelerometer to minimize the effects of temperature variations is presented. The mathematical model of the accelerometer is built. The effects of temperature variations on the output performance of the accelerometer are determined, and thermal deformation of the accelerometer is analyzed. The deviations of the output capacitance and resonance frequency due to temperature fluctuations are calculated and discussed. The sensitivity analysis method is employed to determine the design variables for robust optimization and find out the key structural parameters that have most significant influence on the output capacitance and resonance frequency of the accelerometer. The mathematical model and procedure for the robust optimization of the accelerometer are proposed. The robust optimization problem is solved and discussed. The robust optimization results show that an optimized accelerometer with high sensitivity, high temperature robustness and decoupling structure is finally obtained.
Robust Optimization of a MEMS Accelerometer Considering Temperature Variations
Guangjun Liu
2015-03-01
Full Text Available A robust optimization approach for a MEMS accelerometer to minimize the effects of temperature variations is presented. The mathematical model of the accelerometer is built. The effects of temperature variations on the output performance of the accelerometer are determined, and thermal deformation of the accelerometer is analyzed. The deviations of the output capacitance and resonance frequency due to temperature fluctuations are calculated and discussed. The sensitivity analysis method is employed to determine the design variables for robust optimization and find out the key structural parameters that have most significant influence on the output capacitance and resonance frequency of the accelerometer. The mathematical model and procedure for the robust optimization of the accelerometer are proposed. The robust optimization problem is solved and discussed. The robust optimization results show that an optimized accelerometer with high sensitivity, high temperature robustness and decoupling structure is finally obtained.
An improved robust stability result for uncertain neural networks with multiple time delays.
Arik, Sabri
2014-06-01
This paper proposes a new alternative sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of delayed neural networks under the parameter uncertainties of the neural system. The existence and uniqueness of the equilibrium point is proved by using the Homomorphic mapping theorem. The asymptotic stability of the equilibrium point is established by employing the Lyapunov stability theorems. The obtained robust stability condition establishes a new relationship between the network parameters of the system. We compare our stability result with the previous corresponding robust stability results derived in the past literature. Some comparative numerical examples together with some simulation results are also given to show the applicability and advantages of our result.
A Robust Approach for Redesigning Three Level Supply Chain Warehouses in Uncertain Condition
Mahdi Bashiri
2012-06-01
Full Text Available Nowadays, warehouses dedicate considerable proportion of network's costs in a supply chain and conditions such as uncertainty in cost parameters, production capacity and demands emphasize on necessity of reasonable decisions on warehouse management. In this paper, uncertainty has been investigated under discrete different scenarios. Moreover, a new model has been proposed for redesigning of warehouses considering the min-max cost function for scenarios in specific customer servicing coverage radius. The robust approach used in this paper has been investigated by numerical examples and the obtained costs have been compared with the expected value model results. Findings imply efficiency of the proposed robust approach. Also, the costs resulted from the new relocation model have been evaluated with respect to the costs of continuing the current supply chain configuration and the findings indicate a significant cost improvement.
Robustness analysis of uncertain dynamical neural networks with multiple time delays.
Senan, Sibel
2015-10-01
This paper studies the problem of global robust asymptotic stability of the equilibrium point for the class of dynamical neural networks with multiple time delays with respect to the class of slope-bounded activation functions and in the presence of the uncertainties of system parameters of the considered neural network model. By using an appropriate Lyapunov functional and exploiting the properties of the homeomorphism mapping theorem, we derive a new sufficient condition for the existence, uniqueness and global robust asymptotic stability of the equilibrium point for the class of neural networks with multiple time delays. The obtained stability condition basically relies on testing some relationships imposed on the interconnection matrices of the neural system, which can be easily verified by using some certain properties of matrices. An instructive numerical example is also given to illustrate the applicability of our result and show the advantages of this new condition over the previously reported corresponding results.
PARAMETER COORDINATION AND ROBUST OPTIMIZATION FOR MULTIDISCIPLINARY DESIGN
HU Jie; PENG Yinghong; XIONG Guangleng
2006-01-01
A new parameter coordination and robust optimization approach for multidisciplinary design is presented. Firstly, the constraints network model is established to support engineering change, coordination and optimization. In this model, interval boxes are adopted to describe the uncertainty of design parameters quantitatively to enhance the design robustness. Secondly, the parameter coordination method is presented to solve the constraints network model, monitor the potential conflicts due to engineering changes, and obtain the consistency solution space corresponding to the given product specifications. Finally, the robust parameter optimization model is established, and genetic arithmetic is used to obtain the robust optimization parameter. An example of bogie design is analyzed to show the scheme to be effective.
Senkel, Luise
2016-01-01
This edited book aims at presenting current research activities in the field of robust variable-structure systems. The scope equally comprises highlighting novel methodological aspects as well as presenting the use of variable-structure techniques in industrial applications including their efficient implementation on hardware for real-time control. The target audience primarily comprises research experts in the field of control theory and nonlinear dynamics but the book may also be beneficial for graduate students.
Flight control application of new stability robustness bounds for linear uncertain systems
Yedavalli, Rama K.
1993-01-01
This paper addresses the issue of obtaining bounds on the real parameter perturbations of a linear state-space model for robust stability. Based on Kronecker algebra, new, easily computable sufficient bounds are derived that are much less conservative than the existing bounds since the technique is meant for only real parameter perturbations (in contrast to specializing complex variation case to real parameter case). The proposed theory is illustrated with application to several flight control examples.
Robust Feedback Control of Reconfigurable Multi-Agent Systems in Uncertain Adversarial Environments
2015-07-09
methods in distributed settings and the design of numerical methods to properly compute their trajectories. We have generate results showing that...most exciting contributions have been on distributed robust estimation with performance guarantees and hybrid methods for the analysis and design of...recognized by AACC as a finalist for the Best Student Paper Computation at the 2014 American and Control Conference in Portland. The other important
GROUP-BUYING ONLINE AUCTION AND OPTIMAL INVENTORY POLICY IN UNCERTAIN MARKET
Jian CHEN; Yunhui LIU; Xiping SONG
2004-01-01
In this paper we consider a group-buying online auction (GBA) model for a monopolistic manufacturer selling novel products in the uncertain market. Firstly, we introduce the bidder's dominant strategy, after which we optimize the GBA price curve and the production volume together.Finally, we compare the GBA with the traditional posted pricing mechanism and find that the GBA is highly probable to be advantageous over the posted pricing mechanism in some appropriate market environments.
Robust fault tolerant control of uncertain time-delay linear systems
无
2003-01-01
Robust fault tolerant control for a class of time-delay linear systems with parameter uncertainties is studied, and a time-delay related state feedback control is proposed. On the basis of Lyapunov method , we prove that the proposed control law has integrity against sensor and/or actuator failures if the correspondent sufficient condition can be satisfied. A heuristic algorithm is also provided to facilitate the realization of the fault tolerant control. Finally, a simulation example is presented to show the effectiveness of the proposed approach.
Vafaeinezhad, Moghadaseh; Kia, Reza; Shahnazari-Shahrezaei, Parisa
2016-11-01
Cell formation (CF) problem is one of the most important decision problems in designing a cellular manufacturing system includes grouping machines into machine cells and parts into part families. Several factors should be considered in a cell formation problem. In this work, robust optimization of a mathematical model of a dynamic cell formation problem integrating CF, production planning and worker assignment is implemented with uncertain scenario-based data. The robust approach is used to reduce the effects of fluctuations of the uncertain parameters with regards to all possible future scenarios. In this research, miscellaneous cost parameters of the cell formation and demand fluctuations are subject to uncertainty and a mixed-integer nonlinear programming model is developed to formulate the related robust dynamic cell formation problem. The objective function seeks to minimize total costs including machine constant, machine procurement, machine relocation, machine operation, inter-cell and intra-cell movement, overtime, shifting labors between cells and inventory holding. Finally, a case study is carried out to display the robustness and effectiveness of the proposed model. The tradeoff between solution robustness and model robustness is also analyzed in the obtained results.
Errouissi, Rachid; Yang, Jun; Chen, Wen-Hua; Al-Durra, Ahmed
2016-08-01
In this paper, a robust nonlinear generalised predictive control (GPC) method is proposed by combining an integral sliding mode approach. The composite controller can guarantee zero steady-state error for a class of uncertain nonlinear systems in the presence of both matched and unmatched disturbances. Indeed, it is well known that the traditional GPC based on Taylor series expansion cannot completely reject unknown disturbance and achieve offset-free tracking performance. To deal with this problem, the existing approaches are enhanced by avoiding the use of the disturbance observer and modifying the gain function of the nonlinear integral sliding surface. This modified strategy appears to be more capable of achieving both the disturbance rejection and the nominal prescribed specifications for matched disturbance. Simulation results demonstrate the effectiveness of the proposed approach.
Zhang Jinhui [Department of Automatic Control, Beijing Institute of Technology, Beijing 100081 (China)], E-mail: jinhuizhang82@gmail.com; Shi Peng [Faculty of Advanced Technology, University of Glamorgan, Pontypridd CF37 1DL (United Kingdom); ILSCM, School of Science and Engineering, Victoria University, Melbourne, Vic. 8001 (Australia); School of Mathematics and Statistics, University of South Australia, Mawson Lakes, SA 5095 (Australia)], E-mail: pshi@glam.ac.uk; Yang Hongjiu [Department of Automatic Control, Beijing Institute of Technology, Beijing 100081 (China)], E-mail: yanghongjiu@gmail.com
2009-12-15
This paper deals with the problem of non-fragile robust stabilization and H{sub {infinity}} control for a class of uncertain stochastic nonlinear time-delay systems. The parametric uncertainties are real time-varying as well as norm bounded. The time-delay factors are unknown and time-varying with known bounds. The aim is to design a memoryless non-fragile state feedback control law such that the closed-loop system is stochastically asymptotically stable in the mean square and the effect of the disturbance input on the controlled output is less than a prescribed level for all admissible parameter uncertainties. New sufficient conditions for the existence of such controllers are presented based on the linear matrix inequalities (LMIs) approach. Numerical example is given to illustrate the effectiveness of the developed techniques.
Optimal Robust Fault Detection for Linear Discrete Time Systems
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.
Observer-Based Robust Control of Uncertain Switched Fuzzy Systems with Combined Switching Controller
Hong Yang
2013-01-01
Full Text Available The observer-based robust control for a class of switched fuzzy (SF time-delay systems involving uncertainties and external disturbances is investigated in this paper. A switched fuzzy system, which differs from existing ones, is firstly employed to describe a nonlinear system. Next, a combined switching controller is proposed. The designed controller based on the observer instead of the state information integrates the advantages of both the switching controllers and the supplementary controllers but eliminates their disadvantages. The proposed controller provides good performance during the transient period, and the chattering effect is removed when the system state approaches the origin. Sufficient condition for the solvability of the robust control problem is given for the case that the state of system is not available. Since convex combination techniques are used to derive the delay-independent criteria, some subsystems are allowed to be unstable. Finally, various comparisons of the elaborated examples are conducted to demonstrate the effectiveness of the proposed control design approach.
Moradi, Hojjatullah; Majd, Vahid Johari
2016-05-01
In this paper, the problem of robust stability of nonlinear genetic regulatory networks (GRNs) is investigated. The developed method is an integral sliding mode control based redesign for a class of perturbed dissipative switched GRNs with time delays. The control law is redesigned by modifying the dissipativity-based control law that was designed for the unperturbed GRNs with time delays. The switched GRNs are switched from one mode to another based on time, state, etc. Although, the active subsystem is known in any instance, but the switching law and the transition probabilities are not known. The model for each mode is considered affine with matched and unmatched perturbations. The redesigned control law forces the GRN to always remain on the sliding surface and the dissipativity is maintained from the initial time in the presence of the norm-bounded perturbations. The global stability of the perturbed GRNs is maintained if the unperturbed model is globally dissipative. The designed control law for the perturbed GRNs guarantees robust exponential or asymptotic stability of the closed-loop network depending on the type of stability of the unperturbed model. The results are applied to a nonlinear switched GRN, and its convergence to the origin is verified by simulation.
黄剑; 关治洪; 王仲东
2005-01-01
The data packet dropouts phenomenon is usually inevitable when information transmitted among communication networks. In this paper, the robust stabilization problem for uncertain networked control systems with data packet dropouts is studied. First, an uncertain discrete-time switching system model is presented to describe these networked control systems. The stability equivalence is then proved between this switching system and an uncertain impulsive difference system.Moreover, a sufficient condition is obtained for the asymptotical stability of the nonlinear impulsive difference system. From this condition the robust stabilization problem is dealt with for the uncertain impulsive system. Main results are given in linear matrix inequalities. Finally a numerical example is given to illustrate the theoretical results.
Delay-independent robust guaranteed-cost control for uncertain linear neutral systems
Li Hongfei; Zhou Jun
2007-01-01
This article concerns the delay-independent guaranteed-cost control problem via memoryless state feedback for a class of neutral-type systems with structural uncertainty and a given quadratic cost function. New delay-independent conditions for the existence of the guaranteed-cost controller are presented in the term of LMIs. An algorithm involving optimization is proposed to design a controller achieving an optimal guaranteed-cost, such that, the system can be stabilized for all admissible uncertainties. A numerical example is provided to illustrate the feasibility of the proposed method.
Michael A. Hurni
2015-12-01
Full Text Available The authors develop an approach to a “best” time path for Autonomous Underwater Vehicles conducting oceanographic measurements under uncertain current flows. The numerical optimization tool DIDO is used to compute hybrid minimum time and optimal survey paths for a sample of currents between ebb and flow. A simulated meta-experiment is performed where the vehicle traverses the resulting paths under different current strengths per run. The fastest elapsed time emerges from a payoff table. A multi-objective function is then used to weigh the time to complete a mission versus measurement inaccuracy due to deviation from the desired survey path.
Extending the Scope of Robust Quadratic Optimization
Marandi, Ahmadreza; Ben-Tal, A.; den Hertog, Dick; Melenberg, Bertrand
2017-01-01
In this paper, we derive tractable reformulations of the robust counterparts of convex quadratic and conic quadratic constraints with concave uncertainties for a broad range of uncertainty sets. For quadratic constraints with convex uncertainty, it is well-known that the robust counterpart is, in ge
Robust Airfoil Optimization with Multi-objective Estimation of Distribution Algorithm
Zhong Xiaoping; Ding Jifeng; Li Weiji; Zhang Yong
2008-01-01
A transonic airfoil designed by means of classical point-optimization may result in its dramatically inferior performance under off-design conditious. To overcome this shortcoming, robust design is proposed to fred out the optimal profile of an airfoil to maintain its performance in an uncertain environment. The robust airfoil optimization is aimed to minimize mean values and variances of drag coefficients while satisfying the lift and thickness constraints over a range of Maeb numbers. A multi-objective estimation of distribution algorithm is applied to the robust airfoil optimization on the base of the RAE2822 benchmark airfoil. The shape of the airfoil is obtained through superposing ten Hick-Heune shape functions upon the benchmark airfoil. A set of design points is selected according to a uniform design table for aerodynamic evaluation. A Kriging model of drag coefficient is coustrueted with those points to reduce eumputing costs. Over the Maeh range fi'om 0.7 to 0.8, the airfoil generated by the robust optimization has a configuration characterized by supercritical airfoil with low drag coefficients. The small fluctuation in its drag coefficients means that the performance of the robust airfoil is insensitive to variation of Mach number.
Taha, Ahmad Fayez
Transportation networks, wearable devices, energy systems, and the book you are reading now are all ubiquitous cyber-physical systems (CPS). These inherently uncertain systems combine physical phenomena with communication, data processing, control and optimization. Many CPSs are controlled and monitored by real-time control systems that use communication networks to transmit and receive data from systems modeled by physical processes. Existing studies have addressed a breadth of challenges related to the design of CPSs. However, there is a lack of studies on uncertain CPSs subject to dynamic unknown inputs and cyber-attacks---an artifact of the insertion of communication networks and the growing complexity of CPSs. The objective of this dissertation is to create secure, computational foundations for uncertain CPSs by establishing a framework to control, estimate and optimize the operation of these systems. With major emphasis on power networks, the dissertation deals with the design of secure computational methods for uncertain CPSs, focusing on three crucial issues---(1) cyber-security and risk-mitigation, (2) network-induced time-delays and perturbations and (3) the encompassed extreme time-scales. The dissertation consists of four parts. In the first part, we investigate dynamic state estimation (DSE) methods and rigorously examine the strengths and weaknesses of the proposed routines under dynamic attack-vectors and unknown inputs. In the second part, and utilizing high-frequency measurements in smart grids and the developed DSE methods in the first part, we present a risk mitigation strategy that minimizes the encountered threat levels, while ensuring the continual observability of the system through available, safe measurements. The developed methods in the first two parts rely on the assumption that the uncertain CPS is not experiencing time-delays, an assumption that might fail under certain conditions. To overcome this challenge, networked unknown input
Robust and Reliable Portfolio Optimization Formulation of a Chance Constrained Problem
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.
Robust and optimal attitude control of spacecraft with disturbances
Park, Yonmook
2015-05-01
In this paper, a robust and optimal attitude control design that uses the Euler angles and angular velocities feedback is presented for regulation of spacecraft with disturbances. In the control design, it is assumed that the disturbance signal has the information of the system state. In addition, it is assumed that the disturbance signal tries to maximise the same performance index that the control input tries to minimise. After proposing a robust attitude control law that can stabilise the complete attitude motion of spacecraft with disturbances, the optimal attitude control problem of spacecraft is formulated as the optimal game-theoretic problem. Then it is shown that the proposed robust attitude control law is the optimal solution of the optimal game-theoretic problem. The stability of the closed-loop system for the proposed robust and optimal control law is proven by the LaSalle invariance principle. The theoretical results presented in this paper are illustrated by a numerical example.
Systematic identification and robust control design for uncertain time delay processes
Huusom, Jakob Kjøbsted; Poulsen, Niels Kjølstad; Jørgensen, Sten Bay
be effectively rejected. We proposed a model predictive control implementation with a dead-band on the penalty of the tracking error as a mean to achieve good closed loop performance on time delay system. We have in simulation tested our controller on a SISO system of an industrial furnace and a MIMO system...... is determined as a constrained optimization which utilizes future predictions of the plant behaviour. Hence the controller has a plant model embedded for state estimation. The achieved closed loop performance is therefore dependent on the quality of the future predictions. The performance of the state estimator...... will provide good set-point tracking performance as long as the prediction horizon of the controller is longer than the delay. Hence a predictive controller would perform better in rejecting known disturbances and changes between operation modes than a PI controller with time-delay compensation as e.g. a Smith...
TARCMO: Theory and Algorithms for Robust, Combinatorial, Multicriteria Optimization
2016-11-28
magnitude in computational experiments on portfolio optimization problems. The research on this topic has been published as [CG15a], where details can...AFRL-AFOSR-UK-TR-2017-0001 TARCMO: Theory and Algorithms for Robust, Combinatorial, Multicriteria Optimization Horst Hamacher Technische Universität...To) 15 May 2013 to 12 May 2016 4. TITLE AND SUBTITLE TARCMO: Theory and Algorithms for Robust, Combinatorial, Multicriteria Optimization 5a. CONTRACT
A Robust Optimization Approach Considering the Robustness of Design Objectives and Constraints
LIUChun-tao; LINZhi-hang; ZHOUChunojing
2005-01-01
The problem of robust design is treated as a multi-objective optimization issue in which the performance mean and variation are optimized and minimized respectively, while maintaining the feasibility of design constraints under uncertainty. To effectively address this issue in robust design, this paper presents a novel robust optimization approach which integrates multi-objective optimization concepts with Taguchi's crossed arrays techniques. In this approach,Pareto-optimal robust design solution sets are obtained with the aid of design of experiment set-ups,which utilize the results of Analysis of Variance to quantify relative dominance and significance of design variables. A beam design problem is used to illustrate the effectiveness of the proposed approach.
A minimax optimal control strategy for uncertain quasi-Hamiltonian systems
Yong WANC; Zu-guang YING; Wei-qiu ZHU
2008-01-01
A minimax optimal control strategy for quasi-Hamiltonian systems with bounded parametric and/or external disturbances is proposed based on the stochastic averaging method and stochastic differential game. To conduct the system energy control, the partially averaged It6 stochastic differential equations for the energy processes are first derived by using the stochastic averaging method for quasi-Hamiltonian systems. Combining the above equations with an appropriate performance index, the proposed strategy is searching for an optimal worst-case controller by solving a stochastic differential game problem. The worst-case disturbances and the optimal controls are obtained by solving a Hamilton-Jacobi-Isaacs (HJI) equation. Numerical results for a controlled and stochastically excited Duffing oscillator with uncertain disturbances exhibit the efficacy of the proposed control strategy.
Robust balance shift control with posture optimization
Kavafoglu, Z.; Kavafoglu, Ersan; Egges, J.
2015-01-01
In this paper we present a control framework which creates robust and natural balance shifting behaviours during standing. Given high-level features such as the position of the center of mass projection and the foot configurations, a kinematic posture satisfying these features is synthesized using o
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
Ding, Tao; Li, Cheng; Yang, Yongheng
2017-01-01
Optimally dispatching Photovoltaic (PV) inverters is an efficient way to avoid overvoltage in active distribution networks, which may occur in the case of PV generation surplus load demand. Typically, the dispatching optimization objective is to identify critical PV inverters that have the most...... significant impact on the network voltage level. Following, it ensures the optimal set-points of both active power and reactive power for the selected inverters, guaranteeing the entire system operating constraints (e.g., the network voltage magnitude) within reasonable ranges. However, the intermittent...... against any possible realization within the uncertain PV outputs. In addition, the conic relaxation-based branch flow formulation and second-order cone programming based column-and-constraint generation algorithm are employed to deal with the proposed robust optimization model. Case studies on a 33-bus...
A robust optimization model for blood supply chain in emergency situations
Meysam Fereiduni
2016-09-01
Full Text Available In this paper, a multi-period model for blood supply chain in emergency situation is presented to optimize decisions related to locate blood facilities and distribute blood products after natural disasters. In disastrous situations, uncertainty is an inseparable part of humanitarian logistics and blood supply chain as well. This paper proposes a robust network to capture the uncertain nature of blood supply chain during and after disasters. This study considers donor points, blood facilities, processing and testing labs, and hospitals as the components of blood supply chain. In addition, this paper makes location and allocation decisions for multiple post disaster periods through real data. The study compares the performances of “p-robust optimization” approach and “robust optimization” approach and the results are discussed.
Time-optimal path planning in uncertain flow fields using ensemble method
Wang, Tong
2016-01-06
An ensemble-based approach is developed to conduct time-optimal path planning in unsteady ocean currents under uncertainty. We focus our attention on two-dimensional steady and unsteady uncertain flows, and adopt a sampling methodology that is well suited to operational forecasts, where a set deterministic predictions is used to model and quantify uncertainty in the predictions. In the operational setting, much about dynamics, topography and forcing of the ocean environment is uncertain, and as a result a single path produced by a model simulation has limited utility. To overcome this limitation, we rely on a finitesize ensemble of deterministic forecasts to quantify the impact of variability in the dynamics. The uncertainty of flow field is parametrized using a finite number of independent canonical random variables with known densities, and the ensemble is generated by sampling these variables. For each the resulting realizations of the uncertain current field, we predict the optimal path by solving a boundary value problem (BVP), based on the Pontryagin maximum principle. A family of backward-in-time trajectories starting at the end position is used to generate suitable initial values for the BVP solver. This allows us to examine and analyze the performance of sampling strategy, and develop insight into extensions dealing with regional or general circulation models. In particular, the ensemble method enables us to perform a statistical analysis of travel times, and consequently develop a path planning approach that accounts for these statistics. The proposed methodology is tested for a number of scenarios. We first validate our algorithms by reproducing simple canonical solutions, and then demonstrate our approach in more complex flow fields, including idealized, steady and unsteady double-gyre flows.
Topology optimization of robust superhydrophobic surfaces
Cavalli, Andrea; Bøggild, Peter; Okkels, Fridolin
2013-01-01
the space between the posts, we search for an optimal post cross-section that minimizes the vertical displacement of the liquid–air interface at the base of the drop when a pressure difference is applied. Topology optimisation proves effective in this framework, showing that posts with a branching cross......-section are optimal, which is consistent with several biologic strategies to achieve superhydrophobicity. Through a filtering technique, we can also control the characteristic length scale of the optimal design, thus obtaining geometries feasible via standard lithography....
Mourad Kchaou
2017-01-01
Full Text Available This paper addresses the problem of sliding mode control (SMC design for a class of uncertain switched descriptor systems with state delay and nonlinear input. An integral sliding function is designed and an adaptive sliding mode controller for the reaching motion is then synthesised such that the trajectories of the resulting closed-loop system can be driven onto a prescribed sliding surface and maintained there for all subsequent times. Moreover, based on a new Lyapunov-Krasovskii functional, a delay-dependent sufficient condition is established such that the admissibility as well as the H∞ performance requirement of the sliding mode dynamics can be guaranteed in the presence of time delay, external disturbances, and nonlinear input which comprises dead-zones and/or sector nonlinearities. The major contributions of this paper of this approach include (i the closed-loop system exhibiting strong robustness against nonlinear dynamics and (ii the control scheme enjoying the chattering-free characteristic. Finally, two representative examples are given to illustrate the theoretical developments.
Herman, Jonathan D.; Zeff, Harrison B.; Reed, Patrick M.; Characklis, Gregory W.
2014-10-01
While optimality is a foundational mathematical concept in water resources planning and management, "optimal" solutions may be vulnerable to failure if deeply uncertain future conditions deviate from those assumed during optimization. These vulnerabilities may produce severely asymmetric impacts across a region, making it vital to evaluate the robustness of management strategies as well as their impacts for regional stakeholders. In this study, we contribute a multistakeholder many-objective robust decision making (MORDM) framework that blends many-objective search and uncertainty analysis tools to discover key tradeoffs between water supply alternatives and their robustness to deep uncertainties (e.g., population pressures, climate change, and financial risks). The proposed framework is demonstrated for four interconnected water utilities representing major stakeholders in the "Research Triangle" region of North Carolina, U.S. The utilities supply well over one million customers and have the ability to collectively manage drought via transfer agreements and shared infrastructure. We show that water portfolios for this region that compose optimal tradeoffs (i.e., Pareto-approximate solutions) under expected future conditions may suffer significantly degraded performance with only modest changes in deeply uncertain hydrologic and economic factors. We then use the Patient Rule Induction Method (PRIM) to identify which uncertain factors drive the individual and collective vulnerabilities for the four cooperating utilities. Our framework identifies key stakeholder dependencies and robustness tradeoffs associated with cooperative regional planning, which are critical to understanding the tensions between individual versus regional water supply goals. Cooperative demand management was found to be the key factor controlling the robustness of regional water supply planning, dominating other hydroclimatic and economic uncertainties through the 2025 planning horizon. Results
Codas, Andrés; Hanssen, Kristian G.; Foss, Bjarne
2017-01-01
The production life of oil reservoirs starts under significant uncertainty regarding the actual economical return of the recovery process due to the lack of oil field data. Consequently, investors and operators make management decisions based on a limited and uncertain description of the reservoir....... In this work, we propose a new formulation for robust optimization of reservoir well controls. It is inspired by the multiple shooting (MS) method which permits a broad range of parallelization opportunities and output constraint handling. This formulation exploits coherent risk measures, a concept...
Niu Erzhuo; Wang Qing; Dong Chaoyang
2014-01-01
The observer-based robust fault detection and optimization for a network of unmanned vehicles with imperfect communication channels and norm bounded modeling uncertainties are addressed. The network of unmanned vehicles is modeled as a discrete-time uncertain Markovian jump system. Based on the model, a residual generator is constructed and the sufficient condition for the existence of the desired fault detection filter is derived in terms of linear matrix inequality. Furthermore, a time domain optimization approach is proposed to improve the performance of the fault detection system. The problem of detecting small faults can be formulated as an optimization problem and its solution is given. For preventing false alarms, a new adaptive threshold function is established. The combined fault detection and optimization algorithm and the adaptive threshold are then applied to a network of highly maneuverable technology vehicles to illustrate the effective-ness of the proposed approach.
Shuo Zhang,Yan Zhao,Min Li,; Jianhui Zhao
2015-01-01
The global y optimal recursive filtering problem is stu-died for a class of systems with random parameter matrices, stochastic nonlinearities, correlated noises and missing measure-ments. The stochastic nonlinearities are presented in the system model to reflect multiplicative random disturbances, and the addi-tive noises, process noise and measurement noise, are assumed to be one-step autocorrelated as wel as two-step cross-correlated. A series of random variables is introduced as the missing rates governing the intermittent measurement losses caused by un-favorable network conditions. The aim of the addressed filtering problem is to design an optimal recursive filter for the uncertain systems based on an innovation approach such that the filtering error is global y minimized at each sampling time. A numerical simulation example is provided to il ustrate the effectiveness and applicability of the proposed algorithm.
Stochastic Robust Mathematical Programming Model for Power System Optimization
Liu, Cong; Changhyeok, Lee; Haoyong, Chen; Mehrotra, Sanjay
2016-01-01
This paper presents a stochastic robust framework for two-stage power system optimization problems with uncertainty. The model optimizes the probabilistic expectation of different worst-case scenarios with ifferent uncertainty sets. A case study of unit commitment shows the effectiveness of the proposed model and algorithms.
Hsu, Chen-Chien; Lin, Geng-Yu
2009-07-01
In this paper, a particle swarm optimization (PSO) based approach is proposed to derive an optimal digital controller for redesigned digital systems having an interval plant based on time-response resemblance of the closed-loop systems. Because of difficulties in obtaining time-response envelopes for interval systems, the design problem is formulated as an optimization problem of a cost function in terms of aggregated deviation between the step responses corresponding to extremal energies of the redesigned digital system and those of their continuous counterpart. A proposed evolutionary framework incorporating three PSOs is subsequently presented to minimize the cost function to derive an optimal set of parameters for the digital controller, so that step response sequences corresponding to the extremal sequence energy of the redesigned digital system suitably approximate those of their continuous counterpart under the perturbation of the uncertain plant parameters. Computer simulations have shown that redesigned digital systems incorporating the PSO-derived digital controllers have better system performance than those using conventional open-loop discretization methods.
Towards Robust Designs Via Multiple-Objective Optimization Methods
Man Mohan, Rai
2006-01-01
Fabricating and operating complex systems involves dealing with uncertainty in the relevant variables. In the case of aircraft, flow conditions are subject to change during operation. Efficiency and engine noise may be different from the expected values because of manufacturing tolerances and normal wear and tear. Engine components may have a shorter life than expected because of manufacturing tolerances. In spite of the important effect of operating- and manufacturing-uncertainty on the performance and expected life of the component or system, traditional aerodynamic shape optimization has focused on obtaining the best design given a set of deterministic flow conditions. Clearly it is important to both maintain near-optimal performance levels at off-design operating conditions, and, ensure that performance does not degrade appreciably when the component shape differs from the optimal shape due to manufacturing tolerances and normal wear and tear. These requirements naturally lead to the idea of robust optimal design wherein the concept of robustness to various perturbations is built into the design optimization procedure. The basic ideas involved in robust optimal design will be included in this lecture. The imposition of the additional requirement of robustness results in a multiple-objective optimization problem requiring appropriate solution procedures. Typically the costs associated with multiple-objective optimization are substantial. Therefore efficient multiple-objective optimization procedures are crucial to the rapid deployment of the principles of robust design in industry. Hence the companion set of lecture notes (Single- and Multiple-Objective Optimization with Differential Evolution and Neural Networks ) deals with methodology for solving multiple-objective Optimization problems efficiently, reliably and with little user intervention. Applications of the methodologies presented in the companion lecture to robust design will be included here. The
Linear systems optimal and robust control
Sinha, Alok
2007-01-01
Introduction Overview Contents of the Book State Space Description of a Linear System Transfer Function of a Single Input/Single Output (SISO) System State Space Realizations of a SISO System SISO Transfer Function from a State Space Realization Solution of State Space Equations Observability and Controllability of a SISO System Some Important Similarity Transformations Simultaneous Controllability and Observability Multiinput/Multioutput (MIMO) Systems State Space Realizations of a Transfer Function Matrix Controllability and Observability of a MIMO System Matrix-Fraction Description (MFD) MFD of a Transfer Function Matrix for the Minimal Order of a State Space Realization Controller Form Realization from a Right MFD Poles and Zeros of a MIMO Transfer Function Matrix Stability Analysis State Feedback Control and Optimization State Variable Feedback for a Single Input System Computation of State Feedback Gain Matrix for a Multiinput System State Feedback Gain Matrix for a Multi...
Ying-Yi Hong
2014-01-01
Full Text Available The Kyoto protocol recommended that industrialized countries limit their green gas emissions in 2012 to 5.2% below 1990 levels. Photovoltaic (PV arrays provide clear and sustainable renewable energy to electric power systems. Solar PV arrays can be installed in distribution systems of rural and urban areas, as opposed to wind-turbine generators, which cause noise in surrounding environments. However, a large PV array (several MW may incur several operation problems, for example, low power quality and reverse power. This work presents a novel method to reconfigure the distribution feeders in order to prevent the injection of reverse power into a substation connected to the transmission level. Moreover, a two-stage algorithm is developed, in which the uncertain bus loads and PV powers are clustered by fuzzy-c-means to gain representative scenarios; optimal reconfiguration is then achieved by a novel mean-variance-based particle swarm optimization. The system loss is minimized while the operational constraints, including reverse power and voltage variation, are satisfied due to the optimal feeder reconfiguration. Simulation results obtained from a 70-bus distribution system with 4 large PV arrays validate the proposed method.
Study of the Optimal Timing of Container Ship Orders Considering the Uncertain Shipping Environment
Jun Woo Jeon
2017-07-01
Full Text Available This study aims to apply System Dynamics (SD to analyze the optimal timing of container ship orders by considering the uncertain shipping environment. The collected monthly data for 12 years was obtained from the China seaborne container trade (CSCT and the China Containerized Freight Index (CCFI. Containership fleet development and the prices of new and second-hand container ships were classified based on five container vessel sizes (January of 2004–December of 2015. The period of simulation for this study was from 2004 to 2020. To analyze the optimal timing for the container ship orders, container ship fleet development as a supply factor and the CSCT as a demand factor, both of which are components of CCFI, were simulated. After the first simulation, CCFI was simulated holistically. Based on the CCFI simulation results, it was possible to develop three optimal timing scenarios for ship order placement. The CCFI for October 2016 was in the initial entry status of a short-term rebound, which makes it possible for shipping companies to order ships without the risk of revenue loss. The second best time period is May 2018, before the CCFI recovery of May 2019. The third best time for ship orders is later in 2020 for a CCFI recovery after 2021.
A case study on robust optimal experimental design for model calibration of ω-Transaminase
Daele, Timothy, Van; Van Hauwermeiren, Daan; Ringborg, Rolf Hoffmeyer
and measurement errors. Since the latter was not provided, a conservative standard deviation of 5% was assumed. The confidence analysis yielded that only two (Vr and Kac) out of five parameters were reliable estimates, which means that model predictions and decisions based on them are highly uncertain. The reason...... the experimental space. However, it is expected that more informative experiments can be designed to increase the confidence of the parameter estimates. Therefore, we apply Optimal Experimental Design (OED) to the calibrated model of Shin and Kim (1998). The total number of samples was retained to allow fair......” parameter values are not known before finishing the model calibration. However, it is important that the chosen parameter values are close to the real parameter values, otherwise the OED can possibly yield non-informative experiments. To counter this problem, one can use robust OED. The idea of robust OED...
A toolbox for robust PID controller tuning using convex optimization
Sadeghpour, Mehdi; de Oliveira, Vinicius; Karimi, Alireza
2012-01-01
A robust PID controller design toolbox for Matlab is presented in this paper. The design is based on linearizing or convexifying the conventional non-convex constraints on the classical robustness margins or H∞ constraints. Then the existing optimization solvers can be used to compute the controller parameters. The software can be used in a wide range of controller design problems, including multi-model systems and gain-scheduled controllers. The models can be parametric or non-parametric whi...
Henrichsen, Søren Randrup; Lindgaard, Esben; Lund, Erik
2015-01-01
Robust buckling optimal design of laminated composite structures is conducted in this work. Optimal designs are obtained by considering geometric imperfections in the optimization procedure. Discrete Material Optimization is applied to obtain optimal laminate designs. The optimal geometric...... example. The imperfection sensitivity of the optimized structure decreases during the recurrence optimization for both examples, hence robust buckling optimal structures are designed....
Robust and optimal control a two-port framework approach
Tsai, Mi-Ching
2014-01-01
A Two-port Framework for Robust and Optimal Control introduces an alternative approach to robust and optimal controller synthesis procedures for linear, time-invariant systems, based on the two-port system widespread in electrical engineering. The novel use of the two-port system in this context allows straightforward engineering-oriented solution-finding procedures to be developed, requiring no mathematics beyond linear algebra. A chain-scattering description provides a unified framework for constructing the stabilizing controller set and for synthesizing H2 optimal and H∞ sub-optimal controllers. Simple yet illustrative examples explain each step. A Two-port Framework for Robust and Optimal Control features: · a hands-on, tutorial-style presentation giving the reader the opportunity to repeat the designs presented and easily to modify them for their own programs; · an abundance of examples illustrating the most important steps in robust and optimal design; and · �...
Chien, Yi-Hsing; Wang, Wei-Yen; Leu, Yih-Guang; Lee, Tsu-Tian
2011-04-01
This paper proposes a novel method of online modeling and control via the Takagi-Sugeno (T-S) fuzzy-neural model for a class of uncertain nonlinear systems with some kinds of outputs. Although studies about adaptive T-S fuzzy-neural controllers have been made on some nonaffine nonlinear systems, little is known about the more complicated uncertain nonlinear systems. Because the nonlinear functions of the systems are uncertain, traditional T-S fuzzy control methods can model and control them only with great difficulty, if at all. Instead of modeling these uncertain functions directly, we propose that a T-S fuzzy-neural model approximates a so-called virtual linearized system (VLS) of the system, which includes modeling errors and external disturbances. We also propose an online identification algorithm for the VLS and put significant emphasis on robust tracking controller design using an adaptive scheme for the uncertain systems. Moreover, the stability of the closed-loop systems is proven by using strictly positive real Lyapunov theory. The proposed overall scheme guarantees that the outputs of the closed-loop systems asymptotically track the desired output trajectories. To illustrate the effectiveness and applicability of the proposed method, simulation results are given in this paper.
Efficient infill sampling for unconstrained robust optimization problems
Rehman, Samee Ur; Langelaar, Matthijs
2016-08-01
A novel infill sampling criterion is proposed for efficient estimation of the global robust optimum of expensive computer simulation based problems. The algorithm is especially geared towards addressing problems that are affected by uncertainties in design variables and problem parameters. The method is based on constructing metamodels using Kriging and adaptively sampling the response surface via a principle of expected improvement adapted for robust optimization. Several numerical examples and an engineering case study are used to demonstrate the ability of the algorithm to estimate the global robust optimum using a limited number of expensive function evaluations.
Design optimization for cost and quality: The robust design approach
Unal, Resit
1990-01-01
Designing reliable, low cost, and operable space systems has become the key to future space operations. Designing high quality space systems at low cost is an economic and technological challenge to the designer. A systematic and efficient way to meet this challenge is a new method of design optimization for performance, quality, and cost, called Robust Design. Robust Design is an approach for design optimization. It consists of: making system performance insensitive to material and subsystem variation, thus allowing the use of less costly materials and components; making designs less sensitive to the variations in the operating environment, thus improving reliability and reducing operating costs; and using a new structured development process so that engineering time is used most productively. The objective in Robust Design is to select the best combination of controllable design parameters so that the system is most robust to uncontrollable noise factors. The robust design methodology uses a mathematical tool called an orthogonal array, from design of experiments theory, to study a large number of decision variables with a significantly small number of experiments. Robust design also uses a statistical measure of performance, called a signal-to-noise ratio, from electrical control theory, to evaluate the level of performance and the effect of noise factors. The purpose is to investigate the Robust Design methodology for improving quality and cost, demonstrate its application by the use of an example, and suggest its use as an integral part of space system design process.
The balanced minimum evolution problem under uncertain data
Catanzaro, Daniele; Labbe, Martine; Pesenti, Raffaele
2013-01-01
We investigate the Robust Deviation Balanced Minimum Evolution Problem (RDBMEP), a combinatorial optimization problem that arises in computational biology when the evolutionary distances from taxa are uncertain and varying inside intervals. By exploiting some fundamental properties of the objective
Robust Control of Uncertain Markov Jump Singularly Perturbed Systems%Markov跳变线性奇异摄动系统鲁棒H∞控制
刘华平; 孙富春; 李春文; 孙增圻
2005-01-01
In this paper, we study the robust control for uncertain Markov jump linear singularly perturbed systems (MJLSPS), whose transition probability matrix is unknown. An improved heuristic algorithm is proposed to solve the nonlinear matrix inequalities. The results of this paper can apply not only to standard, but also to nonstandard MJLSPS. Moreover, the proposed approach is independent of the perturbation parameter and therefore avoids the ill-conditioned numerical problems.
Distribution-dependent robust linear optimization with applications to inventory control.
Kang, Seong-Cheol; Brisimi, Theodora S; Paschalidis, Ioannis Ch
2015-08-01
This paper tackles linear programming problems with data uncertainty and applies it to an important inventory control problem. Each element of the constraint matrix is subject to uncertainty and is modeled as a random variable with a bounded support. The classical robust optimization approach to this problem yields a solution with guaranteed feasibility. As this approach tends to be too conservative when applications can tolerate a small chance of infeasibility, one would be interested in obtaining a less conservative solution with a certain probabilistic guarantee of feasibility. A robust formulation in the literature produces such a solution, but it does not use any distributional information on the uncertain data. In this work, we show that the use of distributional information leads to an equally robust solution (i.e., under the same probabilistic guarantee of feasibility) but with a better objective value. In particular, by exploiting distributional information, we establish stronger upper bounds on the constraint violation probability of a solution. These bounds enable us to "inject" less conservatism into the formulation, which in turn yields a more cost-effective solution (by 50% or more in some numerical instances). To illustrate the effectiveness of our methodology, we consider a discrete-time stochastic inventory control problem with certain quality of service constraints. Numerical tests demonstrate that the use of distributional information in the robust optimization of the inventory control problem results in 36%-54% cost savings, compared to the case where such information is not used.
Robust topology optimization accounting for spatially varying manufacturing errors
Schevenels, M.; Lazarov, Boyan Stefanov; Sigmund, Ole
2011-01-01
This paper presents a robust approach for the design of macro-, micro-, or nano-structures by means of topology optimization, accounting for spatially varying manufacturing errors. The focus is on structures produced by milling or etching; in this case over- or under-etching may cause parts...... optimization problem is formulated in a probabilistic way: the objective function is defined as a weighted sum of the mean value and the standard deviation of the structural performance. The optimization problem is solved by means of a Monte Carlo method: in each iteration of the optimization scheme, a Monte...
Robust Design Optimization of an Aerospace Vehicle Prolusion System
Muhammad Aamir Raza
2011-01-01
Full Text Available This paper proposes a robust design optimization methodology under design uncertainties of an aerospace vehicle propulsion system. The approach consists of 3D geometric design coupled with complex internal ballistics, hybrid optimization, worst-case deviation, and efficient statistical approach. The uncertainties are propagated through worst-case deviation using first-order orthogonal design matrices. The robustness assessment is measured using the framework of mean-variance and percentile difference approach. A parametric sensitivity analysis is carried out to analyze the effects of design variables variation on performance parameters. A hybrid simulated annealing and pattern search approach is used as an optimizer. The results show the objective function of optimizing the mean performance and minimizing the variation of performance parameters in terms of thrust ratio and total impulse could be achieved while adhering to the system constraints.
Robust Optimization of Fourth Party Logistics Network Design under Disruptions
Jia Li
2015-01-01
Full Text Available The Fourth Party Logistics (4PL network faces disruptions of various sorts under the dynamic and complex environment. In order to explore the robustness of the network, the 4PL network design with consideration of random disruptions is studied. The purpose of the research is to construct a 4PL network that can provide satisfactory service to customers at a lower cost when disruptions strike. Based on the definition of β-robustness, a robust optimization model of 4PL network design under disruptions is established. Based on the NP-hard characteristic of the problem, the artificial fish swarm algorithm (AFSA and the genetic algorithm (GA are developed. The effectiveness of the algorithms is tested and compared by simulation examples. By comparing the optimal solutions of the 4PL network for different robustness level, it is indicated that the robust optimization model can evade the market risks effectively and save the cost in the maximum limit when it is applied to 4PL network design.
Doubly Robust Estimation of Optimal Dynamic Treatment Regimes
Barrett, Jessica K; Henderson, Robin; Rosthøj, Susanne
2014-01-01
We compare methods for estimating optimal dynamic decision rules from observational data, with particular focus on estimating the regret functions defined by Murphy (in J. R. Stat. Soc., Ser. B, Stat. Methodol. 65:331-355, 2003). We formulate a doubly robust version of the regret-regression appro......We compare methods for estimating optimal dynamic decision rules from observational data, with particular focus on estimating the regret functions defined by Murphy (in J. R. Stat. Soc., Ser. B, Stat. Methodol. 65:331-355, 2003). We formulate a doubly robust version of the regret....... 189-326, 2004). Simulation studies suggest that while the regret-regression approach is most efficient when there is no model misspecification, in the presence of misspecification the efficient g-estimation procedure is more robust. The g-estimation method can be difficult to apply in complex...
Optimizing the robustness of electrical power systems against cascading failures
Zhang, Yingrui
2016-01-01
Electrical power systems are one of the most important infrastructures that support our society. However, their vulnerabilities have raised great concern recently due to several large-scale blackouts around the world. In this paper, we investigate the robustness of power systems against cascading failures initiated by a random attack. This is done under a simple yet useful model based on global and equal redistribution of load upon failures. We provide a complete understanding of system robustness by i) deriving an expression for the final system size as a function of the size of initial attacks; ii) deriving the critical attack size after which system breaks down completely; iii) showing that complete system breakdown takes place through a first-order (i.e., discontinuous) transition in terms of the attack size; and iv) establishing the optimal load-capacity distribution that maximizes robustness. In particular, we show that robustness is maximized when the difference between the capacity and initial load is...
Optimization Strategies to Increase Electrical Distribution Networks Robustness
Dorin Sarchiz
2010-12-01
Full Text Available The paper aims to present a mathematical model to optimize power distribution network graph, in terms of increasing its robustness, ie to reduce the risk of destruction (its removal from service – accidentally or intentionally, with applications to the distribution networks 20 kV and 110 kV, County Mures.
Optimal and robust feedback controller estimation for a vibrating plate
Fraanje, P.R.; Verhaegen, M.; Doelman, N.J.; Berkhoff, A.
2004-01-01
This paper presents a method to estimate the H2 optimal and a robust feedback controller by means of Subspace Model Identification using the internal model control (IMC) approach. Using IMC an equivalent feed forward control problem is obtained, which is solved by the Causal Wiener filter for the H2
Optimal decisions and comparison of VMI and CPFR under price-sensitive uncertain demand
Yasaman Kazemi
2013-06-01
Full Text Available Purpose: The purpose of this study is to compare the performance of two advanced supply chain coordination mechanisms, Vendor Managed Inventory (VMI and Collaborative Planning Forecasting and Replenishment (CPFR, under a price-sensitive uncertain demand environment, and to make the optimal decisions on retail price and order quantity for both mechanisms. Design/ methodology/ approach: Analytical models are first applied to formulate a profit maximization problem; furthermore, by applying simulation optimization solution procedures, the optimal decisions and performance comparisons are accomplished. Findings: The results of the case study supported the widely held view that more advanced coordination mechanisms yield greater supply chain profit than less advanced ones. Information sharing does not only increase the supply chain profit, but also is required for the coordination mechanisms to achieve improved performance. Research limitations/implications: This study considers a single vendor and a single retailer in order to simplify the supply chain structure for modeling. Practical implications: Knowledge obtained from this study about the conditions appropriate for each specific coordination mechanism and the exact functions of coordination programs is critical to managerial decisions for industry practitioners who may apply the coordination mechanisms considered. Originality/value: This study includes the production cost in Economic Order Quantity (EOQ equations and combines it with price-sensitive demand under stochastic settings while comparing VMI and CPFR supply chain mechanisms and maximizing the total profit. Although many studies have worked on information sharing within the supply chain, determining the performance measures when the demand is price-sensitive and stochastic was not reported by researchers in the past literature.
Xu, Hao; Jagannathan, Sarangapani
2013-03-01
The stochastic optimal controller design for the nonlinear networked control system (NNCS) with uncertain system dynamics is a challenging problem due to the presence of both system nonlinearities and communication network imperfections, such as random delays and packet losses, which are not unknown a priori. In the recent literature, neuro dynamic programming (NDP) techniques, based on value and policy iterations, have been widely reported to solve the optimal control of general affine nonlinear systems. However, for realtime control, value and policy iterations-based methodology are not suitable and time-based NDP techniques are preferred. In addition, output feedback-based controller designs are preferred for implementation. Therefore, in this paper, a novel NNCS representation incorporating the system uncertainties and network imperfections is introduced first by using input and output measurements for facilitating output feedback. Then, an online neural network (NN) identifier is introduced to estimate the control coefficient matrix, which is subsequently utilized for the controller design. Subsequently, the critic and action NNs are employed along with the NN identifier to determine the forward-in-time, time-based stochastic optimal control of NNCS without using value and policy iterations. Here, the value function and control inputs are updated once a sampling instant. By using novel NN weight update laws, Lyapunov theory is used to show that all the closed-loop signals and NN weights are uniformly ultimately bounded in the mean while the approximated control input converges close to its target value with time. Simulation results are included to show the effectiveness of the proposed scheme.
唐昊; 奚宏生; 韩江洪; 袁继彬
2005-01-01
The paper is concerned with the robust control problems for exponential controlled closed queuing networks (CCQNs) under uncertain routing probabilities. As the rows of some parameter matrices such as infinitesimal generators may be dependent, we first transform the objective vector under discounted-cost criteria into a weighed-average cost. Through the solution to Poisson equation,i.e., Markov performance potentials, we then unify both discounted-cost and average-cost problems to study, and derive the gradient formula of the new objective function with respect to the routing probabilities. Some solution techniques are related for searching the optimal robust control policy.Finally, a numerical example is presented and analyzed.
Towards robust optimal design of storm water systems
Marquez Calvo, Oscar; Solomatine, Dimitri
2015-04-01
In this study the focus is on the design of a storm water or a combined sewer system. Such a system should be capable to handle properly most of the storm to minimize the damages caused by flooding due to the lack of capacity of the system to cope with rain water at peak times. This problem is a multi-objective optimization problem: we have to take into account the minimization of the construction costs, the minimization of damage costs due to flooding, and possibly other criteria. One of the most important factors influencing the design of storm water systems is the expected amount of water to deal with. It is common that this infrastructure is developed with the capacity to cope with events that occur once in, say 10 or 20 years - so-called design rainfall events. However, rainfall is a random variable and such uncertainty typically is not taken explicitly into account in optimization. Rainfall design data is based on historical information of rainfalls, but many times this data is based on unreliable measures; or in not enough historical information; or as we know, the patterns of rainfall are changing regardless of historical information. There are also other sources of uncertainty influencing design, for example, leakages in the pipes and accumulation of sediments in pipes. In the context of storm water or combined sewer systems design or rehabilitation, robust optimization technique should be able to find the best design (or rehabilitation plan) within the available budget but taking into account uncertainty in those variables that were used to design the system. In this work we consider various approaches to robust optimization proposed by various authors (Gabrel, Murat, Thiele 2013; Beyer, Sendhoff 2007) and test a novel method ROPAR (Solomatine 2012) to analyze robustness. References Beyer, H.G., & Sendhoff, B. (2007). Robust optimization - A comprehensive survey. Comput. Methods Appl. Mech. Engrg., 3190-3218. Gabrel, V.; Murat, C., Thiele, A. (2014
Robust Topology Optimization of Truss with regard to Volume
Mohr, Daniel P; Matzies, Thomas; Knapek, Christina A
2011-01-01
A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints have to be approximated by finite expressions to generate a computable problem. Here, using the example of the topology optimization of a truss, a method is proposed to deal with such uncertainties by using robust optimization techniques, leading to an approach without the necessity of any approximation. With adequately chosen load cases, the final expression is equivalent to the multiple load case. Simple numerical examples of typical problems illustrate the application of the method.
Robust optimization methodologies for water supply systems design
J. Marques
2012-08-01
Full Text Available Water supply systems (WSSs are vital infrastructures for the well-being of people today. To achieve good customer satisfaction the water supply service must always be able to meet people's needs, in terms of both quantity and quality. But unpredictable extreme conditions can cause severe damage to WSSs and lead to poorer levels of service or even to their failure. Operators dealing with a system's day-to-day operation know that events like burst water mains can compromise the functioning of all or part of a system. To increase a system's reliability, therefore, designs should take into account operating conditions other than normal ones. Recent approaches based on robust optimization can be used to solve optimization problems which involve uncertainty and can find designs which are able to cope with a range of operating conditions. This paper presents a robust optimization model for the optimal design of water supply systems operating under different circumstances. The model presented here uses a hydraulic simulator linked to an optimizer based on a simulated annealing heuristic. The results show that robustness can be included in several ways for varying levels reliability and that it leads to more reliable designs for only small cost increases.
Robust topology optimization accounting for misplacement of material
Jansen, Miche; Lombaert, Geert; Diehl, Moritz
2013-01-01
into account this type of geometric imperfections. A density filter based approach is followed, and translations of material are obtained by adding a small perturbation to the center of the filter kernel. The spatial variation of the geometric imperfections is modeled by means of a vector valued random field......The use of topology optimization for structural design often leads to slender structures. Slender structures are sensitive to geometric imperfections such as the misplacement or misalignment of material. The present paper therefore proposes a robust approach to topology optimization taking....... The random field is conditioned in order to incorporate supports in the design where no misplacement of material occurs. In the robust optimization problem, the objective function is defined as a weighted sum of the mean value and the standard deviation of the performance of the structure under uncertainty...
Robust output LQ optimal control via integral sliding modes
Fridman, Leonid; Bejarano, Francisco Javier
2014-01-01
Featuring original research from well-known experts in the field of sliding mode control, this monograph presents new design schemes for implementing LQ control solutions in situations where the output system is the only information provided about the state of the plant. This new design works under the restrictions of matched disturbances without losing its desirable features. On the cutting-edge of optimal control research, Robust Output LQ Optimal Control via Integral Sliding Modes is an excellent resource for both graduate students and professionals involved in linear systems, optimal control, observation of systems with unknown inputs, and automatization. In the theory of optimal control, the linear quadratic (LQ) optimal problem plays an important role due to its physical meaning, and its solution is easily given by an algebraic Riccati equation. This solution turns out to be restrictive, however, because of two assumptions: the system must be free from disturbances and the entire state vector must be kn...
Robust Optimal Adaptive Control Method with Large Adaptive Gain
Nguyen, Nhan T.
2009-01-01
In the presence of large uncertainties, a control system needs to be able to adapt rapidly to regain performance. Fast adaptation is referred to the implementation of adaptive control with a large adaptive gain to reduce the tracking error rapidly. However, a large adaptive gain can lead to high-frequency oscillations which can adversely affect robustness of an adaptive control law. A new adaptive control modification is presented that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. The modification is based on the minimization of the Y2 norm of the tracking error, which is formulated as an optimal control problem. The optimality condition is used to derive the modification using the gradient method. The optimal control modification results in a stable adaptation and allows a large adaptive gain to be used for better tracking while providing sufficient stability robustness. Simulations were conducted for a damaged generic transport aircraft with both standard adaptive control and the adaptive optimal control modification technique. The results demonstrate the effectiveness of the proposed modification in tracking a reference model while maintaining a sufficient time delay margin.
RECOVERY ACT - Robust Optimization for Connectivity and Flows in Dynamic Complex Networks
Balasundaram, Balabhaskar [Oklahoma State Univ., Stillwater, OK (United States); Butenko, Sergiy [Texas A & M Univ., College Station, TX (United States); Boginski, Vladimir [Univ. of Florida, Gainesville, FL (United States); Uryasev, Stan [Univ. of Florida, Gainesville, FL (United States)
2013-12-25
The goal of this project was to study robust connectivity and flow patterns of complex multi-scale systems modeled as networks. Networks provide effective ways to study global, system level properties, as well as local, multi-scale interactions at a component level. Numerous applications from power systems, telecommunication, transportation, biology, social science, and other areas have benefited from novel network-based models and their analysis. Modeling and optimization techniques that employ appropriate measures of risk for identifying robust clusters and resilient network designs in networks subject to uncertain failures were investigated in this collaborative multi-university project. In many practical situations one has to deal with uncertainties associated with possible failures of network components, thereby affecting the overall efficiency and performance of the system (e.g., every node/connection has a probability of partial or complete failure). Some extreme examples include power grid component failures, airline hub failures due to weather, or freeway closures due to emergencies. These are also situations in which people, materials, or other resources need to be managed efficiently. Important practical examples include rerouting flow through power grids, adjusting flight plans, and identifying routes for emergency services and supplies, in the event network elements fail unexpectedly. Solutions that are robust under uncertainty, in addition to being economically efficient, are needed. This project has led to the development of novel models and methodologies that can tackle the optimization problems arising in such situations. A number of new concepts, which have not been previously applied in this setting, were investigated in the framework of the project. The results can potentially help decision-makers to better control and identify robust or risk-averse decisions in such situations. Formulations and optimal solutions of the considered problems need
Integrating robust timetabling in line plan optimization for railway systems
Burggraeve, Sofie; Bull, Simon Henry; Vansteenwegen, Pieter
2017-01-01
We propose a heuristic algorithm to build a railway line plan from scratch that minimizes passenger travel time and operator cost and for which a feasible and robust timetable exists. A line planning module and a timetabling module work iteratively and interactively. The line planning module...... creates an initial line plan. The timetabling module evaluates the line plan and identifies a critical line based on minimum buffer times between train pairs. The line planning module proposes a new line plan in which the time length of the critical line is modified in order to provide more flexibility......, but is constrained by limited shunt capacity. While the operator and passenger cost remain close to those of the initially and (for these costs) optimally built line plan, the timetable corresponding to the finally developed robust line plan significantly improves the minimum buffer time, and thus the robustness...
Robust Output Feedback Control for Uncertain Discrete Systems with Time Delays%不确定时滞离散系统的鲁棒输出反馈控制
刘碧玉; 桂卫华
2005-01-01
Based on design of an observer, the issue of dynamic output feedback control is studied for uncertain discrete systems with delays. A comparison theorem is given for nonlinear uncertain discrete systems with multiple time delays. Based on the comparison theorem with some inequalities,some delay-independent sufficient conditions for the robust stabilization of the systems are presented by means of output feedback.
Martowicz, Adam; Uhl, Tadeusz
2012-10-01
The paper discusses the applicability of a reliability- and performance-based multi-criteria robust design optimization technique for micro-electromechanical systems, considering their technological uncertainties. Nowadays, micro-devices are commonly applied systems, especially in the automotive industry, taking advantage of utilizing both the mechanical structure and electronic control circuit on one board. Their frequent use motivates the elaboration of virtual prototyping tools that can be applied in design optimization with the introduction of technological uncertainties and reliability. The authors present a procedure for the optimization of micro-devices, which is based on the theory of reliability-based robust design optimization. This takes into consideration the performance of a micro-device and its reliability assessed by means of uncertainty analysis. The procedure assumes that, for each checked design configuration, the assessment of uncertainty propagation is performed with the meta-modeling technique. The described procedure is illustrated with an example of the optimization carried out for a finite element model of a micro-mirror. The multi-physics approach allowed the introduction of several physical phenomena to correctly model the electrostatic actuation and the squeezing effect present between electrodes. The optimization was preceded by sensitivity analysis to establish the design and uncertain domains. The genetic algorithms fulfilled the defined optimization task effectively. The best discovered individuals are characterized by a minimized value of the multi-criteria objective function, simultaneously satisfying the constraint on material strength. The restriction of the maximum equivalent stresses was introduced with the conditionally formulated objective function with a penalty component. The yielded results were successfully verified with a global uniform search through the input design domain.
Nitish Katal
2016-01-01
Full Text Available Automation of the robust control system synthesis for uncertain systems is of great practical interest. In this paper, the loop shaping step for synthesizing quantitative feedback theory (QFT based controller for a two-phase permanent magnet stepper motor (PMSM has been automated using teaching learning-based optimization (TLBO algorithm. The QFT controller design problem has been posed as an optimization problem and TLBO algorithm has been used to minimize the proposed cost function. This facilitates designing low-order fixed-structure controller, eliminates the need of manual loop shaping step on the Nichols charts, and prevents the overdesign of the controller. A performance comparison of the designed controller has been made with the classical PID tuning method of Ziegler-Nichols and QFT controller tuned using other optimization algorithms. The simulation results show that the designed QFT controller using TLBO offers robust stability, disturbance rejection, and proper reference tracking over a range of PMSM’s parametric uncertainties as compared to the classical design techniques.
Jiang, Qingsong; Su, Han; Liu, Yong; Zou, Rui; Ye, Rui; Guo, Huaicheng
2017-04-01
Nutrients loading reduction in watershed is essential for lake restoration from eutrophication. The efficient and optimal decision-making on loading reduction is generally based on water quality modeling and the quantitative identification of nutrient sources at the watershed scale. The modeling process is influenced inevitably by inherent uncertainties, especially by uncertain parameters due to equifinality. Therefore, the emerging question is: if there is parameter uncertainty, how to ensure the robustness of the optimal decisions? Based on simulation-optimization models, an integrated approach of pattern identification and analysis of robustness was proposed in this study that focuses on the impact of parameter uncertainty in water quality modeling. Here the pattern represents the discernable regularity of solutions for load reduction under multiple parameter sets. Pattern identification is achieved by using a hybrid clustering analysis (i.e., Ward-Hierarchical and K-means), which was flexible and efficient in analyzing Lake Bali near the Yangtze River in China. The results demonstrated that urban domestic nutrient load is the most potential source that should be reduced, and there are two patterns for Total Nitrogen (TN) reduction and three patterns for Total Phosphorus (TP) reduction. The patterns indicated different total reduction of nutrient loads, which reflect diverse decision preferences. The robust solution was identified by the highest accomplishment with the water quality at monitoring stations that were improved uniformly with this solution. We conducted a process analysis of robust decision-making that was based on pattern identification and uncertainty, which provides effective support for decision-making with preference under uncertainty.
无
2007-01-01
This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump.Based on the extended It(o) stochastic differential formula,sufficient conditions for the solvability of these problems are obtained.Furthermore,It is shown that a desired filter can be constructed by solving a set of linear matrix inequalities.Finally,a simulation example is given to demonstrate the effectiveness of the proposed method.
Stochastic simulation and robust design optimization of integrated photonic filters
Weng Tsui-Wei
2017-01-01
Full Text Available Manufacturing variations are becoming an unavoidable issue in modern fabrication processes; therefore, it is crucial to be able to include stochastic uncertainties in the design phase. In this paper, integrated photonic coupled ring resonator filters are considered as an example of significant interest. The sparsity structure in photonic circuits is exploited to construct a sparse combined generalized polynomial chaos model, which is then used to analyze related statistics and perform robust design optimization. Simulation results show that the optimized circuits are more robust to fabrication process variations and achieve a reduction of 11%–35% in the mean square errors of the 3 dB bandwidth compared to unoptimized nominal designs.
Thresholded Covering Algorithms for Robust and Max-Min Optimization
Gupta, Anupam; Ravi, R
2009-01-01
The general problem of robust optimization is this: one of several possible scenarios will appear tomorrow, but things are more expensive tomorrow than they are today. What should you anticipatorily buy today, so that the worst-case cost (summed over both days) is minimized? Feige et al. and Khandekar et al. considered the k-robust model where the possible outcomes tomorrow are given by all demand-subsets of size k, and gave algorithms for the set cover problem, and the Steiner tree and facility location problems in this model, respectively. In this paper, we give the following simple and intuitive template for k-robust problems: "having built some anticipatory solution, if there exists a single demand whose augmentation cost is larger than some threshold, augment the anticipatory solution to cover this demand as well, and repeat". In this paper we show that this template gives us improved approximation algorithms for k-robust Steiner tree and set cover, and the first approximation algorithms for k-robust Ste...
Robustness-Based Design Optimization Under Data Uncertainty
Zaman, Kais; McDonald, Mark; Mahadevan, Sankaran; Green, Lawrence
2010-01-01
This paper proposes formulations and algorithms for design optimization under both aleatory (i.e., natural or physical variability) and epistemic uncertainty (i.e., imprecise probabilistic information), from the perspective of system robustness. The proposed formulations deal with epistemic uncertainty arising from both sparse and interval data without any assumption about the probability distributions of the random variables. A decoupled approach is proposed in this paper to un-nest the robustness-based design from the analysis of non-design epistemic variables to achieve computational efficiency. The proposed methods are illustrated for the upper stage design problem of a two-stage-to-orbit (TSTO) vehicle, where the information on the random design inputs are only available as sparse point and/or interval data. As collecting more data reduces uncertainty but increases cost, the effect of sample size on the optimality and robustness of the solution is also studied. A method is developed to determine the optimal sample size for sparse point data that leads to the solutions of the design problem that are least sensitive to variations in the input random variables.
Wang, Leimin; Shen, Yi; Sheng, Yin
2016-04-01
This paper is concerned with the finite-time robust stabilization of delayed neural networks (DNNs) in the presence of discontinuous activations and parameter uncertainties. By using the nonsmooth analysis and control theory, a delayed controller is designed to realize the finite-time robust stabilization of DNNs with discontinuous activations and parameter uncertainties, and the upper bound of the settling time functional for stabilization is estimated. Finally, two examples are provided to demonstrate the effectiveness of the theoretical results.
Jun Song
2013-01-01
Full Text Available The nonfragile robust finite-time L2-L∞ control problem for a class of nonlinear uncertain systems with uncertainties and time-delays is considered. The nonlinear parameters are considered to satisfy the Lipschitz conditions and the exogenous disturbances are unknown but energy bounded. By using the Lyapunov function approach, the sufficient condition for the existence of nonfragile robust finite-time L2-L∞ controller is given in terms of linear matrix inequalities (LMIs. The finite-time controller is designed such that the resulting closed-loop system is finite-time bounded for all admissible uncertainties and satisfies the given L2-L∞ control index. Simulation results illustrate the validity of the proposed approach.
无
2007-01-01
The H∞ output feedback control problem for uncertain discrete-time switched systems is reasearched. A new characterization of stability and H∞ performance for the switched system under arbitrary switching is obtained by using switched Lyapunov function.Then,based on the characterization,a linear matrix inequality (LMI)approach is developed to design a switched output feedback controller which guarantees the stability and H∞ performance of the closed-loop system.A numerical example is presented to demonstrate the application of the proposed method.
M.Syed Ali
2011-01-01
In this paper,the global stability of Takagi-Sugeno(TS)uncertain stochastic fuzzy recurrent neural networks with discrete and distributed time-varying delays(TSUSFRNNs)is considered.A novel LMI-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of TSUSFRNNs.The proposed stability conditions are demonstrated through numerical examples.Furthermore,the supplementary requirement that the time derivative of time-varying delays must be smaller than one is removed.Comparison results are demonstrated to show that the proposed method is more able to guarantee the widest stability region than the other methods available in the existing literature.
Optimizing the robustness of electrical power systems against cascading failures.
Zhang, Yingrui; Yağan, Osman
2016-06-21
Electrical power systems are one of the most important infrastructures that support our society. However, their vulnerabilities have raised great concern recently due to several large-scale blackouts around the world. In this paper, we investigate the robustness of power systems against cascading failures initiated by a random attack. This is done under a simple yet useful model based on global and equal redistribution of load upon failures. We provide a comprehensive understanding of system robustness under this model by (i) deriving an expression for the final system size as a function of the size of initial attacks; (ii) deriving the critical attack size after which system breaks down completely; (iii) showing that complete system breakdown takes place through a first-order (i.e., discontinuous) transition in terms of the attack size; and (iv) establishing the optimal load-capacity distribution that maximizes robustness. In particular, we show that robustness is maximized when the difference between the capacity and initial load is the same for all lines; i.e., when all lines have the same redundant space regardless of their initial load. This is in contrast with the intuitive and commonly used setting where capacity of a line is a fixed factor of its initial load.
Vahid Azimi; Mohammad Bagher Menhaj; Ahmad Fakharian
2015-04-01
In this paper, a robust H2/H∞ control with regional Pole-Placement is considered for tool position control of a nonlinear uncertain flexible robot manipulator. The uncertain nonlinear system is first approximated by Takagi and Sugeno's (T-S) fuzzy model. To achieve a better tracking, an extra state (error of tracking) is then augmented to the T-S model. Based on each local linear subsystem with augmented state, a regional pole-placement state feedback H2/H∞ controller is properly designed via linear matrix inequality (LMI) approach. Parallel Distributed Compensation (PDC) is also used to establish the whole controller for the overall system and the total linear system is obtained by using the weighted sum of the local linear systems. A fuzzy weighted online computation (FWOC) component is employed to update fuzzy weights in real time for different operating points of the system. Simula-tion results are presented to validate the effectiveness of the proposed controller like robustness and good load disturbance attenuation and accurate tracking, even in the presence of parameter variations and also load disturbances on the motor and the tool. The superiority of the proposed control scheme is finally highlighted in comparison with the Quantitative feedback theory (QFT) controller, the QFT controller of order 13, a polynomial controller and the so-called linear sliding-mode controller methods.
Distributionally Robust Return-Risk Optimization Models and Their Applications
Li Yang
2014-01-01
Full Text Available Based on the risk control of conditional value-at-risk, distributionally robust return-risk optimization models with box constraints of random vector are proposed. They describe uncertainty in both the distribution form and moments (mean and covariance matrix of random vector. It is difficult to solve them directly. Using the conic duality theory and the minimax theorem, the models are reformulated as semidefinite programming problems, which can be solved by interior point algorithms in polynomial time. An important theoretical basis is therefore provided for applications of the models. Moreover, an application of the models to a practical example of portfolio selection is considered, and the example is evaluated using a historical data set of four stocks. Numerical results show that proposed methods are robust and the investment strategy is safe.
Robust Pitch Estimation Using an Optimal Filter on Frequency Estimates
Karimian-Azari, Sam; Jensen, Jesper Rindom; Christensen, Mads Græsbøll
2014-01-01
In many scenarios, a periodic signal of interest is often contaminated by different types of noise that may render many existing pitch estimation methods suboptimal, e.g., due to an incorrect white Gaussian noise assumption. In this paper, a method is established to estimate the pitch...... against different noise situations. The simulation results confirm that the proposed MVDR method outperforms the state-of-the-art weighted least squares (WLS) pitch estimator in colored noise and has robust pitch estimates against missing harmonics in some time-frames....... of such signals from unconstrained frequency estimates (UFEs). A minimum variance distortionless response (MVDR) method is proposed as an optimal solution to minimize the variance of UFEs considering the constraint of integer harmonics. The MVDR filter is designed based on noise statistics making it robust...
Robust C subroutines for non-linear optimization
Brock, Pernille; Madsen, Kaj; Nielsen, Hans Bruun
2004-01-01
This report presents a package of robust and easy-to-use C subroutines for solving unconstrained and constrained non-linear optimization problems. The intention is that the routines should use the currently best algorithms available. All routines have standardized calls, and the user does not have...... by changing 1 to 0. The present report is a new and updated version of a previous report NI-91-03 with the same title, [16]. Both the previous and the present report describe a collection of subroutines, which have been translated from Fortran to C. The reason for writing the present report is that some...... of the C subroutines have been replaced by more effective and robust versions translated from the original Fortran subroutines to C by the Bandler Group, see [1]. Also the test examples have been modi ed to some extent. For a description of the original Fortran subroutines see the report [17]. The software...
Robust C subroutines for non-linear optimization
Brock, Pernille; Madsen, Kaj; Nielsen, Hans Bruun
2004-01-01
to worry about special parameters controlling the iterations. For convenience we include an option for numerical checking of the user s implementation of the gradient. Note that another report [3] presents a collection of robust subroutines for both unconstrained and constrained optimization...... by changing 1 to 0. The present report is a new and updated version of a previous report NI-91-03 with the same title, [16]. Both the previous and the present report describe a collection of subroutines, which have been translated from Fortran to C. The reason for writing the present report is that some...... of the C subroutines have been replaced by more effective and robust versions translated from the original Fortran subroutines to C by the Bandler Group, see [1]. Also the test examples have been modi ed to some extent. For a description of the original Fortran subroutines see the report [17]. The software...
Seung Hyeop Yang
2013-01-01
Full Text Available This paper describes the synthesis of a robust and nonfragile H∞ Kalman-type filter design for a class of time-delay systems with polytopic uncertainties, filter-gain variations, and disturbances. We present the sufficient condition for filter existence and the method for designing a robust nonfragile H∞ filter by using LMIs (Linear Matrix Inequalities technique. Because the obtained sufficient condition can be represented as PLMIs (Parameterized Linear Matrix Inequalities, which can generate infinite LMIs, we use a relaxation technique to find finite solutions for a robust nonfragile H∞ filter. We show that the proposed filter can minimize estimation error in terms of parameter uncertainties, filter-fragility, and disturbances.
Optimal guaranteed cost control for an uncertain discrete T-S fuzzy system with time-delay
Renming WANG; Thierry Marie GUERRA; Juntao PAN
2009-01-01
This paper considers the guaranteed cost control problem for a class of uncertain discrete T-S fuzzy systems with time delay and a given quadratic cost function. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequalities (LMI) approach by constructing a specific nonquadratic Lyapunov-Krasovskii functional and a nonlinear PDC-like control law. A convex optimization problem is also formulated to select the optimal guaranteed cost controller that minimizes the upper bound of the closed-loop cost function. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed approaches.
Gao, Qing; Feng, Gang; Xi, Zhiyu; Wang, Yong; Qiu, Jianbin
2014-09-01
In this paper, a novel dynamic sliding mode control scheme is proposed for a class of uncertain stochastic nonlinear time-delay systems represented by Takagi-Sugeno fuzzy models. The key advantage of the proposed scheme is that two very restrictive assumptions in most existing sliding mode control approaches for stochastic fuzzy systems have been removed. It is shown that the closed-loop control system trajectories can be driven onto the sliding surface in finite time almost certainly. It is also shown that the stochastic stability of the resulting sliding motion can be guaranteed in terms of linear matrix inequalities; moreover, the sliding-mode controller can be obtained simultaneously. Simulation results illustrating the advantages and effectiveness of the proposed approaches are also provided.
Hard and soft sub-time-optimal controllers for a mechanical system with uncertain mass
Kulczycki, P.; Wisniewski, Rafal; Kowalski, P.
2004-01-01
by parameters selected in accordance with the rules of the statistical decision theory; however, the soft structure allows additionally to eliminate rapid changes in control values. The object is a basic mechanical system, with uncertain (also non-stationary) mass treated as a stochastic process...
Hard and soft Sub-Time-Optimal Controllers for a Mechanical System with Uncertain Mass
Kulczycki, P.; Wisniewski, Rafal; Kowalski, P.
2005-01-01
by parameters selected in accordance with the rules of the statistical decision theory; however, the soft structure allows additionally to eliminate rapid changes in control values. The object is a basic mechanical system, with uncertain (also non-stationary) mass treated as a stochastic process...
嵇小辅; 杨泽斌; 孙玉坤; 苏宏业
2008-01-01
The problem of roust stabilization for linear time-varying uncertain periodic descriptor systems is revisited. Based on the concept of robust stability for linear time-varying uncer-tain periodic descriptor systems, a necessary and sufficient con-dition for robust stability is put forward. The robust stabiliza-tion problem is also studied and the corresponding necessary and sufficient condition is given using the notation of dual system.The obtained matrix inequality conditions can be transformed to linear matrix inequality ones with the introduction of some free matrices, which makes the analysis and design procedure simple and reliable.
A Novel and Robust Evolution Algorithm for Optimizing Complicated Functions
Gao, Yifeng; Zhao, Ge
2011-01-01
In this paper, a novel mutation operator of differential evolution algorithm is proposed. A new algorithm called divergence differential evolution algorithm (DDEA) is developed by combining the new mutation operator with divergence operator and assimilation operator (divergence operator divides population, and, assimilation operator combines population), which can detect multiple solutions and robustness in noisy environment. The new algorithm is applied to optimize Michalewicz Function and to track changing of rain-induced-attenuation process. The results based on DDEA are compared with those based on Differential Evolution Algorithm (DEA). It shows that DDEA algorithm gets better results than DEA does in the same premise. The new algorithm is significant for optimizing and tracking the characteristics of MIMO (Multiple Input Multiple Output) channel at millimeter waves.
DOE Based Robust Optimization Considering Tolerance Bands of Design Parameters
Lee, Jongsoo; Ahn, Byongchul
The paper describes a robust optimization method to account for the tolerance of design variable and the variation in problem parameter. The proposed post-optimization effort is initiated from the deterministic optimum as a baseline. The successive process to find search directions and step sizes toward the robust optimum is conducted by determining the worst design that has the highest level in constraint violation. During the selection of the worst design, an orthogonal array table in the context of design of experiemtns (DOE) is used to reduce the constraint function evaluations especially for higher dimensionality problem. The analysis of means (ANOM) is adopted in a case where the variation in problem parameter is considered. The measurement criterion to select the worst design is based on the degree of cumulative constraint violation. A mathematical function problem is first conducted to examine the tolerance of design variable. A cantilever beam problem described by four design variables and a bracket problem with seven design variables are subsequently explored by considering both tolerance of design variable and variation in problem parameter.
B. Bisselink
2016-12-01
New hydrological insights: Results indicate large discrepancies in terms of the linear correlation (r, bias (β and variability (γ between the observed and simulated streamflows when using different precipitation estimates as model input. The best model performance was obtained with products which ingest gauge data for bias correction. However, catchment behavior was difficult to be captured using a single parameter set and to obtain a single robust parameter set for each catchment, which indicate that transposing model parameters should be carried out with caution. Model parameters depend on the precipitation characteristics of the calibration period and should therefore only be used in target periods with similar precipitation characteristics (wet/dry.
无
2011-01-01
This paper proposed a design method for delay-dependent robust H-infinity filter of linear systems with uncertainty and time-varying interval delay.The proposed method was shown to be much simpler than existing ones while giving significant improvement to the existing results.The key step in the method was to construct a special type of Lyapunov functional for the filter design problem.Unlike the existing techniques,the proposed method employed neither free weighting matrices nor any model transformation,le...
Xianming ZHANG; Min WU; Jinhua SHE; Dongsheng HAN
2006-01-01
This paper examines the delay-dependent H-infinity control problem for discrete-time linear systems with time-varying state delays and norm-bounded uncertainties. A new inequality for the finite sum of quadratic terms is first established. Then, some new delay-dependent criteria are derived by employing the new inequality to guarantee the robust stability of a closed-loop system with a prescribed H-infinity norm bound for all admissible uncertainties and bounded time-vary delays. A numerical example demonstrates that the proposed method is an improvement over existing ones.
Kaibo Shi
2014-01-01
Full Text Available This paper is concerned with the problem of delay-dependent robust stability analysis for a class of uncertain neutral type Lur’e systems with mixed time-varying delays. The system has not only time-varying uncertainties and sector-bounded nonlinearity, but also discrete and distributed delays, which has never been discussed in the previous literature. Firstly, by employing one effective mathematical technique, some less conservative delay-dependent stability results are established without employing the bounding technique and the mode transformation approach. Secondly, by constructing an appropriate new type of Lyapunov-Krasovskii functional with triple terms, improved delay-dependent stability criteria in terms of linear matrix inequalities (LMIs derived in this paper are much brief and valid. Furthermore, both nonlinearities located in finite sector and infinite one have been also fully taken into account. Finally, three numerical examples are presented to illustrate lesser conservatism and the advantage of the proposed main results.
Niu, Gang; Zhao, Yajun; Defoort, Michael; Pecht, Michael
2015-01-01
To improve reliability, safety and efficiency, advanced methods of fault detection and diagnosis become increasingly important for many technical fields, especially for safety related complex systems like aircraft, trains, automobiles, power plants and chemical plants. This paper presents a robust fault detection and diagnostic scheme for a multi-energy domain system that integrates a model-based strategy for system fault modeling and a data-driven approach for online anomaly monitoring. The developed scheme uses LFT (linear fractional transformations)-based bond graph for physical parameter uncertainty modeling and fault simulation, and employs AAKR (auto-associative kernel regression)-based empirical estimation followed by SPRT (sequential probability ratio test)-based threshold monitoring to improve the accuracy of fault detection. Moreover, pre- and post-denoising processes are applied to eliminate the cumulative influence of parameter uncertainty and measurement uncertainty. The scheme is demonstrated on the main unit of a locomotive electro-pneumatic brake in a simulated experiment. The results show robust fault detection and diagnostic performance.
Xiaomei Qi
2012-01-01
Full Text Available A robust fault-tolerant controller design problem for networked control system (NCS with random packet dropout in both sensor-to-controller link and controller-to-actuator link is investigated. A novel stochastic NCS model with state-delay, model uncertainty, disturbance, probabilistic sensor failure, and actuator failure is proposed. The random packet dropout, sensor failures, and actuator failures are characterized by a binary random variable. The sufficient condition for asymptotical mean-square stability of NCS is derived and the closed-loop NCS satisfies H∞ performance constraints caused by the random packet dropout and disturbance. The fault-tolerant controller is designed by solving a linear matrix inequality. A numerical example is presented to illustrate the effectiveness of the proposed method.
Jinxing Lin; Shumin Fei; Jiong Shen
2010-01-01
The problems of robust stability and stabilization via memoryless state feedback for a class of discrete-time switched singular systems with time-varying delays and linear fractional uncertainties are investigated.By constructing a novel switched Lyapunov-Krasovskii functional,a delay-dependent criterion for the unforced system to be regular,causal and uniformly asymptotically stable is established in terms of linear matrix inequalities(LMIs).An explicit expression for the desired memoryless state feedback stabilization controller is also given.The merits of the proposed criteria lie in their less conservativeness and relative simplicity,which are achieved by considering additionally useful terms(ignored in previous methods)when estimating the upper bound of the forward difference of the Lyapunov-Krasovskii functional and by avoiding utilizing any model augmentation transformation.Some numerical examples are provided to illustrate the validity of the proposed methods.
Hiwa Farughi
2016-05-01
Full Text Available In this paper, robust optimization of a bi-objective mathematical model in a dynamic cell formation problem considering labor utilization with uncertain data is carried out. The robust approach is used to reduce the effects of fluctuations of the uncertain parameters with regards to all the possible future scenarios. In this research, cost parameters of the cell formation and demand fluctuations are subject to uncertainty and a mixed-integer programming (MIP model is developed to formulate the related robust dynamic cell formation problem. Then the problem is transformed into a bi-objective linear one. The first objective function seeks to minimize relevant costs of the problem including machine procurement and relocation costs, machine variable cost, inter-cell movement and intra-cell movement costs, overtime cost and labor shifting cost between cells, machine maintenance cost, inventory, holding part cost. The second objective function seeks to minimize total man-hour deviations between cells or indeed labor utilization of the modeled.
Robust Source Localization in Shallow Water Based on Vector Optimization
SONG Hai-yan; SHI Jie; LIU Bo-sheng
2013-01-01
Owing to the multipath effect,the source localization in shallow water has been an area of active interest.However,most methods for source localization in shallow water are sensitive to the assumed model of the underwater environment and have poor robustness against the underwater channel uncertainty,which limit their further application in practical engineering.In this paper,a new method of source localization in shallow water,based on vector optimization concept,is described,which is highly robust against environmental factors affecting the localization,such as the channel depth,the bottom reflection coefficients,and so on.Through constructing the uncertainty set of the source vector errors and extracting the multi-path sound rays from the sea surface and bottom,the proposed method can accurately localize one or more sources in shallow water dominated by multipath propagation.It turns out that the natural formulation of our approach involves minimization of two quadratic functions subject to infinitely many nonconvex quadratic constraints.It shows that this problem (originally intractable) can be reformulated in a convex form as the so-called second-order cone program (SOCP) and solved efficiently by using the well-established interior point method,such as the software tool,SeDuMi.Computer simulations show better performance of the proposed method as compared with existing algorithms and establish a theoretical foundation for the practical engineering application.
Robust source localization in shallow water based on vector optimization
Song, Hai-yan; Shi, Jie; Liu, Bo-sheng
2013-06-01
Owing to the multipath effect, the source localization in shallow water has been an area of active interest. However, most methods for source localization in shallow water are sensitive to the assumed model of the underwater environment and have poor robustness against the underwater channel uncertainty, which limit their further application in practical engineering. In this paper, a new method of source localization in shallow water, based on vector optimization concept, is described, which is highly robust against environmental factors affecting the localization, such as the channel depth, the bottom reflection coefficients, and so on. Through constructing the uncertainty set of the source vector errors and extracting the multi-path sound rays from the sea surface and bottom, the proposed method can accurately localize one or more sources in shallow water dominated by multipath propagation. It turns out that the natural formulation of our approach involves minimization of two quadratic functions subject to infinitely many nonconvex quadratic constraints. It shows that this problem (originally intractable) can be reformulated in a convex form as the so-called second-order cone program (SOCP) and solved efficiently by using the well-established interior point method, such as the software tool, SeDuMi. Computer simulations show better performance of the proposed method as compared with existing algorithms and establish a theoretical foundation for the practical engineering application.
Robust Optimization of the Self- scheduling and Market Involvement for an Electricity Producer
Lima, Ricardo
2015-01-07
This work address the optimization under uncertainty of the self-scheduling, forward contracting, and pool involvement of an electricity producer operating a mixed power generation station, which combines thermal, hydro and wind sources, and uses a two-stage adaptive robust optimization approach. In this problem the wind power production and the electricity pool price are considered to be uncertain, and are described by uncertainty convex sets. Two variants of a constraint generation algorithm are proposed, namely a primal and dual version, and they are used to solve two case studies based on two different producers. Their market strategies are investigated for three different scenarios, corresponding to as many instances of electricity price forecasts. The effect of the producers’ approach, whether conservative or more risk prone, is also investigated by solving each instance for multiple values of the so-called budget parameter. It was possible to conclude that this parameter influences markedly the producers’ strategy, in terms of scheduling, profit, forward contracting, and pool involvement. Regarding the computational results, these show that for some instances, the two variants of the algorithms have a similar performance, while for a particular subset of them one variant has a clear superiority
Dezhi Zhang
2015-12-01
Full Text Available This article proposes a new model to address the design problem of a sustainable regional logistics network with uncertainty in future logistics demand. In the proposed model, the future logistics demand is assumed to be a random variable with a given probability distribution. A set of chance constraints with regard to logistics service capacity and environmental impacts is incorporated to consider the sustainability of logistics network design. The proposed model is formulated as a two-stage robust optimization problem. The first-stage problem before the realization of future logistics demand aims to minimize a risk-averse objective by determining the optimal location and size of logistics parks with CO2 emission taxes consideration. The second stage after the uncertain logistics demand has been determined is a scenario-based stochastic logistics service route choices equilibrium problem. A heuristic solution algorithm, which is a combination of penalty function method, genetic algorithm, and Gauss–Seidel decomposition approach, is developed to solve the proposed model. An illustrative example is given to show the application of the proposed model and solution algorithm. The findings show that total social welfare of the logistics system depends very much on the level of uncertainty in future logistics demand, capital budget for logistics parks, and confidence levels of the chance constraints.
Robust optimization of robotic pick and place operations for deformable objects through simulation
Bo Jorgensen, Troels; Debrabant, Kristian; Kruger, Norbert
2016-01-01
This paper discusses various optimization schemes for partly stochastic and bound optimization, particular with application to solve robotic optimization problems, where robustness of the solutions is crucial. The use case revolves around grasping and manipulation of deformable objects. These kin...
Stretching the limits of forming processes by robust optimization: A demonstrator
Wiebenga, J.H.; Atzema, E.H.; Atzema, E.H.; van den Boogaard, Antonius H.; Yoon, Jeong Whan; Stoughton, Thomas B.; Rolfe, Bernard; Beynon, John H.; Hodgson, Peter
2014-01-01
Robust design of forming processes using numerical simulations is gaining attention throughout the industry. In this work, it is demonstrated how robust optimization can assist in further stretching the limits of metal forming processes. A deterministic and a robust optimization study are performed,
Robust Optimization Design Algorithm for High-Frequency TWTs
Wilson, Jeffrey D.; Chevalier, Christine T.
2010-01-01
Traveling-wave tubes (TWTs), such as the Ka-band (26-GHz) model recently developed for the Lunar Reconnaissance Orbiter, are essential as communication amplifiers in spacecraft for virtually all near- and deep-space missions. This innovation is a computational design algorithm that, for the first time, optimizes the efficiency and output power of a TWT while taking into account the effects of dimensional tolerance variations. Because they are primary power consumers and power generation is very expensive in space, much effort has been exerted over the last 30 years to increase the power efficiency of TWTs. However, at frequencies higher than about 60 GHz, efficiencies of TWTs are still quite low. A major reason is that at higher frequencies, dimensional tolerance variations from conventional micromachining techniques become relatively large with respect to the circuit dimensions. When this is the case, conventional design- optimization procedures, which ignore dimensional variations, provide inaccurate designs for which the actual amplifier performance substantially under-performs that of the design. Thus, this new, robust TWT optimization design algorithm was created to take account of and ameliorate the deleterious effects of dimensional variations and to increase efficiency, power, and yield of high-frequency TWTs. This design algorithm can help extend the use of TWTs into the terahertz frequency regime of 300-3000 GHz. Currently, these frequencies are under-utilized because of the lack of efficient amplifiers, thus this regime is known as the "terahertz gap." The development of an efficient terahertz TWT amplifier could enable breakthrough applications in space science molecular spectroscopy, remote sensing, nondestructive testing, high-resolution "through-the-wall" imaging, biomedical imaging, and detection of explosives and toxic biochemical agents.
MohammadReza Davoodi
2009-12-01
Full Text Available This paper offers a design procedure for robust stability, robust H-infinity control and robust H2 control via dynamic output feedback for a class of uncertain linear systems. The uncertainties are of norm bounded type. Then in order to support a high-speed energy storage flywheel, these procedures are applied to an active radial magnetic bearing system. The state space matrices of this controller are the solution of some linear matrix inequalities (LMIs.
Optimal Investment and Reinsurance for Insurers with Uncertain Time-Horizon
Ailing Gu
2014-01-01
state hits the barrier. The objective of the insurer is to maximize the expected discounted exponential utility of her terminal wealth. By dynamic programming approach and Feynman-Kac representation theorem, we derive the expressions for optimal value functions and optimal investment-reinsurance strategies in two special cases. Furthermore, an example is considered under the diffusion-approximation model, which shows some interesting results.
Further Result on Robust Stabilization for Uncertain Nonlinear Time-delay Systems%不确定非线性时滞系统鲁棒镇定化研究
焦晓红; 申铁龙; 孙元章
2007-01-01
The systematic recursive design method of the robust stabilizing controller for general uncertain nonlinear time-delay systems is investigated in this paper. A delay-independent state feedback control law can be obtained by recursively constructing Lyapunov-Razumikhin function. It is shown that by some design techniques the obstacle that is intrinsic to the application of the Razumikhin condition can be removed such that the design of the robust stabilizing control law is free of any restriction for the systems.
A robust Kalman framework with resampling and optimal smoothing.
Kautz, Thomas; Eskofier, Bjoern M
2015-02-27
The Kalman filter (KF) is an extremely powerful and versatile tool for signal processing that has been applied extensively in various fields. We introduce a novel Kalman-based analysis procedure that encompasses robustness towards outliers, Kalman smoothing and real-time conversion from non-uniformly sampled inputs to a constant output rate. These features have been mostly treated independently, so that not all of their benefits could be exploited at the same time. Here, we present a coherent analysis procedure that combines the aforementioned features and their benefits. To facilitate utilization of the proposed methodology and to ensure optimal performance, we also introduce a procedure to calculate all necessary parameters. Thereby, we substantially expand the versatility of one of the most widely-used filtering approaches, taking full advantage of its most prevalent extensions. The applicability and superior performance of the proposed methods are demonstrated using simulated and real data. The possible areas of applications for the presented analysis procedure range from movement analysis over medical imaging, brain-computer interfaces to robot navigation or meteorological studies.
A Robust Kalman Framework with Resampling and Optimal Smoothing
Thomas Kautz
2015-02-01
Full Text Available The Kalman filter (KF is an extremely powerful and versatile tool for signal processing that has been applied extensively in various fields. We introduce a novel Kalman-based analysis procedure that encompasses robustness towards outliers, Kalman smoothing and real-time conversion from non-uniformly sampled inputs to a constant output rate. These features have been mostly treated independently, so that not all of their benefits could be exploited at the same time. Here, we present a coherent analysis procedure that combines the aforementioned features and their benefits. To facilitate utilization of the proposed methodology and to ensure optimal performance, we also introduce a procedure to calculate all necessary parameters. Thereby, we substantially expand the versatility of one of the most widely-used filtering approaches, taking full advantage of its most prevalent extensions. The applicability and superior performance of the proposed methods are demonstrated using simulated and real data. The possible areas of applications for the presented analysis procedure range from movement analysis over medical imaging, brain-computer interfaces to robot navigation or meteorological studies.
Dual-mode nested search method for categorical uncertain multi-objective optimization
Tang, Long; Wang, Hu
2016-10-01
Categorical multi-objective optimization is an important issue involved in many matching design problems. Non-numerical variables and their uncertainty are the major challenges of such optimizations. Therefore, this article proposes a dual-mode nested search (DMNS) method. In the outer layer, kriging metamodels are established using standard regular simplex mapping (SRSM) from categorical candidates to numerical values. Assisted by the metamodels, a k-cluster-based intelligent sampling strategy is developed to search Pareto frontier points. The inner layer uses an interval number method to model the uncertainty of categorical candidates. To improve the efficiency, a multi-feature convergent optimization via most-promising-area stochastic search (MFCOMPASS) is proposed to determine the bounds of objectives. Finally, typical numerical examples are employed to demonstrate the effectiveness of the proposed DMNS method.
加工时间不确定的柔性作业车间鲁棒调度方法%Robust Scheduling on Flexible Job Shop with Uncertain Processing Time
汪俊亮; 张洁; 秦威; 银莉; 陈定方
2015-01-01
This paper investigated the flexible job-shop scheduling problem (FJSP)with uncertain processing time in a multi-type and low-volume environment.A minimax regret based robust schedu-ling model was built to minimize the makespan.A novel sequential search rule was put forward to re-duce the calculation amount of the algorithm and a two stage genetic algorithm was designed to figure out the redundant and optimal solutions.Orthogonal test was designed to optimize significant parame-ters,and then,a simulation model was established to evaluate the robustness and obj ective perform-ance of the algorithm.The results show the proposed algorithm has a better performance than genetic algorithm on flexible j ob-shop scheduling problem under uncertain and dynamic environment.%针对中小批量环境下加工时间不确定的柔性作业车间调度问题，采用冗余处理方法构建了以最大完工时间为目标的鲁棒调度模型。为降低算法的搜索规模和提高算法的求解速度，提出了顺序搜索机制，并设计两阶段遗传算法，分阶段获取冗余状态和最优结果。采用某柔性生产线的数据进行正交试验，优化了算法关键参数，并构建了柔性生产线仿真模型，对调度结果的鲁棒性和优化目标性能进行了分析。结果表明，该算法在目标性能和鲁棒性上都显著优于标准遗传算法，能有效处理加工时间不确定的柔性作业车间调度问题。
Mixed H2／H∞ Optimal Guaranteed Cost Control of Uncertain Linear Systems
GuodingChen; MayingYang; LiYu
2004-01-01
The mixed H2/H∞ guaranteed cost control problem via state feedback control laws is considered in this paper for linear systems with norm-bounded parameter uncertainty. Based on the linear matrix inequality (LMI) approach, sufficient conditions are derived for the existence of guaranteed cost controllers whihc guarantee not only a prespecified H∞ disturbance attenuation level on one controlled output for all admissible parameter uncertainties, but also the worst-case H2 performance index on the other controlled output to be no more than a specified bound. Furthermore, a convex optimization problem is formulated to design an optimal H2/H∞ guaranteed cost controller.
Tossaporn Chamsai
2015-01-01
Full Text Available The sliding mode control (SMC technique with a first-order low-pass filter (LPF is incorporated with a new adaptive PID controller. It is proposed for tracking control of an uncertain nonlinear system. In the proposed control scheme, the adaptation law is able to update the PID controller online during the control process within a short period. The chattering phenomenon of the SMC can be alleviated by incorporation of a first-order LPF, while the robustness of the control system is similar to that of the sliding mode. In the closed-loop control analysis, the convergence condition in the reaching phase and the existence condition of the sliding mode were analyzed. The stability of the closed-loop control is guaranteed in the sense of Lyapunov’s direct method. The simulations and experimental applications of a speed tracking control of a spark ignition (SI engine via electronic throttle valve control architecture are provided to verify the effectiveness and the feasibility of the proposed control scheme.
A new pragmatic approach to solve the problems of vector optimization with uncertain parameters
Reizlin, V. I.; Nefedova, A. A.
2016-04-01
In this paper, we consider the method for solving problems of multi-criteria optimization with mathematical models that contain a lot of variables. The values of these variables are not regulated by a decision-maker. We introduce a new concept of 'tolerance of the decision variant'. This concept is similar to such concepts as stability, survivability, etc.
Hartcher-O'Brien, Jess; Di Luca, Massimiliano; Ernst, Marc O.
2014-01-01
Often multisensory information is integrated in a statistically optimal fashion where each sensory source is weighted according to its precision. This integration scheme is statistically optimal because it theoretically results in unbiased perceptual estimates with the highest precision possible. There is a current lack of consensus about how the nervous system processes multiple sensory cues to elapsed time. In order to shed light upon this, we adopt a computational approach to pinpoint the integration strategy underlying duration estimation of audio/visual stimuli. One of the assumptions of our computational approach is that the multisensory signals redundantly specify the same stimulus property. Our results clearly show that despite claims to the contrary, perceived duration is the result of an optimal weighting process, similar to that adopted for estimates of space. That is, participants weight the audio and visual information to arrive at the most precise, single duration estimate possible. The work also disentangles how different integration strategies – i.e. considering the time of onset/offset of signals - might alter the final estimate. As such we provide the first concrete evidence of an optimal integration strategy in human duration estimates. PMID:24594578
Stochastic optimization of mine production scheduling with uncertain ore/metal/waste supply
Leite Andre; Dimitrakopoulos Roussos
2014-01-01
Optimization of long-term mine production scheduling in open pit mines deals with the management of cash flows, typically in the order of hundreds of millions of dollars. Conventional mine scheduling utilizes optimization methods that are not capable of accounting for inherent technical uncertainties such as uncertainty in the expected ore/metal supply from the underground, acknowledged to be the most critical factor. To integrate ore/metal uncertainty into the optimization of mine production scheduling a stochastic integer programming (SIP) formulation is tested at a copper deposit. The stochastic solution maximizes the economic value of a project and minimizes deviations from production targets in the pres-ence of ore/metal uncertainty. Unlike the conventional approach, the SIP model accounts and manages risk in ore supply, leading to a mine production schedule with a 29%higher net present value than the schedule obtained from the conventional, industry-standard optimization approach, thus contributing to improving the management and sustainable utilization of mineral resources.
Optimized Energy Procurement for Cellular Networks with Uncertain Renewable Energy Generation
Rached, Nadhir B.
2017-02-07
Renewable energy (RE) is an emerging solution for reducing carbon dioxide (CO2) emissions from cellular networks. One of the challenges of using RE sources is to handle its inherent uncertainty. In this paper, a RE powered cellular network is investigated. For a one-day operation cycle, the cellular network aims to reduce energy procurement costs from the smart grid by optimizing the amounts of energy procured from their locally deployed RE sources as well as from the smart grid. In addition to that, it aims to determine the extra amount of energy to be sold to the electrical grid at each time period. Chance constrained optimization is first proposed to deal with the randomness in the RE generation. Then, to make the optimization problem tractable, two well- know convex approximation methods, namely; Chernoff and Chebyshev based-approaches, are analyzed in details. Numerical results investigate the optimized energy procurement for various daily scenarios and compare between the performances of the employed convex approximation approaches.
Optimization Models for Robust and Power Efficient Networks
2016-01-01
With the ever increasing traffic demands in the networks, it has become essential to design networks that are robust to different traffic conditions. The common approach of proceeding by over-provisioning to accommodate traffic change, or events such as link failures, leads to a massive waste of resource and energy. On the other hand, it is challenging to provide solutions which are robust to traffic change due to unpredictable nature of the traffic. This thesis focuses on providing robust op...
WANG, Qingrong; ZHU, Changfeng; LI, Ying; ZHANG, Zhengkun
2017-06-01
Considering the time dependence of emergency logistic network and complexity of the environment that the network exists in, in this paper the time dependent network optimization theory and robust discrete optimization theory are combined, and the emergency logistics dynamic network optimization model with characteristics of robustness is built to maximize the timeliness of emergency logistics. On this basis, considering the complexity of dynamic network and the time dependence of edge weight, an improved ant colony algorithm is proposed to realize the coupling of the optimization algorithm and the network time dependence and robustness. Finally, a case study has been carried out in order to testify validity of this robustness optimization model and its algorithm, and the value of different regulation factors was analyzed considering the importance of the value of the control factor in solving the optimal path. Analysis results show that this model and its algorithm above-mentioned have good timeliness and strong robustness.
Fuzzy controller for an uncertain dynamical system
Kulczycki, P.; Wisniewski, Rafal
2002-01-01
The present paper deals with the time-optimal control for mechanical systems with uncertain load. A fuzzy approach is used in the design of suboptimal feedback controllers, robust with respect to the load. Statistical kernel estimators are used for the specification of crucial parameters. The met......The present paper deals with the time-optimal control for mechanical systems with uncertain load. A fuzzy approach is used in the design of suboptimal feedback controllers, robust with respect to the load. Statistical kernel estimators are used for the specification of crucial parameters....... The methodology proposed in this work may be easily adopted to other modeling uncertainties of mechanical systems, e.g. motion resistance....
Yang, Wen; Fung, Richard Y. K.
2014-06-01
This article considers an order acceptance problem in a make-to-stock manufacturing system with multiple demand classes in a finite time horizon. Demands in different periods are random variables and are independent of one another, and replenishments of inventory deviate from the scheduled quantities. The objective of this work is to maximize the expected net profit over the planning horizon by deciding the fraction of the demand that is going to be fulfilled. This article presents a stochastic order acceptance optimization model and analyses the existence of the optimal promising policies. An example of a discrete problem is used to illustrate the policies by applying the dynamic programming method. In order to solve the continuous problems, a heuristic algorithm based on stochastic approximation (HASA) is developed. Finally, the computational results of a case example illustrate the effectiveness and efficiency of the HASA approach, and make the application of the proposed model readily acceptable.
Optimally managing water resources in large river basins for an uncertain future
Edwin A. Roehl, Jr.; Conrads, Paul A.
2014-01-01
Managers of large river basins face conflicting needs for water resources such as wildlife habitat, water supply, wastewater assimilative capacity, flood control, hydroelectricity, and recreation. The Savannah River Basin for example, has experienced three major droughts since 2000 that resulted in record low water levels in its reservoirs, impacting local economies for years. The Savannah River Basin’s coastal area contains municipal water intakes and the ecologically sensitive freshwater tidal marshes of the Savannah National Wildlife Refuge. The Port of Savannah is the fourth busiest in the United States, and modifications to the harbor have caused saltwater to migrate upstream, reducing the freshwater marsh’s acreage more than 50 percent since the 1970s. There is a planned deepening of the harbor that includes flow-alteration features to minimize further migration of salinity. The effectiveness of the flow-alteration features will only be known after they are constructed. One of the challenges of basin management is the optimization of water use through ongoing development, droughts, and climate change. This paper describes a model of the Savannah River Basin designed to continuously optimize regulated flow to meet prioritized objectives set by resource managers and stakeholders. The model was developed from historical data by using machine learning, making it more accurate and adaptable to changing conditions than traditional models. The model is coupled to an optimization routine that computes the daily flow needed to most efficiently meet the water-resource management objectives. The model and optimization routine are packaged in a decision support system that makes it easy for managers and stakeholders to use. Simulation results show that flow can be regulated to significantly reduce salinity intrusions in the Savannah National Wildlife Refuge while conserving more water in the reservoirs. A method for using the model to assess the effectiveness of the
Optimizing fermentation process miscanthus-to-ethanol biorefinery scale under uncertain conditions
Bomberg, Matthew; Sanchez, Daniel L.; Lipman, Timothy E.
2014-05-01
Ethanol produced from cellulosic feedstocks has garnered significant interest for greenhouse gas abatement and energy security promotion. One outstanding question in the development of a mature cellulosic ethanol industry is the optimal scale of biorefining activities. This question is important for companies and entrepreneurs seeking to construct and operate cellulosic ethanol biorefineries as it determines the size of investment needed and the amount of feedstock for which they must contract. The question also has important implications for the nature and location of lifecycle environmental impacts from cellulosic ethanol. We use an optimization framework similar to previous studies, but add richer details by treating many of these critical parameters as random variables and incorporating a stochastic sub-model for land conversion. We then use Monte Carlo simulation to obtain a probability distribution for the optimal scale of a biorefinery using a fermentation process and miscanthus feedstock. We find a bimodal distribution with a high peak at around 10-30 MMgal yr-1 (representing circumstances where a relatively low percentage of farmers elect to participate in miscanthus cultivation) and a lower and flatter peak between 150 and 250 MMgal yr-1 (representing more typically assumed land-conversion conditions). This distribution leads to useful insights; in particular, the asymmetry of the distribution—with significantly more mass on the low side—indicates that developers of cellulosic ethanol biorefineries may wish to exercise caution in scale-up.
When are Static and Adjustable Robust Optimization with Constraint-Wise Uncertainty Equivalent?
Marandi, Ahmadreza; den Hertog, Dick
2015-01-01
Adjustable Robust Optimization (ARO) yields, in general, better worst-case solutions than static Robust Optimization (RO). However, ARO is computationally more difficult than RO. In this paper, we derive conditions under which the worst-case objective values of ARO and RO problems are equal. We prov
The Evolutionary Algorithm to Find Robust Pareto-Optimal Solutions over Time
Meirong Chen
2015-01-01
Full Text Available In dynamic multiobjective optimization problems, the environmental parameters change over time, which makes the true pareto fronts shifted. So far, most works of research on dynamic multiobjective optimization methods have concentrated on detecting the changed environment and triggering the population based optimization methods so as to track the moving pareto fronts over time. Yet, in many real-world applications, it is not necessary to find the optimal nondominant solutions in each dynamic environment. To solve this weakness, a novel method called robust pareto-optimal solution over time is proposed. It is in fact to replace the optimal pareto front at each time-varying moment with the series of robust pareto-optimal solutions. This means that each robust solution can fit for more than one time-varying moment. Two metrics, including the average survival time and average robust generational distance, are present to measure the robustness of the robust pareto solution set. Another contribution is to construct the algorithm framework searching for robust pareto-optimal solutions over time based on the survival time. Experimental results indicate that this definition is a more practical and time-saving method of addressing dynamic multiobjective optimization problems changing over time.
Study on Stochastic Optimal Electric Power Procurement Strategies with Uncertain Market Prices
Sakchai, Siripatanakulkhajorn; Saisho, Yuichi; Fujii, Yasumasa; Yamaji, Kenji
The player in deregulated electricity markets can be categorized into three groups of GENCO (Generator Companies), TRNASCO (Transmission Companies), DISCO (Distribution Companies). This research focuses on the role of Distribution Companies, which purchase electricity from market at randomly fluctuating prices, and provide it to their customers at given fixed prices. Therefore Distribution companies have to take the risk stemming from price fluctuation of electricity instead of the customers. This entails the necessity to develop a certain method to make an optimal strategy for electricity procurement. In such a circumstance, this research has the purpose for proposing the mathematical method based on stochastic dynamic programming to evaluate the value of a long-term bilateral contract of electricity trade, and also a project of combination of the bilateral contract and power generation with their own generators for procuring electric power in deregulated market.
The Orienteering Problem under Uncertainty Stochastic Programming and Robust Optimization compared
Evers, L.; Glorie, K.; Ster, S. van der; Barros, A.I.; Monsuur, H.
2012-01-01
The Orienteering Problem (OP) is a generalization of the well-known traveling salesman problem and has many interesting applications in logistics, tourism and defense. To reflect real-life situations, we focus on an uncertain variant of the OP. Two main approaches that deal with optimization under u
Multivariable robust digital controller design by convex optimization
2004-01-01
The dissertation is essentially concerned with methods of robust digital multivariable and monovariable controller design. For controller desing, a linear discrete-time model of plant to be controlled is used. The controller robustness is treated by sensitivity frequency analysis(sensitivity is transfer function/matrix of closed loop). Correspondingly to H∞ design, the singular values of frequency responses are used for the analysis.The work is divided into five parts. The first part concerns...
Manfredi, Sabato
2016-06-01
Large-scale dynamic systems are becoming highly pervasive in their occurrence with applications ranging from system biology, environment monitoring, sensor networks, and power systems. They are characterised by high dimensionality, complexity, and uncertainty in the node dynamic/interactions that require more and more computational demanding methods for their analysis and control design, as well as the network size and node system/interaction complexity increase. Therefore, it is a challenging problem to find scalable computational method for distributed control design of large-scale networks. In this paper, we investigate the robust distributed stabilisation problem of large-scale nonlinear multi-agent systems (briefly MASs) composed of non-identical (heterogeneous) linear dynamical systems coupled by uncertain nonlinear time-varying interconnections. By employing Lyapunov stability theory and linear matrix inequality (LMI) technique, new conditions are given for the distributed control design of large-scale MASs that can be easily solved by the toolbox of MATLAB. The stabilisability of each node dynamic is a sufficient assumption to design a global stabilising distributed control. The proposed approach improves some of the existing LMI-based results on MAS by both overcoming their computational limits and extending the applicative scenario to large-scale nonlinear heterogeneous MASs. Additionally, the proposed LMI conditions are further reduced in terms of computational requirement in the case of weakly heterogeneous MASs, which is a common scenario in real application where the network nodes and links are affected by parameter uncertainties. One of the main advantages of the proposed approach is to allow to move from a centralised towards a distributed computing architecture so that the expensive computation workload spent to solve LMIs may be shared among processors located at the networked nodes, thus increasing the scalability of the approach than the network
Robust Optimization Using Supremum of the Objective Function for Nonlinear Programming Problems
Lee, Se Jung; Park, Gyung Jin [Hanyang University, Seoul (Korea, Republic of)
2014-05-15
In the robust optimization field, the robustness of the objective function emphasizes an insensitive design. In general, the robustness of the objective function can be achieved by reducing the change of the objective function with respect to the variation of the design variables and parameters. However, in conventional methods, when an insensitive design is emphasized, the performance of the objective function can be deteriorated. Besides, if the numbers of the design variables are increased, the numerical cost is quite high in robust optimization for nonlinear programming problems. In this research, the robustness index for the objective function and a process of robust optimization are proposed. Moreover, a method using the supremum of linearized functions is also proposed to reduce the computational cost. Mathematical examples are solved for the verification of the proposed method and the results are compared with those from the conventional methods. The proposed approach improves the performance of the objective function and its efficiency.
Sørensen, John Dalsgaard; Rizzuto, Enrico; Narasimhan, Harikrishna
2012-01-01
More frequent use of advanced types of structures with limited redundancy and serious consequences in case of failure combined with increased requirements to efficiency in design and execution followed by increased risk of human errors has made the need of requirements to robustness of structures......, a theoretical and risk-based framework is presented which facilitates the quantification of robustness, and thus supports the formulation of pre-normative guidelines....
Optimal Design on Robustness of Scale-Free Networks Based on Degree Distribution
Jianhua Zhang
2016-01-01
Full Text Available This paper uses 2-norm degree and coefficient of variation on degree to analyze the basic characteristics and to discuss the robustness of scale-free networks. And we design two optimal nonlinear mixed integer programming schemes to investigate the optimal robustness and analyze the characteristic parameters of different schemes. In this paper, we can obtain the optimal values of the corresponding parameters of optimal designs, and we find that coefficient of variation is a better measure than 2-norm degree and two-step degree to study the robustness of scale-free networks. Meanwhile, we discover that there is a tradeoff among the robustness, the degree, and the cost of scale-free networks, and we find that when average degree equals 6, this point is a tradeoff point between the robustness and cost of scale-free networks.
Gao, Hao
2016-04-01
For the treatment planning during intensity modulated radiation therapy (IMRT) or volumetric modulated arc therapy (VMAT), beam fluence maps can be first optimized via fluence map optimization (FMO) under the given dose prescriptions and constraints to conformally deliver the radiation dose to the targets while sparing the organs-at-risk, and then segmented into deliverable MLC apertures via leaf or arc sequencing algorithms. This work is to develop an efficient algorithm for FMO based on alternating direction method of multipliers (ADMM). Here we consider FMO with the least-square cost function and non-negative fluence constraints, and its solution algorithm is based on ADMM, which is efficient and simple-to-implement. In addition, an empirical method for optimizing the ADMM parameter is developed to improve the robustness of the ADMM algorithm. The ADMM based FMO solver was benchmarked with the quadratic programming method based on the interior-point (IP) method using the CORT dataset. The comparison results suggested the ADMM solver had a similar plan quality with slightly smaller total objective function value than IP. A simple-to-implement ADMM based FMO solver with empirical parameter optimization is proposed for IMRT or VMAT.
Meta-Regression: A Framework for Robust Reactive Optimization
McClary, Dan; Syrotiuk, Violet R.; Kulahci, Murat
2007-01-01
, in which system components self-organize to changing conditions in a manner that is robust, or affected minimally by other sources of variability. Meta-regression extends profiling, providing a methodology for model-building when there is incomplete knowledge of the mechanisms and interactions...
Design of robust and efficient photonic switches using topology optimization
Elesin, Yuriy; Lazarov, Boyan Stefanov; Jensen, Jakob Søndergaard
2012-01-01
are insensitive with respect to variations of signal parameters, such as signal amplitudes and phase shifts. The obtained robust designs of a 1D photonic switch can substantially outperform simple bandgap designs, known from the literature, where switching takes place due to the bandgap shift produced by a strong...
Meta-Regression: A Framework for Robust Reactive Optimization
McClary, Dan; Syrotiuk, Violet R.; Kulahci, Murat
2007-01-01
Maintaining optimal performance as the conditions of a system change is a challenging problem. To solve this problem, we present meta-regression, a general methodology for alleviating traditional difficulties in nonlinear regression modelling. Meta-regression allows for reactive optimization, in ...... of a nonlinear system....
Model-based Optimization of Oil Recovery: Robust Operational Strategies
Van Essen, G.M.
2015-01-01
The process of depleting an oil reservoir can be poured into an optimal control problem with the objective to maximize economic performance over the life of the ﬁeld. Despite its large potential, life-cycle optimization has not yet found its way into operational environments. The objective of this t
Robust Algorithms for Multiple View Geometry: Outliers and Optimality
Olof Enqvist
2011-01-01
This thesis is concerned with the geometrical parts of computer vision, or more precisely, with the three-dimensional geometry. The overall aim is to extract geometric information from a set of images. Most methods for estimating the geometry of multiple views rely on the existence of robust solvers for a set of basic problems. Such a basic problem can be estimating the relative orientation of two cameras or estimating the position of a camera given a model of the scene. The f...
Robust Topology Optimization Based on Stochastic Collocation Methods under Loading Uncertainties
Qinghai Zhao
2015-01-01
Full Text Available A robust topology optimization (RTO approach with consideration of loading uncertainties is developed in this paper. The stochastic collocation method combined with full tensor product grid and Smolyak sparse grid transforms the robust formulation into a weighted multiple loading deterministic problem at the collocation points. The proposed approach is amenable to implementation in existing commercial topology optimization software package and thus feasible to practical engineering problems. Numerical examples of two- and three-dimensional topology optimization problems are provided to demonstrate the proposed RTO approach and its applications. The optimal topologies obtained from deterministic and robust topology optimization designs under tensor product grid and sparse grid with different levels are compared with one another to investigate the pros and cons of optimization algorithm on final topologies, and an extensive Monte Carlo simulation is also performed to verify the proposed approach.
APPLICATION OF GENETIC ALGORITHMS FOR ROBUST PARAMETER OPTIMIZATION
N. Belavendram
2010-12-01
Full Text Available Parameter optimization can be achieved by many methods such as Monte-Carlo, full, and fractional factorial designs. Genetic algorithms (GA are fairly recent in this respect but afford a novel method of parameter optimization. In GA, there is an initial pool of individuals each with its own specific phenotypic trait expressed as a ‘genetic chromosome’. Different genes enable individuals with different fitness levels to reproduce according to natural reproductive gene theory. This reproduction is established in terms of selection, crossover and mutation of reproducing genes. The resulting child generation of individuals has a better fitness level akin to natural selection, namely evolution. Populations evolve towards the fittest individuals. Such a mechanism has a parallel application in parameter optimization. Factors in a parameter design can be expressed as a genetic analogue in a pool of sub-optimal random solutions. Allowing this pool of sub-optimal solutions to evolve over several generations produces fitter generations converging to a pre-defined engineering optimum. In this paper, a genetic algorithm is used to study a seven factor non-linear equation for a Wheatstone bridge as the equation to be optimized. A comparison of the full factorial design against a GA method shows that the GA method is about 1200 times faster in finding a comparable solution.
Qinghua Zeng
2015-07-01
Full Text Available This article proposes a linear matrix inequality–based robust controller design approach to implement the synchronous design of aircraft control discipline and other disciplines, in which the variation in design parameters is treated as equivalent perturbations. Considering the complicated mapping relationships between the coefficient arrays of aircraft motion model and the aircraft design parameters, the robust controller designed is directly based on the variation in these coefficient arrays so conservative that the multidisciplinary design optimization problem would be too difficult to solve, or even if there is a solution, the robustness of design result is generally poor. Therefore, this article derives the uncertainty model of disciplinary design parameters based on response surface approximation, converts the design problem of the robust controller into a problem of solving a standard linear matrix inequality, and theoretically gives a less conservative design method of the robust controller which is based on the variation in design parameters. Furthermore, the concurrent subspace approach is applied to the multidisciplinary system with this kind of robust controller in the design loop. A multidisciplinary design optimization of a tailless aircraft as example is shown that control discipline can be synchronous optimal design with other discipline, especially this method will greatly reduce the calculated amount of multidisciplinary design optimization and make multidisciplinary design optimization results more robustness of flight performance.
Robust optimization of 2x2 multimode interference couplers with fabrication uncertainties
Rehman, Samee ur; Langelaar, Matthijs; Van Keulen, Fred
2013-03-01
In this paper, we propose a novel design-for-manufacture strategy for integrated photonics which specifically addresses the commonly encountered scenario in which probability distributions of the manufacturing variations are not available, however their bounds are known. The best design point for the device, in the presence of these uncertainties, can be found by applying robust optimization. This is performed by minimizing the maximum realizable value of the objective with respect to the uncertainty set so that an optimum is found whose performance is relatively immune to fabrication variations. Instead of applying robust optimization directly on a computationally expensive simulation model of the integrated photonic device, we construct a cheap surrogate model by uniformly sampling the simulated device at different values of the design variables and interpolating the resulting objective using a Kriging metamodel. By applying robust optimization on the constructed surrogate, the global robust optimum can be found at low computational cost. As an illustration of the method's general applicability, we apply the robust optimization approach on a 2x2 multimode interference (MMI) coupler. We robustly minimize the imbalance in the presence of uncertainties arising from variations in the fabricated design geometry. For this example device, we also study the influence of the number of sample points on the quality of the metamodel and on the robust optimization process.
Robust Optimization for Time-Cost Tradeoff Problem in Construction Projects
Ming Li; Guangdong Wu
2014-01-01
Construction projects are generally subject to uncertainty, which influences the realization of time-cost tradeoff in project management. This paper addresses a time-cost tradeoff problem under uncertainty, in which activities in projects can be executed in different construction modes corresponding to specified time and cost with interval uncertainty. Based on multiobjective robust optimization method, a robust optimization model for time-cost tradeoff problem is developed. In order to illus...
Benefits and Challenges when Performing Robust Topology Optimization for Interior Acoustic Problems
Christiansen, Rasmus Ellebæk; Jensen, Jakob Søndergaard; Lazarov, Boyan Stefanov
The objective of this work is to present benets and challenges of using robust topology optimization techniques for minimizing the sound pressure in interior acoustic problems. The focus is on creating designs which maintain high performance under uniform spatial variations. This work takes offset...... in previous work considering topology optimization for interior acoustic problems, [1]. However in the previous work the robustness of the designs was not considered....
A new digital approach to design multivariable robust optimal control systems
LIU Xiang; CHEN Lin; SUN You-xian
2005-01-01
This paper presents a new design of robust optimal controller for multivariable system. The row characteristic functions of a linear multivariable system and dynamic decoupling of its equivalent system, were applied to change the transfer function matrix of a closed-loop system into a normal function matrix, so that robustH∞ optimal stability is guaranteed. Furthermore,for the decoupled equivalent control system the l∞ optimization approach is used to have the closed-loop system embody optimal time domain indexes. A successful application on a heater control system verified the excellence of the new control scheme.
Robust Pitch Estimation Using an Optimal Filter on Frequency Estimates
Karimian-Azari, Sam; Jensen, Jesper Rindom; Christensen, Mads Græsbøll
2014-01-01
In many scenarios, a periodic signal of interest is often contaminated by different types of noise that may render many existing pitch estimation methods suboptimal, e.g., due to an incorrect white Gaussian noise assumption. In this paper, a method is established to estimate the pitch of such sig...... against different noise situations. The simulation results confirm that the proposed MVDR method outperforms the state-of-the-art weighted least squares (WLS) pitch estimator in colored noise and has robust pitch estimates against missing harmonics in some time-frames....
Hou, Liqiang; Cai, Yuanli; Liu, Jin; Hou, Chongyuan
2016-04-01
A variable fidelity robust optimization method for pulsed laser orbital debris removal (LODR) under uncertainty is proposed. Dempster-shafer theory of evidence (DST), which merges interval-based and probabilistic uncertainty modeling, is used in the robust optimization. The robust optimization method optimizes the performance while at the same time maximizing its belief value. A population based multi-objective optimization (MOO) algorithm based on a steepest descent like strategy with proper orthogonal decomposition (POD) is used to search robust Pareto solutions. Analytical and numerical lifetime predictors are used to evaluate the debris lifetime after the laser pulses. Trust region based fidelity management is designed to reduce the computational cost caused by the expensive model. When the solutions fall into the trust region, the analytical model is used to reduce the computational cost. The proposed robust optimization method is first tested on a set of standard problems and then applied to the removal of Iridium 33 with pulsed lasers. It will be shown that the proposed approach can identify the most robust solutions with minimum lifetime under uncertainty.
Hard and Soft Sub-Time-Optimal Robust Controllers
Kulczycki, Piotr; Wisniewski, Rafal; Kowalski, Piotr
2010-01-01
has been treated as a stochastic process, is presented in this paper. As a result, through a generalization of the classic switching curve occurring in the time-optimal approach, two control structures have been investigated: the hard, defined on the basis of the rules of the statistical decision...... theory, and also the soft, which additionally allows the elimination of rapid changes in control values. The methodology proposed here may be easily adopted for other elements commonly found in mechanical systems, e.g. parameters of drive or motion resistance, giving the sub-time-optimal controlling...
Nickel-Cadmium Battery Operation Management Optimization Using Robust Design
Blosiu, Julian O.; Deligiannis, Frank; DiStefano, Salvador
1996-01-01
In recent years following several spacecraft battery anomalies, it was determined that managing the operational factors of NASA flight NiCd rechargeable battery was very important in order to maintain space flight battery nominal performance. The optimization of existing flight battery operational performance was viewed as something new for a Taguchi Methods application.
Robust Optimization for Time-Cost Tradeoff Problem in Construction Projects
Ming Li
2014-01-01
Full Text Available Construction projects are generally subject to uncertainty, which influences the realization of time-cost tradeoff in project management. This paper addresses a time-cost tradeoff problem under uncertainty, in which activities in projects can be executed in different construction modes corresponding to specified time and cost with interval uncertainty. Based on multiobjective robust optimization method, a robust optimization model for time-cost tradeoff problem is developed. In order to illustrate the robust model, nondominated sorting genetic algorithm-II (NSGA-II is modified to solve the project example. The results show that, by means of adjusting the time and cost robust coefficients, the robust Pareto sets for time-cost tradeoff can be obtained according to different acceptable risk level, from which the decision maker could choose the preferred construction alternative.
Robust design and optimization for autonomous PV-wind hybrid power systems
Jun-hai SHI; Zhi-dan ZHONG; Xin-jian ZHU; Guang-yi CAO
2008-01-01
This study presents a robust design method for autonomous photovoltaic (PV)-wind hybrid power systems to obtain an optimum system configuration insensitive to design variable variations. This issue has been formulated as a constraint multi-objective optimization problem, which is solved by a multi-objective genetic algorithm, NSGA-Ⅱ. Monte Carlo Simulation (MCS) method, combined with Latin Hypercube Sampling (LHS), is applied to evaluate the stochastic system performance. The potential of the proposed method has been demonstrated by a conceptual system design. A comparative study between the proposed robust method and the deterministic method presented in literature has been conducted. The results indicate that the proposed method can find a large mount of Pareto optimal system configurations with better compromising performance than the deterministic method. The trade-off information may be derived by a systematical comparison of these configurations. The proposed robust design method should be useful for hybrid power systems that require both optimality and robustness.
Synergetic material and structure optimization yields robust spider web anchorages.
Pugno, Nicola M; Cranford, Steven W; Buehler, Markus J
2013-08-26
Millions of years of evolution have adapted spider webs to achieve a range of properties, including the well-known capture of prey, with efficient use of materials. One feature that remains poorly understood is the attachment disc, a network of silk fibers that mechanically anchors a web to its environment. Experimental observations suggest that one possible attachment disc adheres to a substrate through multiple symmetrically branched structures composed of sub-micrometer scale silk fibers. Here, a theoretical model is used to explore the adaptation of the strength of attachment of such an anchorage, and complementary mesoscale simulations are applied to demonstrate a novel mechanism of synergetic material and structural optimization, such that the maximum anchorage strength can be achieved regardless of the initial anchor placement or material type. The optimal delamination (peeling) angle is facilitated by the inherent extensibility of silk, and is attained automatically during the process of delamination. This concept of self-optimizing peeling angle suggests that attachment discs do not require precise placement by the spider, irrespective of adhesion strength. Additional hierarchical branching of the anchorage increases efficiency, where both the delamination force and toughness modulus increase with a splitting of the cross-sectional area.
不确定切换系统的鲁棒H∞控制:滑模控制设计%Robust H∞ Control of Uncertain Switched Systems: a Sliding Mode Control Design
连捷; 赵军
2009-01-01
This paper develops a new method to the robust H control problem for a class of uncertain switched systems by constructing a single robust H sliding surface. The method consists of two phases. One is to construct a single sliding surface such that the reduced-order equivalent sliding motion restricted to the sliding surface is robustly stabilizable with H disturbance attenuation level γ under a hysteresis switching law; the other phase is to design variable structure controllers of subsystems to drive the state of the switched system to reach the single sliding surface in finite time and remain on it thereafter. A numerical example is given to illustrate the effectiveness of the proposed method.
Robust fault reconstruction of uncertain system using sliding-mode observer%滑模观测器实现不确定系统的鲁棒故障重构
赵瑾; 申忠宇
2011-01-01
This paper considers the problem of fault reconstruction for uncertain dynamical systems by using the sliding-mode observer. First, the system is processed by the canonical transformation u-sing the singular value decomposition (SVD). The linear matrix inequality ( LMI) method of the robust sliding-mode observer is designed, and the nonlinear injection is applied in the observers in order to make the observer have robustness for uncertainties and convergence for tracking states. Then, based on the proposed method of the sliding-mode observer, the actuator fault and sensor fault reconstruction algorithms are developed by using the equivalence output error injection, the optimization concept and the output filter approach in order to directly obtain fault information. Finally, the numerical simulation results of sliding-mode observer estimation states and reconstruction actuators are presented to validate the effectiveness of the proposed method.%讨论了利用滑模观测器实现不确定系统的在线故障重构问题.首先应用奇异值分解,对系统进行规范化处理,设计了鲁棒滑模观测器的LMI算法,并通过非线性介入使设计观测器对系统不确定性具有鲁棒性及跟踪系统状态的收敛性；然后根据滑模观测器设计方法,利用等价输出误差介入、H∞约束优化原理以及加入输出滤波器方法,提出了执行器故障和传感器故障在线重构算法,直接获取故障信息；最后,通过实例给出滑模观测器估计状态以及重构执行器故障的仿真结果,并验证所提方法的有效性.
A ROBUST SQP METHOD FOR OPTIMIZATION WITH INEQUALITY CONSTRAINTS
Juliang Zhang; Xiangsun Zhang
2003-01-01
A new algorithm for inequality constrained optimization is presented, which solves a linear programming subproblem and a quadratic subproblem at each iteration. The algorithm can circumvent the difficulties associated with the possible inconsistency of QP subproblem of the original SQP method. Moreover, the algorithm can converge to a point which satisfies a certain first-order necessary condition even if the original problem is itself infeasible. Under certain condition, some global convergence results are proved and local superlinear convergence results are also obtained. Preliminary numerical results are reported.
Performance Trades Study for Robust Airfoil Shape Optimization
Li, Wu; Padula, Sharon
2003-01-01
From time to time, existing aircraft need to be redesigned for new missions with modified operating conditions such as required lift or cruise speed. This research is motivated by the needs of conceptual and preliminary design teams for smooth airfoil shapes that are similar to the baseline design but have improved drag performance over a range of flight conditions. The proposed modified profile optimization method (MPOM) modifies a large number of design variables to search for nonintuitive performance improvements, while avoiding off-design performance degradation. Given a good initial design, the MPOM generates fairly smooth airfoils that are better than the baseline without making drastic shape changes. Moreover, the MPOM allows users to gain valuable information by exploring performance trades over various design conditions. Four simulation cases of airfoil optimization in transonic viscous ow are included to demonstrate the usefulness of the MPOM as a performance trades study tool. Simulation results are obtained by solving fully turbulent Navier-Stokes equations and the corresponding discrete adjoint equations using an unstructured grid computational fluid dynamics code FUN2D.
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.
Chen, Yaohui; Wang, Fengwen; Ek, Sara;
2011-01-01
In this paper, we present a theoretical analysis of slow-light enhanced light amplification in an active semiconductor photonic crystal line defect waveguide. The impact of enhanced light-matter interactions on propagation effects and local carrier dynamics are investigated in the framework...... of the Lorentz reciprocity theorem. We highlight topology optimization as a systematic and robust design methodology considering manufacturing imperfections in optimizing active photonic crystal device performances, and compare the performance of standard photonic crystal waveguides with optimized structures....
A Robust and Reliability-Based Optimization Framework for Conceptual Aircraft Wing Design
Paiva, Ricardo Miguel
A robustness and reliability based multidisciplinary analysis and optimization framework for aircraft design is presented. Robust design optimization and Reliability Based Design Optimization are merged into a unified formulation which streamlines the setup of optimization problems and aims at preventing foreseeable implementation issues in uncertainty based design. Surrogate models are evaluated to circumvent the intensive computations resulting from using direct evaluation in nondeterministic optimization. Three types of models are implemented in the framework: quadratic interpolation, regression Kriging and artificial neural networks. Regression Kriging presents the best compromise between performance and accuracy in deterministic wing design problems. The performance of the simultaneous implementation of robustness and reliability is evaluated using simple analytic problems and more complex wing design problems, revealing that performance benefits can still be achieved while satisfying probabilistic constraints rather than the simpler (and not as computationally intensive) robust constraints. The latter are proven to to be unable to follow a reliability constraint as uncertainty in the input variables increases. The computational effort of the reliability analysis is further reduced through the implementation of a coordinate change in the respective optimization sub-problem. The computational tool developed is a stand-alone application and it presents a user-friendly graphical user interface. The multidisciplinary analysis and design optimization tool includes modules for aerodynamics, structural, aeroelastic and cost analysis, that can be used either individually or coupled.
Robust Homography Estimation Based on Nonlinear Least Squares Optimization
Wei Mou
2014-01-01
Full Text Available The homography between image pairs is normally estimated by minimizing a suitable cost function given 2D keypoint correspondences. The correspondences are typically established using descriptor distance of keypoints. However, the correspondences are often incorrect due to ambiguous descriptors which can introduce errors into following homography computing step. There have been numerous attempts to filter out these erroneous correspondences, but it is unlikely to always achieve perfect matching. To deal with this problem, we propose a nonlinear least squares optimization approach to compute homography such that false matches have no or little effect on computed homography. Unlike normal homography computation algorithms, our method formulates not only the keypoints’ geometric relationship but also their descriptor similarity into cost function. Moreover, the cost function is parametrized in such a way that incorrect correspondences can be simultaneously identified while the homography is computed. Experiments show that the proposed approach can perform well even with the presence of a large number of outliers.
Robust Estimation of Diffusion-Optimized Ensembles for Enhanced Sampling
Tian, Pengfei; Jónsson, Sigurdur Æ.; Ferkinghoff-Borg, Jesper
2014-01-01
The multicanonical, or flat-histogram, method is a common technique to improve the sampling efficiency of molecular simulations. The idea is that free-energy barriers in a simulation can be removed by simulating from a distribution where all values of a reaction coordinate are equally likely......, and subsequently reweight the obtained statistics to recover the Boltzmann distribution at the temperature of interest. While this method has been successful in practice, the choice of a flat distribution is not necessarily optimal. Recently, it was proposed that additional performance gains could be obtained...... by taking the position-dependent diffusion coefficient into account, thus placing greater emphasis on regions diffusing slowly. Although some promising examples of applications of this approach exist, the practical usefulness of the method has been hindered by the difficulty in obtaining sufficiently...
Robustness and Optimality of Light Harvesting in Cyanobacterial Photosystem I
Sener, M K; Ritz, T; Park, S; Fromme, P; Schulten, K; Sener, Melih K.; Lu, Deyu; Ritz, Thorsten; Park, Sanghyun; Fromme, Petra; Schulten, Klaus
2002-01-01
As most biological species, photosynthetic lifeforms have evolved to function optimally, despite thermal disorder and with fault tolerance. It remains a challenge to understand how this is achieved. To address this challenge the function of the protein-pigment complex photosystem I (PSI) of the cyanobacterium Synechococcus elongatus is investigated theoretically. The recently obtained high resolution structure of this complex exhibits an aggregate of 96 chlorophylls that are electronically coupled to function as a light-harvesting antenna complex. This paper constructs an effective Hamiltonian for the chlorophyll aggregate to describe excitation transfer dynamics and spectral properties of PSI. For this purpose, a new kinetic expansion method, the sojourn expansion, is introduced. Our study shows that at room temperature fluctuations of site energies have little effect on the calculated excitation lifetime and quantum yield, which compare favorably with experimental results. The efficiency of the system is fo...
Kirshen, P. H.; Hecht, J. S.; Vogel, R. M.
2015-12-01
Prescribing long-term urban floodplain management plans under the deep uncertainty of climate change is a challenging endeavor. To address this, we have implemented and tested with stakeholders a parsimonious multi-stage mixed integer programming (MIP) model that identifies the optimal time period(s) for implementing publicly and privately financed adaptation measures. Publicly funded measures include reach-scale flood barriers, flood insurance, and buyout programs to encourage property owners in flood-prone areas to retreat from the floodplain. Measures privately funded by property owners consist of property-scale floodproofing options, such as raising building foundations, as well as investments in flood insurance or retreat from flood-prone areas. The objective function to minimize the sum of flood control and damage costs in all planning stages for different property types during floods of different severities. There are constraints over time for flow mass balances, construction of flood management alternatives and their cumulative implementation, budget allocations, and binary decisions. Damages are adjusted for flood control investments. In recognition of the deep uncertainty of GCM-derived climate change scenarios, we employ the minimax regret criterion to identify adaptation portfolios robust to different climate change trajectories. As an example, we identify publicly and privately funded adaptation measures for a stylized community based on the estuarine community of Exeter, New Hampshire, USA. We explore the sensitivity of recommended portfolios to different ranges of climate changes, and costs associated with economies of scale and flexible infrastructure design as well as different municipal budget constraints.
Robust Secure Transmission in MISO Channels Based on Worst-Case Optimization
Huang, Jing
2011-01-01
This paper studies robust transmission schemes for multiple-input single-output (MISO) wiretap channels. Both the cases of direct transmission and cooperative jamming with a helper are investigated with imperfect channel state information (CSI) for the eavesdropper links. Robust transmit covariance matrices are obtained based on worst-case secrecy rate maximization, under both individual and global power constraints. For the case of an individual power constraint, we show that the non-convex maximin optimization problem can be transformed into a quasiconvex problem that can be efficiently solved with existing methods. For a global power constraint, the joint optimization of the transmit covariance matrices and power allocation between the source and the helper is studied via geometric programming. We also study the robust wiretap transmission problem for the case with a quality-of-service constraint at the legitimate receiver. Numerical results show the advantage of the proposed robust design. In particular, ...
Reed, Patrick; Trindade, Bernardo; Jonathan, Herman; Harrison, Zeff; Gregory, Characklis
2016-04-01
Emerging water scarcity concerns in southeastern US are associated with several deeply uncertain factors, including rapid population growth, limited coordination across adjacent municipalities and the increasing risks for sustained regional droughts. Managing these uncertainties will require that regional water utilities identify regionally coordinated, scarcity-mitigating strategies that trigger the appropriate actions needed to avoid water shortages and financial instabilities. This research focuses on the Research Triangle area of North Carolina, seeking to engage the water utilities within Raleigh, Durham, Cary and Chapel Hill in cooperative and robust regional water portfolio planning. Prior analysis of this region through the year 2025 has identified significant regional vulnerabilities to volumetric shortfalls and financial losses. Moreover, efforts to maximize the individual robustness of any of the mentioned utilities also have the potential to strongly degrade the robustness of the others. This research advances a multi-stakeholder Many-Objective Robust Decision Making (MORDM) framework to better account for deeply uncertain factors when identifying cooperative management strategies. Results show that the sampling of deeply uncertain factors in the computational search phase of MORDM can aid in the discovery of management actions that substantially improve the robustness of individual utilities as well as the overall region to water scarcity. Cooperative water transfers, financial risk mitigation tools, and coordinated regional demand management must be explored jointly to decrease robustness conflicts between the utilities. The insights from this work have general merit for regions where adjacent municipalities can benefit from cooperative regional water portfolio planning.
APPLICATION OF MODERN ROBUST OPTIMAL DESIGN METHOD TO THE SHOCK ABSORBER IN A CAR
无
2003-01-01
To reduce the variation of velocity characteristic of the shock absorber in a car, a modern robust optimal design method is applied to its structural parameters design. Firstly, the method is used to obtain the robust values which have low sensitivity to velocity characteristic and analyze the influences of the parameters on velocity characteristic. Secondly, the method is used to obtain their maximum tolerances under the condition of ensuring product quality. The results obviously improve the velocity characteristic.
An Optimization Approach for Selecting Blocks of Embedding Process in Robust Watermarking System
Ababneh M.F. Mohammad
2006-01-01
Full Text Available This study, discusses several kinds of attacks that may meet the watermarked image such as JPEG compression, Gaussian noise and median filter. The study introduces an approach capable of selecting the optimal blocks in cover image to be used in embedding process. Also, in this study, we propose a technique in robust digital watermarking system looking for finding a relation between the contrast of cover image and robustness to increase the resistance of previous attacks.
Pan, Indranil; Ghosh, Soumyajit; Gupta, Amitava; 10.1109/PACC.2011.5978958
2012-01-01
Networked Control Systems (NCSs) are often associated with problems like random data losses which might lead to system instability. This paper proposes a method based on the use of variable controller gains to achieve maximum parametric robustness of the plant controlled over a network. Stability using variable controller gains under data loss conditions is analyzed using a suitable Linear Matrix Inequality (LMI) formulation. Also, a Particle Swarm Optimization (PSO) based technique is used to maximize parametric robustness of the plant.
吴争光; 周武能
2007-01-01
This paper considers the problem of delay-dependent robust stabilization for uncertain singular delay systems. In terms of linear matrix inequality (LMI) approach, a delay-dependent stability criterion is given to ensure that the nominal system is regular, impulse free, and stable. Based on the criterion, the problem is solved via state feedback controller, which guarantees that the resultant closed-loop system is regular, impulse free, and stable for all admissible uncertainties. An explicit expression for the desired controller is also given. Some numerical examples are provided to illustrate the validity of the proposed methods.
吴敏; 何勇; 佘锦华
2005-01-01
This paper concerns problem of the delay-dependent robust stability and stabilization for uncertain neutral systems. Some new delay-dependent stability criteria are derived by taking matrices are given to express the relationship between the terms in the Leibniz-Newton formula and the new criteria are based on linear matrix inequalities such that the free weighting matrices can be easily obtained. Moreover, the stability criteria are also used to design the state-feedback controller.Numerical examples demonstrates that the proposed criteria are effective and are an improvement over the previous papers.
JU Yaping; ZHANG Chuhua
2016-01-01
Blade fouling has been proved to be a great threat to compressor performance in operating stage. The current researches on fouling-induced performance degradations of centrifugal compressors are based mainly on simplified roughness models without taking into account the realistic factors such as spatial non-uniformity and randomness of the fouling-induced surface roughness. Moreover, little attention has been paid to the robust design optimization of centrifugal compressor impellers with considerations of blade fouling. In this paper, a multi-objective robust design optimization method is developed for centrifugal impellers under surface roughness uncertainties due to blade fouling. A three-dimensional surface roughness map is proposed to describe the nonuniformity and randomness of realistic fouling accumulations on blades. To lower computational cost in robust design optimization, the support vector regression (SVR) metamodel is combined with the Monte Carlo simulation (MCS) method to conduct the uncertainty analysis of fouled impeller performance. The analyzed results show that the critical fouled region associated with impeller performance degradations lies at the leading edge of blade tip. The SVR metamodel has been proved to be an efficient and accurate means in the detection of impeller performance variations caused by roughness uncertainties. After design optimization, the robust optimal design is found to be more efficient and less sensitive to fouling uncertainties while maintaining good impeller performance in the clean condition. This research proposes a systematic design optimization method for centrifugal compressors with considerations of blade fouling, providing a practical guidance to the design of advanced centrifugal compressors.
Ju, Yaping; Zhang, Chuhua
2016-03-01
Blade fouling has been proved to be a great threat to compressor performance in operating stage. The current researches on fouling-induced performance degradations of centrifugal compressors are based mainly on simplified roughness models without taking into account the realistic factors such as spatial non-uniformity and randomness of the fouling-induced surface roughness. Moreover, little attention has been paid to the robust design optimization of centrifugal compressor impellers with considerations of blade fouling. In this paper, a multi-objective robust design optimization method is developed for centrifugal impellers under surface roughness uncertainties due to blade fouling. A three-dimensional surface roughness map is proposed to describe the nonuniformity and randomness of realistic fouling accumulations on blades. To lower computational cost in robust design optimization, the support vector regression (SVR) metamodel is combined with the Monte Carlo simulation (MCS) method to conduct the uncertainty analysis of fouled impeller performance. The analyzed results show that the critical fouled region associated with impeller performance degradations lies at the leading edge of blade tip. The SVR metamodel has been proved to be an efficient and accurate means in the detection of impeller performance variations caused by roughness uncertainties. After design optimization, the robust optimal design is found to be more efficient and less sensitive to fouling uncertainties while maintaining good impeller performance in the clean condition. This research proposes a systematic design optimization method for centrifugal compressors with considerations of blade fouling, providing a practical guidance to the design of advanced centrifugal compressors.
Hêriş Golpîra
2017-01-01
Full Text Available This paper introduces the problem of designing a single-product supply chain network in an agile manufacturing setting under a vendor managed inventory (VMI strategy to seize a new market opportunity. The problem addresses the level of risk aversion of the retailer when dealing with the uncertainty of market related information through a conditional value at risk (CVaR approach. This approach leads to a bilevel programming problem. The Karush-Kuhn-Tucker (KKT conditions are employed to transform the model into a single-level, mixed-integer linear programming problem by considering some relaxations. Since realizations of imprecisely known parameters are the only information available, a data-driven approach is employed as a suitable, more practical, methodology of avoiding distributional assumptions. Finally, the effectiveness of the proposed model is demonstrated through a numerical example. (original abstract
Tun, F A Hla Myo; Naing, T C Zaw Min
2010-01-01
In this paper, the minimum channel gain flow with uncertainty in the demand vector is examined. The approach is based on a transformation of uncertainty in the demand vector to uncertainty in the gain vector. OFDM systems are known to overcome the impairment of the wireless channel by splitting the given system bandwidth into parallel sub-carriers, on which data-symbols can be transmitted simultaneously. This enables the possibility of enhancing the system's performance by deploying adaptive mechanisms, namely power distribution and dynamic sub-carrier assignments. The performances of maximizing the minimum throughput have been analyzed by MATLAB codes.
Robust Optimal Design of a Nonlinear Dynamic Vibration Absorber Combining Sensitivity Analysis
R.A. Borges
2010-01-01
Full Text Available Dynamic vibration absorbers are discrete devices developed in the beginning of the last century used to attenuate the vibrations of different engineering structures. They have been used in several engineering applications, such as ships, power lines, aeronautic structures, civil engineering constructions subjected to seismic induced excitations, compressor systems, etc. However, in the context of nonlinear dynamics, few works have been proposed regarding the robust optimal design of nonlinear dynamic vibration absorbers. In this paper, a robust optimization strategy combined with sensitivity analysis of systems incorporating nonlinear dynamic vibration absorbers is proposed. Although sensitivity analysis is a well known numerical technique, the main contribution intended for this study is its extension to nonlinear systems. Due to the numerical procedure used to solve the nonlinear equations, the sensitivities addressed herein are computed from the first-order finite-difference approximations. With the aim of increasing the efficiency of the nonlinear dynamic absorber into a frequency band of interest, and to augment the robustness of the optimal design, a robust optimization strategy combined with the previous sensitivities is addressed. After presenting the underlying theoretical foundations, the proposed robust design methodology is performed for a two degree-of-freedom system incorporating a nonlinear dynamic vibration absorber. Based on the obtained results, the usefulness of the proposed methodology is highlighted.
Robust stabilization of stochastic systems based on the LQ controller
Jundong BAO; Feiqi DENG; Qi LUO
2005-01-01
The robust exponential stability in mean square for a class of linear stochastic uncertain control systems is dealt with.For the uncertain stochastic systems,we have designed an optimal controller which guarantees the exponential stability of the system.Actually,we employed Lyapunov function approach and the stochastic algebraic Riccati equation (SARE) to have shown the robustness of the linear quadratic(LQ) optimal control law.And the algebraic criteria for the exponential stability on the linear stochastic uncertain closed-loop systems are given.
Feng, Ju; Ying, Zu-Guang; Zhu, Wei-Qiu
2012-01-01
A minimax stochastic optimal semi-active control strategy for stochastically excited quasi-integrable Hamiltonian systems with parametric uncertainty by using magneto-rheological (MR) dampers is proposed. Firstly, the control problem is formulated as an n-degree-of-freedom (DOF) controlled......, uncertain quasi-integrable Hamiltonian system and the control forces produced by MR dampers are split into the passive part and the semi-active part. Then the passive part is incorporated into the uncontrolled system. After that, the stochastic optimal semi-active control problem is solved by applying...... the minimax stochastic optimal control strategy based on the stochastic averaging method and stochastic differential game. The worst-case disturbances and the optimal controls are obtained by the minimax dynamical programming equation with the constraints of disturbance bounds and MR damper dynamics. Finally...
Chaojun Wu
2015-01-01
Full Text Available An efficient approach of inverse optimal control and adaptive control is developed for global asymptotic stabilization of a novel fractional-order four-wing hyperchaotic system with uncertain parameter. Based on the inverse optimal control methodology and fractional-order stability theory, a control Lyapunov function (CLF is constructed and an adaptive state feedback controller is designed to achieve inverse optimal control of a novel fractional-order hyperchaotic system with four-wing attractor. Then, an electronic oscillation circuit is designed to implement the dynamical behaviors of the fractional-order four-wing hyperchaotic system and verify the satisfactory performance of the controller. Comparing with other fractional-order chaos control methods which may have more than one nonlinear state feedback controller, the inverse optimal controller has the advantages of simple structure, high reliability, and less control effort that is required and can be implemented by electronic oscillation circuit.
Quadratic stabilization for uncertain stochastic systems
Jun'e FENG; Weihai ZHANG
2005-01-01
This paper discusses the robust quadratic stabilization control problem for stochastic uncertain systems,where the uncertain matrix is norm bounded,and the external disturbance is a stochastic process.Two kinds of controllers are designed,which include state feedback case and output feedback case.The conditions for the robust quadratic stabilization of stochastic uncertain systems are given via linear matrix inequalities.The detailed design methods are presented.Numerical examples show the effectiveness of our results.
王惠姣; 林岳松; 薛安克; 潘海鹏; 鲁仁全
2008-01-01
The problem of reliable robust H∞ tracking control for a class of uncertain Lur'e singular systems is studied. A practical and general failure model of actuator and sensor is considered by using convex polytopic uncertainties to describe control surface impairment. Some sufficient conditions are presented for the case of actuator, sensor and control surface failures in terms of linear matrix inequalities (LMIs). The resultant control systems are reliable in that they guarantee closed-loop system robust stability with H∞ performance and the output tracking the reference signal without steady-state error when all control components are operational as well as when some control components experience failures. Finally, a numerical example is given to show the effectiveness of the proposed methods.
Joelsson, Daniel; Moravec, Phil; Troutman, Matthew; Pigeon, Joseph; DePhillips, Pete
2008-08-20
Transferring manual ELISAs to automated platforms requires optimizing the assays for each particular robotic platform. These optimization experiments are often time consuming and difficult to perform using a traditional one-factor-at-a-time strategy. In this manuscript we describe the development of an automated process using statistical design of experiments (DOE) to quickly optimize immunoassays for precision and robustness on the Tecan EVO liquid handler. By using fractional factorials and a split-plot design, five incubation time variables and four reagent concentration variables can be optimized in a short period of time.
Ji, H F; Huang, M Y; Xu, S Y; Wang, N; Wang, S
2016-01-01
The Robust Conjugate Direction Search (RCDS) method is used to optimize the collimation system for Rapid Cycling Synchrotron (RCS) of the Chinese Spallation Neutron Source (CSNS). The parameters of secondary collimators are optimized for a better performance of the collimation system. To improve the efficiency of the optimization, the Objective Ring Beam Injection and Tracking (ORBIT) parallel module combined with MATLAB parallel computing is used, which can run multiple ORBIT instances simultaneously. This study presents a way to figure out an optimal parameter combination of the secondary collimators for a machine model in preparation for CSNS/RCS commissioning.
Polymorphic Uncertain Linear Programming for Generalized Production Planning Problems
Xinbo Zhang
2014-01-01
Full Text Available A polymorphic uncertain linear programming (PULP model is constructed to formulate a class of generalized production planning problems. In accordance with the practical environment, some factors such as the consumption of raw material, the limitation of resource and the demand of product are incorporated into the model as parameters of interval and fuzzy subsets, respectively. Based on the theory of fuzzy interval program and the modified possibility degree for the order of interval numbers, a deterministic equivalent formulation for this model is derived such that a robust solution for the uncertain optimization problem is obtained. Case study indicates that the constructed model and the proposed solution are useful to search for an optimal production plan for the polymorphic uncertain generalized production planning problems.
A robust optimization model for distribution and evacuation in the disaster response phase
Fereiduni, Meysam; Shahanaghi, Kamran
2017-10-01
Natural disasters, such as earthquakes, affect thousands of people and can cause enormous financial loss. Therefore, an efficient response immediately following a natural disaster is vital to minimize the aforementioned negative effects. This research paper presents a network design model for humanitarian logistics which will assist in location and allocation decisions for multiple disaster periods. At first, a single-objective optimization model is presented that addresses the response phase of disaster management. This model will help the decision makers to make the most optimal choices in regard to location, allocation, and evacuation simultaneously. The proposed model also considers emergency tents as temporary medical centers. To cope with the uncertainty and dynamic nature of disasters, and their consequences, our multi-period robust model considers the values of critical input data in a set of various scenarios. Second, because of probable disruption in the distribution infrastructure (such as bridges), the Monte Carlo simulation is used for generating related random numbers and different scenarios; the p-robust approach is utilized to formulate the new network. The p-robust approach can predict possible damages along pathways and among relief bases. We render a case study of our robust optimization approach for Tehran's plausible earthquake in region 1. Sensitivity analysis' experiments are proposed to explore the effects of various problem parameters. These experiments will give managerial insights and can guide DMs under a variety of conditions. Then, the performances of the "robust optimization" approach and the "p-robust optimization" approach are evaluated. Intriguing results and practical insights are demonstrated by our analysis on this comparison.
A robust optimization model for distribution and evacuation in the disaster response phase
Fereiduni, Meysam; Shahanaghi, Kamran
2016-10-01
Natural disasters, such as earthquakes, affect thousands of people and can cause enormous financial loss. Therefore, an efficient response immediately following a natural disaster is vital to minimize the aforementioned negative effects. This research paper presents a network design model for humanitarian logistics which will assist in location and allocation decisions for multiple disaster periods. At first, a single-objective optimization model is presented that addresses the response phase of disaster management. This model will help the decision makers to make the most optimal choices in regard to location, allocation, and evacuation simultaneously. The proposed model also considers emergency tents as temporary medical centers. To cope with the uncertainty and dynamic nature of disasters, and their consequences, our multi-period robust model considers the values of critical input data in a set of various scenarios. Second, because of probable disruption in the distribution infrastructure (such as bridges), the Monte Carlo simulation is used for generating related random numbers and different scenarios; the p-robust approach is utilized to formulate the new network. The p-robust approach can predict possible damages along pathways and among relief bases. We render a case study of our robust optimization approach for Tehran's plausible earthquake in region 1. Sensitivity analysis' experiments are proposed to explore the effects of various problem parameters. These experiments will give managerial insights and can guide DMs under a variety of conditions. Then, the performances of the "robust optimization" approach and the "p-robust optimization" approach are evaluated. Intriguing results and practical insights are demonstrated by our analysis on this comparison.
Lihui Guo
2015-01-01
Full Text Available With the increasing penetration of wind power, the randomness and volatility of wind power output would have a greater impact on safety and steady operation of power system. In allusion to the uncertainty of wind speed and load demand, this paper applied box set robust optimization theory in determining the maximum allowable installed capacity of wind farm, while constraints of node voltage and line capacity are considered. Optimized duality theory is used to simplify the model and convert uncertainty quantities in constraints into certainty quantities. Under the condition of multi wind farms, a bilevel optimization model to calculate penetration capacity is proposed. The result of IEEE 30-bus system shows that the robust optimization model proposed in the paper is correct and effective and indicates that the fluctuation range of wind speed and load and the importance degree of grid connection point of wind farm and load point have impact on the allowable capacity of wind farm.
Dollerup, Niels; Jepsen, Michael S.; Frier, Christian;
2014-01-01
A robust and effective finite element based implementation of lower bound limit state analysis applying an interior point formulation is presented in this paper. The lower bound formulation results in a convex optimization problem consisting of a number of linear constraints from the equilibrium...... equations and a number of convex non-linear constraints from the yield criteria. The computational robustness has been improved by eliminating a large number of the equilibrium equations a priori leaving only the statical redundant variables as free optimization variables. The elimination of equilibrium...... equations is based on a optimized numbering of elements and stress variables based on the frontal method approach used in the standard finite element method. The optimized numbering secures sparsity in the formulation. The convex non-linear yield criteria are treated directly in the interior point...
Robust topology optimization of three-dimensional photonic-crystal band-gap structures.
Men, H; Lee, K Y K; Freund, R M; Peraire, J; Johnson, S G
2014-09-22
We perform full 3D topology optimization (in which "every voxel" of the unit cell is a degree of freedom) of photonic-crystal structures in order to find optimal omnidirectional band gaps for various symmetry groups, including fcc (including diamond), bcc, and simple-cubic lattices. Even without imposing the constraints of any fabrication process, the resulting optimal gaps are only slightly larger than previous hand designs, suggesting that current photonic crystals are nearly optimal in this respect. However, optimization can discover new structures, e.g. a new fcc structure with the same symmetry but slightly larger gap than the well known inverse opal, which may offer new degrees of freedom to future fabrication technologies. Furthermore, our band-gap optimization is an illustration of a computational approach to 3D dispersion engineering which is applicable to many other problems in optics, based on a novel semidefinite-program formulation for nonconvex eigenvalue optimization combined with other techniques such as a simple approach to impose symmetry constraints. We also demonstrate a technique for robust topology optimization, in which some uncertainty is included in each voxel and we optimize the worst-case gap, and we show that the resulting band gaps have increased robustness to systematic fabrication errors.
Dynamic optimization and robust explicit model predictive control of hydrogen storage tank
Panos, C.
2010-09-01
We present a general framework for the optimal design and control of a metal-hydride bed under hydrogen desorption operation. The framework features: (i) a detailed two-dimension dynamic process model, (ii) a design and operational dynamic optimization step, and (iii) an explicit/multi-parametric model predictive controller design step. For the controller design, a reduced order approximate model is obtained, based on which nominal and robust multi-parametric controllers are designed. © 2010 Elsevier Ltd.
Robust design of broadband EUV multilayer beam splitters based on particle swarm optimization
Jiang, Hui, E-mail: jianghui@sinap.ac.cn [Shanghai Synchrotron Radiation Facility, Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Zhangheng Road 239, Pudong District, Shanghai 201204 (China); King' s College London, Department of Physics, Strand, London WC2R 2LS (United Kingdom); Michette, Alan G. [King' s College London, Department of Physics, Strand, London WC2R 2LS (United Kingdom)
2013-03-01
A robust design idea for broadband EUV multilayer beam splitters is introduced that achieves the aim of decreasing the influence of layer thickness errors on optical performances. Such beam splitters can be used in interferometry to determine the quality of EUVL masks by comparing with a reference multilayer. In the optimization, particle swarm techniques were used for the first time in such designs. Compared to conventional genetic algorithms, particle swarm optimization has stronger ergodicity, simpler processing and faster convergence.
Fushing Hsieh
2016-11-01
Full Text Available Discrete combinatorial optimization problems in real world are typically defined via an ensemble of potentially high dimensional measurements pertaining to all subjects of a system under study. We point out that such a data ensemble in fact embeds with system's information content that is not directly used in defining the combinatorial optimization problems. Can machine learning algorithms extract such information content and make combinatorial optimizing tasks more efficient? Would such algorithmic computations bring new perspectives into this classic topic of Applied Mathematics and Theoretical Computer Science? We show that answers to both questions are positive. One key reason is due to permutation invariance. That is, the data ensemble of subjects' measurement vectors is permutation invariant when it is represented through a subject-vs-measurement matrix. An unsupervised machine learning algorithm, called Data Mechanics (DM, is applied to find optimal permutations on row and column axes such that the permuted matrix reveals coupled deterministic and stochastic structures as the system's information content. The deterministic structures are shown to facilitate geometry-based divide-and-conquer scheme that helps optimizing task, while stochastic structures are used to generate an ensemble of mimicries retaining the deterministic structures, and then reveal the robustness pertaining to the original version of optimal solution. Two simulated systems, Assignment problem and Traveling Salesman problem, are considered. Beyond demonstrating computational advantages and intrinsic robustness in the two systems, we propose brand new robust optimal solutions. We believe such robust versions of optimal solutions are potentially more realistic and practical in real world settings.
A theoretical estimation for the optimal network robustness measure R against malicious node attacks
Ma, Liangliang; Liu, Jing; Duan, Boping; Zhou, Mingxing
2015-07-01
In a recent work (Schneider C. M. et al., Proc. Natl. Acad. Sci. U.S.A., 108 (2011) 3838), Schneider et al. introduced an effective measure R to evaluate the network robustness against malicious attacks on nodes. Take R as the objective function, they used a heuristic algorithm to optimize the network robustness. In this paper, a theoretical analysis is conducted to estimate the value of R for different types of networks, including regular networks, WS networks, ER networks, and BA networks. The experimental results show that the theoretical value of R is approximately equal to that of optimized networks. Furthermore, the theoretical analysis also shows that regular networks are the most robust than other networks. To validate this result, a heuristic method is proposed to optimize the network structure, in which the degree distribution can be changed and the number of nodes and edges remains invariant. The optimization results show that the degree of most nodes in the optimal networks is close to the average degree, and the optimal network topology is close to regular networks, which confirms the theoretical analysis.
Approximating the Pareto Set of Multiobjective Linear Programs via Robust Optimization
Gorissen, B.L.; den Hertog, D.
2012-01-01
Abstract: The Pareto set of a multiobjective optimization problem consists of the solutions for which one or more objectives can not be improved without deteriorating one or more other objectives. We consider problems with linear objectives and linear constraints and use Adjustable Robust Optimizati
Vonk, E.; Xu, YuePing; Booij, Martijn J.; Augustijn, Dionysius C.M.
2016-01-01
In this research we investigate the robustness of the common implicit stochastic optimization (ISO) method for dam reoperation. As a case study, we focus on the Xinanjiang-Fuchunjiang reservoir cascade in eastern China, for which adapted operating rules were proposed as a means to reduce the impact
Vonk, E.; Xu, Y.P.; Booij, M.J.; Augustijn, D.C.M.
2016-01-01
In this research we investigate the robustness of the common implicit stochastic optimization (ISO) method for dam reoperation. As a case study, we focus on the Xinanjiang-Fuchunjiang reservoir cascade in eastern China, for which adapted operating rules were proposed as a means to reduce the impact
Systematic and robust design of photonic crystal waveguides by topology optimization
Wang, Fengwen; Jensen, Jakob Søndergaard; Sigmund, Ole
2010-01-01
on a threshold projection. The objective is formulated to minimize the maximum error between actual group indices and a prescribed group index among these three designs. Novel photonic crystal waveguide facilitating slow light with a group index of n(g) = 40 is achieved by the robust optimization approach...
Mahmood, Faisal; Gehl, Julie
2011-01-01
and genes to intracranial tumors in humans, and demonstrate a method to optimize the design (i.e. geometry) of the electrode device prototype to improve both clinical performance and geometrical tolerance (robustness). We have employed a semiempirical objective function based on constraints similar to those...
Kleijnen, J.P.C.; Gaury, E.G.A.
2001-01-01
Whereas Operations Research has always paid much attention to optimization, practitioners judge the robustness of the 'optimum' solution to be of greater importance.Therefore this paper proposes a practical methodology that is a stagewise combination of the following four proven techniques: (1) disc
Kleijnen, J.P.C.; Gaury, E.G.A.
2001-01-01
Whereas Operations Research has always paid much attention to optimization, practitioners judge the robustness of the 'optimum' solution to be of greater importance.Therefore this paper proposes a practical methodology that is a stagewise combination of the following four proven techniques: (1)
郝建红; 汪筱巍; 张恒
2014-01-01
针对永磁同步电动机混沌系统，考虑受不确定因素的影响，对其数学模型采用基于微分几何理论的精确反馈线性化法，建立鲁棒控制模型，设计鲁棒控制器，实现永磁同步电动机混沌系统的鲁棒镇定和输出跟踪控制。数值仿真的结果证明了所提出方法的有效性及控制器的鲁棒性。%In this paper, targeting the permanent magnet synchronous motor chaotic system, we consider the system influenced by uncertain factors. We use the method of the exact feedback linearization which is based on differential geometry theory to establish the nonlinear robust control model and design the robust controller for realizing the robust stabilization and output tracking control of the permanent magnet synchronous motor chaotic system. Numerical simulation results demonstrate the effectiveness of the proposed method and the robustness of the controller.
SU-E-T-07: 4DCT Robust Optimization for Esophageal Cancer Using Intensity Modulated Proton Therapy
Liao, L [Proton Therapy Center, UT MD Anderson Cancer Center, Houston, TX (United States); Department of Industrial Engineering, University of Houston, Houston, TX (United States); Yu, J; Zhu, X; Li, H; Zhang, X [Proton Therapy Center, UT MD Anderson Cancer Center, Houston, TX (United States); Li, Y [Proton Therapy Center, UT MD Anderson Cancer Center, Houston, TX (United States); Varian Medical Systems, Houston, TX (United States); Lim, G [Department of Industrial Engineering, University of Houston, Houston, TX (United States)
2015-06-15
Purpose: To develop a 4DCT robust optimization method to reduce the dosimetric impact from respiratory motion in intensity modulated proton therapy (IMPT) for esophageal cancer. Methods: Four esophageal cancer patients were selected for this study. The different phases of CT from a set of 4DCT were incorporated into the worst-case dose distribution robust optimization algorithm. 4DCT robust treatment plans were designed and compared with the conventional non-robust plans. Result doses were calculated on the average and maximum inhale/exhale phases of 4DCT. Dose volume histogram (DVH) band graphic and ΔD95%, ΔD98%, ΔD5%, ΔD2% of CTV between different phases were used to evaluate the robustness of the plans. Results: Compare to the IMPT plans optimized using conventional methods, the 4DCT robust IMPT plans can achieve the same quality in nominal cases, while yield a better robustness to breathing motion. The mean ΔD95%, ΔD98%, ΔD5% and ΔD2% of CTV are 6%, 3.2%, 0.9% and 1% for the robustly optimized plans vs. 16.2%, 11.8%, 1.6% and 3.3% from the conventional non-robust plans. Conclusion: A 4DCT robust optimization method was proposed for esophageal cancer using IMPT. We demonstrate that the 4DCT robust optimization can mitigate the dose deviation caused by the diaphragm motion.
Robust Optimization of Thermal Aspects of Friction Stir Welding Using Manifold Mapping Techniques
Larsen, Anders Astrup; Lahaye, Domenico; Schmidt, Henrik Nikolaj Blicher;
2008-01-01
and use the manifold mapping technique to solve the optimization problems using a fast analytical coarse and an expensive accurate fine model. The statistics of the response are calculated using Taylor expansions and are compared to Monte Carlo simulations. The results show that the use of manifold......The aim of this paper is to optimize a friction stir welding process taking robustness into account. The optimization problems are formulated with the goal of obtaining desired mean responses while reducing the variance of the response. We restrict ourselves to a thermal model of the process...
Robust optimal sun-pointing control of a large solar power satellite
Wu, Shunan; Zhang, Kaiming; Peng, Haijun; Wu, Zhigang; Radice, Gianmarco
2016-10-01
The robust optimal sun-pointing control strategy for a large geostationary solar power satellite (SPS) is addressed in this paper. The SPS is considered as a huge rigid body, and the sun-pointing dynamics are firstly proposed in the state space representation. The perturbation effects caused by gravity gradient, solar radiation pressure and microwave reaction are investigated. To perform sun-pointing maneuvers, a periodically time-varying robust optimal LQR controller is designed to assess the pointing accuracy and the control inputs. It should be noted that, to reduce the pointing errors, the disturbance rejection technique is combined into the proposed LQR controller. A recursive algorithm is then proposed to solve the optimal LQR control gain. Simulation results are finally provided to illustrate the performance of the proposed closed-loop system.
时滞不确定采样控制系统的鲁棒稳定性%Robust stability of sampled-data control systems with uncertain time-delays
刘彦文; 王广雄; 綦志刚; 许保同
2013-01-01
本文给出了一种可定量分析采样控制系统的时滞鲁棒稳定性的方法.因为采样系统的对象是连续时间的,所以对象中的时滞也应该是按连续时间来处理.文中指出,一个整数倍时滞是稳定的采样系统,可能会因为有并不很大的连续时间时滞而失稳.定义了一个新的变量w(t),用来描述这个不确定连续时间时滞带来的动特性.将w(t)的反馈回路分成与时滞无关和有关的两个部分,并提出了一种用频率响应来确定是否存在由不确定时滞引起的周期解的方法.用修正z-变换法和仿真验证了这个由图解解析所求得的解.本方法既可用于采样系统,也可用于一般的连续时间系统.%We propose a quantitative method for analyzing the robust stability of sampled-data systems with uncertain time-delays. Because the sampled-data systems are obtained from continuous-time systems by sampling, the time-delay in the sampled-data system must also be treated in the continuous-time system. It is pointed out that a stable sampled-data system with a time-delay equal to the integer-multiple of the sampling period may be destabilized by a small continuous time-delay. A new variable w(t) is defined to describe the dynamic response caused by the uncertain continuous time-delay. The feedback loop of w(t) is then divided into two parts. One depends on the uncertain time-delay, and the other is independent of the time-delay. A special frequency response method is proposed to determine the existence of the periodic solution of the system caused by the uncertain time-delay. The graphic-analytical solution is then verified by the modified z-transform method and by simulation. The proposed method can also be used for robust stability analysis of continuous-time systems with time-delays.
Wang Nan; Shen Lincheng; Liu Hongfu; Chen Jing; Hu Tianjiang
2013-01-01
Conventional trajectory optimization techniques have been challenged by their inability to handle threats with irregular shapes and the tendency to be sensitive to control variations of aircraft.Aiming to overcome these difficulties,this paper presents an alternative approach for trajectory optimization,where the problem is formulated into a parametric optimization of the maneuver variables under a tactics template framework.To reduce the size of the problem,global sensitivity analysis (GSA) is performed to identify the less-influential maneuver variables.The probability collectives (PC) algorithm,which is well-suited to discrete and discontinuous optimization,is applied to solve the trajectory optimization problem.The robustness of the trajectory is assessed through multiple sampling around the chosen values of the maneuver variables.Meta-models based on radius basis function (RBF) are created for evaluations of the means and deviations of the problem objectives and constraints.To guarantee the approximation accuracy,the meta-models are adaptively updated during optimization.The proposed approach is demonstrated on a typical airground attack mission scenario.Results reveal that the proposed approach is capable of generating robust and optimal trajectories with both accuracy and efficiency.
Trindade, B. C.; Reed, P. M.; Herman, J. D.; Zeff, H. B.; Characklis, G. W.
2017-06-01
Emerging water scarcity concerns in many urban regions are associated with several deeply uncertain factors, including rapid population growth, limited coordination across adjacent municipalities and the increasing risks for sustained regional droughts. Managing these uncertainties will require that regional water utilities identify coordinated, scarcity-mitigating strategies that trigger the appropriate actions needed to avoid water shortages and financial instabilities. This research focuses on the Research Triangle area of North Carolina, seeking to engage the water utilities within Raleigh, Durham, Cary and Chapel Hill in cooperative and robust regional water portfolio planning. Prior analysis of this region through the year 2025 has identified significant regional vulnerabilities to volumetric shortfalls and financial losses. Moreover, efforts to maximize the individual robustness of any of the mentioned utilities also have the potential to strongly degrade the robustness of the others. This research advances a multi-stakeholder Many-Objective Robust Decision Making (MORDM) framework to better account for deeply uncertain factors when identifying cooperative drought management strategies. Our results show that appropriately designing adaptive risk-of-failure action triggers required stressing them with a comprehensive sample of deeply uncertain factors in the computational search phase of MORDM. Search under the new ensemble of states-of-the-world is shown to fundamentally change perceived performance tradeoffs and substantially improve the robustness of individual utilities as well as the overall region to water scarcity. Search under deep uncertainty enhanced the discovery of how cooperative water transfers, financial risk mitigation tools, and coordinated regional demand management must be employed jointly to improve regional robustness and decrease robustness conflicts between the utilities. Insights from this work have general merit for regions where
Sahali M.A.
2015-01-01
Full Text Available In this contribution, a bi-objective robust optimization of cutting parameters, with the taking into account uncertainties inherent in the tool wear and the tool deflection for a turning operation is presented. In a first step, we proceed to the construction of substitution models that connect the cutting parameters to the variables of interest based on design of experiments. Our two objectives are the best machined surface quality and the maximum productivity under consideration of limitations related to the vibrations and the range of the three cutting parameters. Then, using the developed genetic algorithm that based on a robust evaluation mechanism of chromosomes by Monte-Carlo simulations, the influence and interest of the uncertainties integration in the machining optimization is demonstrated. After comparing the classical and robust Pareto fronts, A surface quality less efficient but robust can be obtained with the consideration of uncontrollable factors or uncertainties unlike that provides the deterministic and classical optimization for the same values of productivity.
Babaei, Masoud; Pan, Indranil; Alkhatib, Ali
2015-12-01
The paper aims to solve a robust optimization problem (optimization in presence of uncertainty) for finding the optimal locations of a number of CO2 injection wells for geological sequestration of carbon dioxide in a saline aquifer. The parametric uncertainties are the interfacial tension between CO2 and aquifer brine, the Land's trapping coefficient and the boundary aquifer's absolute permeability. The spatial uncertainties are due to the channelized permeability field which exhibits a binary channel-non-channel system. The objective function of the optimization is the amount of residually trapped CO2 due to the hysteresis of the relative permeability curves. A risk-averse value derived from the cumulative density function of the distribution of the amount of trapped gas is chosen as the objective function value. In order to ensure that the uncertainties are effectively taken into account, Monte Carlo simulation and Polynomial Chaos Expansion (PCE)-based methods are used and compared with each other. For different cases of parametric and spatial uncertainties, the most accurate uncertainty quantification (UQ) method is chosen to be integrated within the optimization algorithm. While for parametric uncertainty cases of up to two uncertain variables, PCE-based methods computationally outperform Monte Carlo simulations, it is shown that for the multimodal distributions of the function of trapped gas occurring for the spatial uncertainty case, Monte Carlo simulations are more reliable than PCE-based UQ methods. For the discrete (integer) optimization problem, various mixed response surface surrogate models are tested and the robust optimization resulted in optimal CO2 injection well locations.
On the relation between flexibility analysis and robust optimization for linear systems
Zhang, Qi
2016-03-05
Flexibility analysis and robust optimization are two approaches to solving optimization problems under uncertainty that share some fundamental concepts, such as the use of polyhedral uncertainty sets and the worst-case approach to guarantee feasibility. The connection between these two approaches has not been sufficiently acknowledged and examined in the literature. In this context, the contributions of this work are fourfold: (1) a comparison between flexibility analysis and robust optimization from a historical perspective is presented; (2) for linear systems, new formulations for the three classical flexibility analysis problems—flexibility test, flexibility index, and design under uncertainty—based on duality theory and the affinely adjustable robust optimization (AARO) approach are proposed; (3) the AARO approach is shown to be generally more restrictive such that it may lead to overly conservative solutions; (4) numerical examples show the improved computational performance from the proposed formulations compared to the traditional flexibility analysis models. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3109–3123, 2016
Kubota, S.; Kanomata, K.; Momiyama, K.; Suzuki, T.; Hirose, F.
2013-10-01
We propose an optimization algorithm to design multilayer antireflection (AR) structure, which has robustness against variations in layer thicknesses, for organic photovoltaic cells. When a set of available materials are given, the proposed method searches for the material and thickness of each AR layer to maximize the short-circuit current density (Jsc). This algorithm allows for obtaining a set of solutions, including optimal and quasi-optimal solutions, at the same time, so that we can clearly make comparison between them. In addition, the effects of deviations in the thicknesses of the AR layers are examined for the (quasi-)optimal solutions obtained. The expectation of the decrease in the AR performance is estimated by calculating the changes in Jsc when the thicknesses of all AR layers are varied independently. We show that some of quasi-optimal solutions may have simpler layer configuration and can be more robust against the deviations in film thicknesses, than the optimal solution. This method indicates the importance of actively searching valuable, nonoptimal solutions for practical design of AR films. We also discuss the optical conditions that lead to light absorption in the back metal contact and the effects of changing active layer thicknesses.
不确定Sigma-Delta调制器的鲁棒滤波%Robust filtering for uncertain Sigma-Delta modulators
王英俊; 王武; 王骞
2013-01-01
研究级联Sigma-Delta调制器在非理想性电路中的鲁棒校正滤波器设计问题.基于MARKOV区间算法和线性区间系统的等价描述,将扰动抑制问题转化为增广系统的鲁棒稳定问题.给出以线性矩阵不等式描述的鲁棒滤波器存在的充分条件,该条件保证所设计的校正滤波器能有效抑制电路不确定性对调制器性能的影响.仿真结果表明,与传统校正滤波器相比,该调制器获得了更好的信号噪声比.方案降低了电路实现过程中器件精确度的要求,从而达到低应用成本的目的.%The design of robust correction filter for cascaded Sigma - Delta modulators with analog circuit imperfection is studied. Based on MARKOV interval algorithm and the equivalent description of linear interval system, the problem related to disturbance suppression is transformed into a robust stability problem. A linear matrix inequality approach is developed to obtain the parameters of a robust filter, which guarantees that the correction filter can effectively suppress the influence of analog circuit imperfection to the modulators. Simulation results show that the modulators exhibit lower variation in the signal - to - noise and distortion ratio over the nominal correction filter. The proposed scheme decreases requirements of accuracy during the circuit implementation, then achieve the purpose of low cost application.
Design of Robust Optimal Fixed Structure Controller Using Self Adaptive Differential Evolution
Joe Amali, S. Miruna; Baskar, S.
This paper presents a design of robust optimal fixed structure controller for systems with uncertainties and disturbance using Self Adaptive Differential Evolution (SaDE) algorithm. PID controller and second order polynomial structure are considered for fixed structure controller. The design problem is formulated as minimization of maximum value of real part of the poles subject to the robust stability criteria and load disturbance attenuation criteria. The performance of the proposed method is demonstrated with a test system. SaDE self adapts the trial vector generation strategy and crossover rate (CR) value during evolution. Self adaptive Penalty (SP) method is used for constraint handling. The results are compared with constrained PSO and mixed Deterministic/Randomized algorithms. It is shown experimentally that the SaDE adapts automatically to the best strategy and CR value. Performance of the SaDE-based controller is superior to other methods in terms of success rate, robust stability, and disturbance attenuation.
一类不确定线性系统的非脆弱鲁棒有限时间 H∞控制研究%Non-fragile robust finite-time H∞ control for uncertain linear systems
侯林林; 任航丽
2016-01-01
The problem of non‐fragile robust finite‐time H∞ control for a class of uncertain linear systems was studied .The pro‐posed system had the properties that the state was uncertainty ,and the disturbances were generated by an external system .Mo‐reover ,the designed controller was also state uncertain .Using the Lyapunov function theory ,the finite‐time stabilization of the closed‐loop system was analyzed ,and the solved conditions were presented in the form of linear matrix inequality .Numerical sim‐ulation demonstrated the effectiveness of the proposed method .%研究了一类不确定线性系统的非脆弱鲁棒有限时间 H∞控制问题，所考虑的系统具有状态不确定性，且扰动是由外部系统生成的，所设计的控制器具有非脆弱性。利用Lyapunov 函数理论分析了闭环系统的有限时间可镇定性，并以线性矩阵不等式的形式给出了可解的条件。数值仿真验证了所提方法的有效性。
程媛媛; 蒋威
2012-01-01
介绍了不确定时变时滞退化系统的一种新的鲁棒稳定性判据,该判据的提出利用适当的Lyapunov-Krasovskii函数方法,由一组线性矩阵不等式表示出来,判据可借助Matlab软件中LMI工具箱中得以验证.最后,数值实例证明了方法的有效性和优势.%This paper presents a new result of stability analysis for uncertain descriptor systems with time-varying delay,new delay-dependent robust stability criterion of uncertain time-delay descriptor systems is proposed by exploiting appropriate Lyapunov-Krasovskii functional candidate.This criterion is expressed by a set of linear matrix inequalities,which can be tested by using the LMI toolbox in Matlab.Finally,illustrative examples demonstrate the effectiveness and the advantage of the proposed method.
Whitaker, May
2016-01-01
Purpose Inverse planning simulated annealing (IPSA) optimized brachytherapy treatment plans are characterized with large isolated dwell times at the first or last dwell position of each catheter. The potential of catheter shifts relative to the target and organs at risk in these plans may lead to a more significant change in delivered dose to the volumes of interest relative to plans with more uniform dwell times. Material and methods This study aims to determine if the Nucletron Oncentra dwell time deviation constraint (DTDC) parameter can be optimized to improve the robustness of high-dose-rate (HDR) prostate brachytherapy plans to catheter displacements. A set of 10 clinically acceptable prostate plans were re-optimized with a DTDC parameter of 0 and 0.4. For each plan, catheter displacements of 3, 7, and 14 mm were retrospectively applied and the change in dose volume histogram (DVH) indices and conformity indices analyzed. Results The robustness of clinically acceptable prostate plans to catheter displacements in the caudal direction was found to be dependent on the DTDC parameter. A DTDC value of 0 improves the robustness of planning target volume (PTV) coverage to catheter displacements, whereas a DTDC value of 0.4 improves the robustness of the plans to changes in hotspots. Conclusions The results indicate that if used in conjunction with a pre-treatment catheter displacement correction protocol and a tolerance of 3 mm, a DTDC value of 0.4 may produce clinically superior plans. However, the effect of the DTDC parameter in plan robustness was not observed to be as strong as initially suspected. PMID:27504129
Poder, Joel; Whitaker, May
2016-06-01
Inverse planning simulated annealing (IPSA) optimized brachytherapy treatment plans are characterized with large isolated dwell times at the first or last dwell position of each catheter. The potential of catheter shifts relative to the target and organs at risk in these plans may lead to a more significant change in delivered dose to the volumes of interest relative to plans with more uniform dwell times. This study aims to determine if the Nucletron Oncentra dwell time deviation constraint (DTDC) parameter can be optimized to improve the robustness of high-dose-rate (HDR) prostate brachytherapy plans to catheter displacements. A set of 10 clinically acceptable prostate plans were re-optimized with a DTDC parameter of 0 and 0.4. For each plan, catheter displacements of 3, 7, and 14 mm were retrospectively applied and the change in dose volume histogram (DVH) indices and conformity indices analyzed. The robustness of clinically acceptable prostate plans to catheter displacements in the caudal direction was found to be dependent on the DTDC parameter. A DTDC value of 0 improves the robustness of planning target volume (PTV) coverage to catheter displacements, whereas a DTDC value of 0.4 improves the robustness of the plans to changes in hotspots. The results indicate that if used in conjunction with a pre-treatment catheter displacement correction protocol and a tolerance of 3 mm, a DTDC value of 0.4 may produce clinically superior plans. However, the effect of the DTDC parameter in plan robustness was not observed to be as strong as initially suspected.
UPI: A Primary Index for Uncertain Databases
Kimura, Hideaki; Madden, Samuel R.; Zdonik, Stanley B.
2010-01-01
Uncertain data management has received growing attention from industry and academia. Many efforts have been made to optimize uncertain databases, including the development of special index data structures. However, none of these efforts have explored primary (clustered) indexes for uncertain databases, despite the fact that clustering has the potential to offer substantial speedups for non-selective analytic queries on large uncertain databases. In this paper, we propose a new index called a ...
Robust non-gradient C subroutines for non-linear optimization
Brock, Pernille; Madsen, Kaj; Nielsen, Hans Bruun
2004-01-01
This report presents a package of robust and easy-to-use C subroutines for solving unconstrained and constrained non-linear optimization problems, where gradient information is not required. The intention is that the routines should use the currently best algorithms available. All routines have...... subroutines are obtained by changing 0 to 1. The present report is a new and updated version of a previous report NI-91-04 with the title Non-gradient c Subroutines for Non- Linear Optimization, [16]. Both the previous and the present report describe a collection of subroutines, which have been translated...... from Fortran to C. The reason for writing the present report is that some of the C subroutines have been replaced by more e ective and robust versions translated from the original Fortran subroutines to C by the Bandler Group, see [1]. Also the test examples have been modified to some extent...
Robust Video Stabilization Using Particle Keypoint Update and l₁-Optimized Camera Path.
Jeon, Semi; Yoon, Inhye; Jang, Jinbeum; Yang, Seungji; Kim, Jisung; Paik, Joonki
2017-02-10
Acquisition of stabilized video is an important issue for various type of digital cameras. This paper presents an adaptive camera path estimation method using robust feature detection to remove shaky artifacts in a video. The proposed algorithm consists of three steps: (i) robust feature detection using particle keypoints between adjacent frames; (ii) camera path estimation and smoothing; and (iii) rendering to reconstruct a stabilized video. As a result, the proposed algorithm can estimate the optimal homography by redefining important feature points in the flat region using particle keypoints. In addition, stabilized frames with less holes can be generated from the optimal, adaptive camera path that minimizes a temporal total variation (TV). The proposed video stabilization method is suitable for enhancing the visual quality for various portable cameras and can be applied to robot vision, driving assistant systems, and visual surveillance systems.
Robust state feedback controller design of STATCOM using chaotic optimization algorithm
Safari Amin
2010-01-01
Full Text Available In this paper, a new design technique for the design of robust state feedback controller for static synchronous compensator (STATCOM using Chaotic Optimization Algorithm (COA is presented. The design is formulated as an optimization problem which is solved by the COA. Since chaotic planning enjoys reliability, ergodicity and stochastic feature, the proposed technique presents chaos mapping using Lozi map chaotic sequences which increases its convergence rate. To ensure the robustness of the proposed damping controller, the design process takes into account a wide range of operating conditions and system configurations. The simulation results reveal that the proposed controller has an excellent capability in damping power system low frequency oscillations and enhances greatly the dynamic stability of the power systems. Moreover, the system performance analysis under different operating conditions shows that the phase based controller is superior compare to the magnitude based controller.
Including robustness in multi-criteria optimization for intensity-modulated proton therapy
Chen, Wei; Trofimov, Alexei; Madden, Thomas; Kooy, Hanne; Bortfeld, Thomas; Craft, David
2011-01-01
We present a method to include robustness into a multi-criteria optimization (MCO) framework for intensity-modulated proton therapy (IMPT). The approach allows one to simultaneously explore the trade-off between different objectives as well as the trade-off between robustness and nominal plan quality. In MCO, a database of plans each emphasizing different treatment planning objectives, is pre-computed to approximate the Pareto surface. An IMPT treatment plan that strikes the best balance between the different objectives can be selected by navigating on the Pareto surface. In our approach, robustness is integrated into MCO by adding robustified objectives and constraints to the MCO problem. Uncertainties of the robust problem are modeled by pre-calculated dose-influence matrices for a nominal scenario and a number of pre-defined error scenarios. A robustified objective represents the worst objective function value that can be realized for any of the error scenarios. The optimization method is based on a linear...
陈志旺; 薛佳伟
2012-01-01
针对具有参数不确定性和未知外部干扰的机械手轨迹跟踪问题提出了一种多输入多输出自适应鲁棒预测控制方法．首先根据机械手模型设计非线性鲁棒预测控制律，并在控制律中引入监督控制项；然后利用函数逼近的方法逼近控制律中因模型不确定性以及外部干扰引起的未知项．理论证明了所设计的控制律能够使机械手无静差跟踪期望的关节角轨迹．仿真验证了本文设计方法的有效性．%A multi-input-multi-output adaptive robust predictive control method is presented to solve the trajectory tracking problem of robotic manipulator system with uncertain parameters and unknown external disturbances. A nonlinear robust predictive controller is first designed for the robotic manipulator system, and then a supervisory control is added to the controller. The function approximation is employed to approximate the unknown terms in the predictive control law caused by uncertain system model and external disturbances. It is proved that the proposed controller can make robotic manipulator track the desired joint angle trajectory without static error. Simulation results show the effectiveness of the method.
Robustness of "cut and splice" genetic algorithms in the structural optimization of atomic clusters
Froltsov, V.; Reuter, K.
2009-01-01
We return to the geometry optimization problem of Lennard-Jones clusters to analyze the performance dependence of 'cut and splice' genetic algorithms (GAs) on the employed population size. We generally find that admixing twinning mutation moves leads to an improved robustness of the algorithm efficiency with respect to this a priori unknown technical parameter. The resulting very stable performance of the corresponding mutation + mating GA implementation over a wide range of population sizes...
Lotfi, Babak; Wang, Qiuwang
2013-07-01
The performance of thermal control systems has, in recent years, improved in numerous ways due to developments in control theory and information technology. The shell-and-tube heat exchanger (STHX) is a medium where heat transfer process occurred. The accuracy of the heat exchanger depends on the performance of both elements. Therefore, both components need to be controlled in order to achieve a substantial result in the process. For this purpose, the actual dynamics of both shell and tube of the heat exchanger is crucial. In this paper, optimal reliability-based multi-objective Pareto design of robust state feedback controllers for a STHX having parameters with probabilistic uncertainties. Accordingly, the probabilities of failure of those objective functions are also considered in the reliability-based design optimization (RBDO) approach. A new multi-objective uniform-diversity genetic algorithm (MUGA) is presented and used for Pareto optimum design of linear state feedback controllers for STHX problem. In this way, Pareto front of optimum controllers is first obtained for the nominal deterministic STHX using the conflicting objective functions in time domain. Such Pareto front is then obtained for STHX having probabilistic uncertainties in its parameters using the statistical moments of those objective functions through a Hammersley Sequence Sampling (HSS) approach. It is shown that multi-objective reliability-based Pareto optimization of the robust state feedback controllers using MUGA includes those that may be obtained by various crisp threshold values of probability of failures and, thus, remove the difficulty of selecting suitable crisp values. Besides, the multi-objective Pareto optimization of such robust feedback controllers using MUGA unveils some very important and informative trade-offs among those objective functions. Consequently, some optimum robust state feedback controllers can be compromisingly chosen from the Pareto frontiers.
Robust subspace estimation using low-rank optimization theory and applications
Oreifej, Omar
2014-01-01
Various fundamental applications in computer vision and machine learning require finding the basis of a certain subspace. Examples of such applications include face detection, motion estimation, and activity recognition. An increasing interest has been recently placed on this area as a result of significant advances in the mathematics of matrix rank optimization. Interestingly, robust subspace estimation can be posed as a low-rank optimization problem, which can be solved efficiently using techniques such as the method of Augmented Lagrange Multiplier. In this book,?the authors?discuss fundame
Optimal Control for Fast and Robust Generation of Entangled States in Anisotropic Heisenberg Chains
Zhang, Xiong-Peng; Shao, Bin; Zou, Jian
2017-05-01
Motivated by some recent results of the optimal control (OC) theory, we study anisotropic XXZ Heisenberg spin-1/2 chains with control fields acting on a single spin, with the aim of exploring how maximally entangled state can be prepared. To achieve the goal, we use a numerical optimization algorithm (e.g., the Krotov algorithm, which was shown to be capable of reaching the quantum speed limit) to search an optimal set of control parameters, and then obtain OC pulses corresponding to the target fidelity. We find that the minimum time for implementing our target state depending on the anisotropy parameter Δ of the model. Finally, we analyze the robustness of the obtained results for the optimal fidelities and the effectiveness of the Krotov method under some realistic conditions.
Ji, Hong-Fei; Jiao, Yi; Huang, Ming-Yang; Xu, Shou-Yan; Wang, Na; Wang, Sheng
2016-09-01
The Robust Conjugate Direction Search (RCDS) method is used to optimize the collimation system for the Rapid Cycling Synchrotron (RCS) of the China Spallation Neutron Source (CSNS). The parameters of secondary collimators are optimized for a better performance of the collimation system. To improve the efficiency of the optimization, the Objective Ring Beam Injection and Tracking (ORBIT) parallel module combined with MATLAB parallel computing is used, which can run multiple ORBIT instances simultaneously. This study presents a way to find an optimal parameter combination of the secondary collimators for a machine model in preparation for CSNS/RCS commissioning. Supported by National Natural Science Foundation of China (11475202, 11405187, 11205185) and Youth Innovation Promotion Association of Chinese Academy of Sciences (2015009)
A robust approach to optimal matched filter design in ultrasonic non-destructive evaluation (NDE)
Li, Minghui; Hayward, Gordon
2017-02-01
The matched filter was demonstrated to be a powerful yet efficient technique to enhance defect detection and imaging in ultrasonic non-destructive evaluation (NDE) of coarse grain materials, provided that the filter was properly designed and optimized. In the literature, in order to accurately approximate the defect echoes, the design utilized the real excitation signals, which made it time consuming and less straightforward to implement in practice. In this paper, we present a more robust and flexible approach to optimal matched filter design using the simulated excitation signals, and the control parameters are chosen and optimized based on the real scenario of array transducer, transmitter-receiver system response, and the test sample, as a result, the filter response is optimized and depends on the material characteristics. Experiments on industrial samples are conducted and the results confirm the great benefits of the method.
Optimal Control for Fast and Robust Generation of Entangled States in Anisotropic Heisenberg Chains
Zhang, Xiong-Peng; Shao, Bin; Zou, Jian
2017-02-01
Motivated by some recent results of the optimal control (OC) theory, we study anisotropic XXZ Heisenberg spin-1/2 chains with control fields acting on a single spin, with the aim of exploring how maximally entangled state can be prepared. To achieve the goal, we use a numerical optimization algorithm (e.g., the Krotov algorithm, which was shown to be capable of reaching the quantum speed limit) to search an optimal set of control parameters, and then obtain OC pulses corresponding to the target fidelity. We find that the minimum time for implementing our target state depending on the anisotropy parameter Δ of the model. Finally, we analyze the robustness of the obtained results for the optimal fidelities and the effectiveness of the Krotov method under some realistic conditions.
Sarjaš, Andrej; Chowdhury, Amor; Svečko, Rajko
2016-09-01
This paper presents the synthesis of an optimal robust controller design using the polynomial pole placement technique and multi-criteria optimisation procedure via an evolutionary computation algorithm - differential evolution. The main idea of the design is to provide a reliable fixed-order robust controller structure and an efficient closed-loop performance with a preselected nominally characteristic polynomial. The multi-criteria objective functions have quasi-convex properties that significantly improve convergence and the regularity of the optimal/sub-optimal solution. The fundamental aim of the proposed design is to optimise those quasi-convex functions with fixed closed-loop characteristic polynomials, the properties of which are unrelated and hard to present within formal algebraic frameworks. The objective functions are derived from different closed-loop criteria, such as robustness with metric ?∞, time performance indexes, controller structures, stability properties, etc. Finally, the design results from the example verify the efficiency of the controller design and also indicate broader possibilities for different optimisation criteria and control structures.
Xiaomin Tian
2014-02-01
Full Text Available In this paper, the problem of stabilizing a class of fractional-order chaotic systems with sector and dead-zone nonlinear inputs is investigated. The effects of model uncertainties and external disturbances are fully taken into account. Moreover, the bounds of both model uncertainties and external disturbances are assumed to be unknown in advance. To deal with the system’s nonlinear items and unknown bounded uncertainties, an adaptive fractional-order sliding mode (AFSM controller is designed. Then, Lyapunov’s stability theory is used to prove the stability of the designed control scheme. Finally, two simulation examples are given to verify the effectiveness and robustness of the proposed control approach.
Vilas Carlos
2012-07-01
Full Text Available Abstract Background Systems biology allows the analysis of biological systems behavior under different conditions through in silico experimentation. The possibility of perturbing biological systems in different manners calls for the design of perturbations to achieve particular goals. Examples would include, the design of a chemical stimulation to maximize the amplitude of a given cellular signal or to achieve a desired pattern in pattern formation systems, etc. Such design problems can be mathematically formulated as dynamic optimization problems which are particularly challenging when the system is described by partial differential equations. This work addresses the numerical solution of such dynamic optimization problems for spatially distributed biological systems. The usual nonlinear and large scale nature of the mathematical models related to this class of systems and the presence of constraints on the optimization problems, impose a number of difficulties, such as the presence of suboptimal solutions, which call for robust and efficient numerical techniques. Results Here, the use of a control vector parameterization approach combined with efficient and robust hybrid global optimization methods and a reduced order model methodology is proposed. The capabilities of this strategy are illustrated considering the solution of a two challenging problems: bacterial chemotaxis and the FitzHugh-Nagumo model. Conclusions In the process of chemotaxis the objective was to efficiently compute the time-varying optimal concentration of chemotractant in one of the spatial boundaries in order to achieve predefined cell distribution profiles. Results are in agreement with those previously published in the literature. The FitzHugh-Nagumo problem is also efficiently solved and it illustrates very well how dynamic optimization may be used to force a system to evolve from an undesired to a desired pattern with a reduced number of actuators. The presented
ROBUST TOPOLOGY OPTIMIZATION DESIGN OF STRUCTURES WITH MULTIPLE LOAD CASES%多工况下结构鲁棒性拓扑优化设计
罗阳军; 亢战; 邓子辰
2011-01-01
In practical engineering, the structural performance always exhibit some degree of variations due to the fact that the applied loads fluctuate dramatically throughout its service life-cycle.Thus, the need is highlighted to account for uncertainties in topology optimization stage of the structural design.Conventional deterministic topology optimization searches for minimum compliance without considering the uncertainties in operating processes.Recently, the robust structural design has attracted intensive attentions because it can reduce the variability of structural performance.However, existing robust design methods are confined to the size and shape optimization problems.This paper aims to incorporate the robust design strategy into the continuum topology optimization problem under multiple uncertain load cases by minimizing variation of the objective performance.Following the SIMP approach, an artificial isotropic material model with penalization for elastic constants is assumed and elemental relative density variables are used for describing the structural layout.The considered robust topology optimization problem is thus formulated as to find the optimal structural topology that minimizes the standard deviation of structural total compliance under the constraint on material volume.To avoid the difficulties associated with directly evaluating the standard deviation of the structural compliance, a convenient computing formula of the objective function is presented based on the stochastic finite element method.In addition, an adjoint variable method is employed for the efficient sensitivity analysis of the objective function.Then, the gradient based optimization algorithm (Method of Moving Asymptotes, MMA)is used to update the design variables in the optimization loop.Finally, three numerical examples for topology optimization of 2D and 3D structures illustrate the applicability and the validity of the present model as well as the proposed numerical techniques
Autonomous Modelling of X-ray Spectra Using Robust Global Optimization Methods
Rogers, Adam; Safi-Harb, Samar; Fiege, Jason
2015-08-01
The standard approach to model fitting in X-ray astronomy is by means of local optimization methods. However, these local optimizers suffer from a number of problems, such as a tendency for the fit parameters to become trapped in local minima, and can require an involved process of detailed user intervention to guide them through the optimization process. In this work we introduce a general GUI-driven global optimization method for fitting models to X-ray data, written in MATLAB, which searches for optimal models with minimal user interaction. We directly interface with the commonly used XSPEC libraries to access the full complement of pre-existing spectral models that describe a wide range of physics appropriate for modelling astrophysical sources, including supernova remnants and compact objects. Our algorithm is powered by the Ferret genetic algorithm and Locust particle swarm optimizer from the Qubist Global Optimization Toolbox, which are robust at finding families of solutions and identifying degeneracies. This technique will be particularly instrumental for multi-parameter models and high-fidelity data. In this presentation, we provide details of the code and use our techniques to analyze X-ray data obtained from a variety of astrophysical sources.
Bagherpoor, H M; Salmasi, Farzad R
2015-07-01
In this paper, robust model reference adaptive tracking controllers are considered for Single-Input Single-Output (SISO) and Multi-Input Multi-Output (MIMO) linear systems containing modeling uncertainties, unknown additive disturbances and actuator fault. Two new lemmas are proposed for both SISO and MIMO, under which dead-zone modification rule is improved such that the tracking error for any reference signal tends to zero in such systems. In the conventional approach, adaption of the controller parameters is ceased inside the dead-zone region which results tracking error, while preserving the system stability. In the proposed scheme, control signal is reinforced with an additive term based on tracking error inside the dead-zone which results in full reference tracking. In addition, no Fault Detection and Diagnosis (FDD) unit is needed in the proposed approach. Closed loop system stability and zero tracking error are proved by considering a suitable Lyapunov functions candidate. It is shown that the proposed control approach can assure that all the signals of the close loop system are bounded in faulty conditions. Finally, validity and performance of the new schemes have been illustrated through numerical simulations of SISO and MIMO systems in the presence of actuator faults, modeling uncertainty and output disturbance.
Robust Nearfield Wideband Beamforming Design Based on Adaptive-Weighted Convex Optimization
Guo Ye-Cai
2017-01-01
Full Text Available Nearfield wideband beamformers for microphone arrays have wide applications in multichannel speech enhancement. The nearfield wideband beamformer design based on convex optimization is one of the typical representatives of robust approaches. However, in this approach, the coefficient of convex optimization is a constant, which has not used all the freedom provided by the weighting coefficient efficiently. Therefore, it is still necessary to further improve the performance. To solve this problem, we developed a robust nearfield wideband beamformer design approach based on adaptive-weighted convex optimization. The proposed approach defines an adaptive-weighted function by the adaptive array signal processing theory and adjusts its value flexibly, which has improved the beamforming performance. During each process of the adaptive updating of the weighting function, the convex optimization problem can be formulated as a SOCP (Second-Order Cone Program problem, which could be solved efficiently using the well-established interior-point methods. This method is suitable for the case where the sound source is in the nearfield range, can work well in the presence of microphone mismatches, and is applicable to arbitrary array geometries. Several design examples are presented to verify the effectiveness of the proposed approach and the correctness of the theoretical analysis.
Robust H2 estimation and control
Lihua XIE; Yeng Chai SOH; Chunling DU; Yun ZOU
2004-01-01
This paper is concerned with the H2 estimation and control problems for uncertain discretetime systems with norm-bounded parameter uncertainty. We first present an analysis result on H2 norm bound for a stable uncertain system in terms of linearmatrix inequalities (LMIs). A solution to the robust H2 estimation problem is then derived in terms of two LMIs. As compared tothe existing results, our result on robust H2 estimation is more general. In addition, explicit search of appropriate scaling parametersis not needed as the optimization is convex in the scaling parameters. The LMI approach is also extended to solve the robust H2control problem which has been difficult for the traditional Riccati equation approach since no separation principle has been knownfor uncertain systems. The design approach is demonstrated through a simple example.
Robust model of emergency material allocation under uncertain network structure%不确定网络结构下的应急物资鲁棒配置模型
俞武扬
2013-01-01
灾害发生前的应急物资配置问题具有两个重要的不确定性，即交通网络中受自然灾害影响而阻断的道路以及受灾点的应急物资需求量。通过引入两个控制水平参数建立了不确定网络结构下的两阶段应急物资鲁棒配置模型，并在线性化第2阶段的回溯问题后提出了求解模型的Benders分解算法。数值实验结果表明了所提出的模型的有效性以及所得配置方案的鲁棒性。%There are two important uncertainties in the emergency material allocation problem before disaster occur:One is of the damaged transportation system by nature disaster, and the other one is of the resource requirements of demand points. A robust model of emergency materials allocation problem under the uncertain network structure is proposed by introducing two control parameters. An algorithm using Benders decomposition is developed via linearize the second stage recourse problem. Finally, a case study shows the effectiveness of the proposed model and robustness of the solution strategy.
Mikhalchenko, V. V.; Rubanik, Yu T.
2016-10-01
The work is devoted to the problem of cost-effective adaptation of coal mines to the volatile and uncertain market conditions. Conceptually it can be achieved through alignment of the dynamic characteristics of the coal mining system and power spectrum of market demand for coal product. In practical terms, this ensures the viability and competitiveness of coal mines. Transformation of dynamic characteristics is to be done by changing the structure of production system as well as corporate, logistics and management processes. The proposed methods and algorithms of control are aimed at the development of the theoretical foundations of adaptive optimization as basic methodology for coal mine enterprise management in conditions of high variability and uncertainty of economic and natural environment. Implementation of the proposed methodology requires a revision of the basic principles of open coal mining enterprises design.
Uncertain Optimization and Solution of Green Product Module Partition%绿色产品模块划分的不确定优化及求解
刘电霆; 胡浩平
2015-01-01
针对绿色模块划分中出现定性变量参数等问题，研究了绿色设计中包含不确定性因素的产品模块划分，给出绿色模块划分的方法，以模块内部最大聚合度量、模块之间最小耦合度量和模块划分最高绿色度量为目标函数，建立了产品绿色模块划分的不确定优化模型，继而转化为确定性优化模型。基于离散二进制粒子群算法提出一种十三进制离散粒子群解决方法，以MJ-50型号数控机床为例，验证了其结构模块构造的合理有效性，实验证明所提出的方法可行，有一定实用价值。%Aiming at the qualitative variable green module partition problem, to study the green design includes the uncertain factors of product module partition, module partition method is green, the module maximum polymerization degree, minimumdegree of coupling between modules and module partition of the highest green degree as the objective function, a green product module partition is uncertain optimization model. Discrete binary particle swarm algorithm provides a thirteen band discrete particle swarm optimization method based on the MJ-50 model, NCmachine tool as an example, verify the effectiveness of the reasonable structure module structure, the proposed method is demonstrated experimentally feasible,and has certain practical value.
Commitment and dispatch of heat and power units via affinely adjustable robust optimization
Zugno, Marco; Morales González, Juan Miguel; Madsen, Henrik
2016-01-01
The joint management of heat and power systems is believed to be key to the integration of renewables into energy systems with a large penetration of district heating. Determining the day-ahead unit commitment and production schedules for these systems is an optimization problem subject...... to uncertainty stemming from the unpredictability of demand and prices for heat and electricity. Furthermore, owing to the dynamic features of production and heat storage units as well as to the length and granularity of the optimization horizon (e.g., one whole day with hourly resolution), this problem...... approach. Secondly, we appraise the gain obtained by switching from linear to piecewise-linear decision rules within robust optimization. Furthermore, we give directions for selecting the parameters defining the uncertainty set (size, budget) and assess the resulting trade-off between average profit...
Optimal and robust design of brain-state-in-a-box neural associative memories.
Park, Yonmook
2010-03-01
This paper presents a new optimization approach to the design of associative memories via the brain-state-in-a-box (BSB) neural network. The optimization approach proposed in this paper provides the large and uniform domains of attraction of the prototype patterns, the large robustness margin for the weight matrix of the perturbed BSB neural network, the asymptotic stability of the prototype patterns, and the global stability of the BSB neural network. Based on some known qualitative properties of the BSB neural network and theoretical results presented in this paper, a synthesis method of the BSB-based associative memory is established. The synthesis method presented in this paper is given in the form of a linear matrix inequality-based optimization problem, which can be efficiently solved by a readily available software. Design examples are given to demonstrate the applicability of the proposed method and to compare with the existing synthesis methods.
Robust optimal control of material flows in demand-driven supply networks
Laumanns, Marco; Lefeber, Erjen
2006-04-01
We develop a model based on stochastic discrete-time controlled dynamical systems in order to derive optimal policies for controlling the material flow in supply networks. Each node in the network is described as a transducer such that the dynamics of the material and information flows within the entire network can be expressed by a system of first-order difference equations, where some inputs to the system act as external disturbances. We apply methods from constrained robust optimal control to compute the explicit control law as a function of the current state. For the numerical examples considered, these control laws correspond to certain classes of optimal ordering policies from inventory management while avoiding, however, any a priori assumptions about the general form of the policy.
Robust Optimization of Thermal Aspects of Friction Stir Welding Using Manifold Mapping Techniques
Larsen, Anders Astrup; Lahaye, Domenico; Schmidt, Henrik Nikolaj Blicher
2008-01-01
The aim of this paper is to optimize a friction stir welding process taking robustness into account. The optimization problems are formulated with the goal of obtaining desired mean responses while reducing the variance of the response. We restrict ourselves to a thermal model of the process...... and use the manifold mapping technique to solve the optimization problems using a fast analytical coarse and an expensive accurate fine model. The statistics of the response are calculated using Taylor expansions and are compared to Monte Carlo simulations. The results show that the use of manifold...... mapping reduces the number of fine model evaluations required and that the Taylor expansion approach gives good results when compared to Monte Carlo simulations....
Robust method optimization strategy-a useful tool for method transfer: the case of SFC.
Dispas, Amandine; Lebrun, Pierre; Andri, Bertyl; Rozet, Eric; Hubert, Philippe
2014-01-01
The concept of Quality by Design (QbD) is now well established in pharmaceutical industry and should be applied to the development of any analytical methods. In this context, the key concept of Design Space (DS) was introduced in the field of analytical method optimization. In chromatographic words, the DS is the space of chromatographic conditions that will ensure the quality of peaks separation, thus DS is a zone of robustness. In the present study, the interest of robust method optimization strategy was investigated in the context of direct method transfer from sending to receiving laboratory. The benefit of this approach is to speed up the method life cycle by performing only one quantitative validation step in the final environment of method use. A Supercritical Fluid Chromatography (SFC) method previously developed was used as a case study in this work. Moreover, the interest of geometric transfer was investigated simultaneously in order to stress a little bit more the transfer exercise and, by the way, emphasize the additional benefit of DS strategy in this particular context. Three successful transfers were performed on two column geometries. In order to compare original and transferred methods, the observed relative retention times (RT) were modelled as a function of the predicted relative RT and of the method type (original or transferred). The observed relative RT of the original and transferred methods are not statistically different and thus the method transfer is successfully achieved thanks to the robust optimization strategy. Furthermore, the analytical method was improved considering analysis time (reduced five times) and peak capacity (increased three times). To conclude, the advantage of using a DS strategy implemented for the optimization and transfer of SFC method was successfully demonstrated in this work.
Amribt, Z; Dewasme, L; Vande Wouwer, A; Bogaerts, Ph
2014-08-01
The maximization of biomass productivity in fed-batch cultures of hybridoma cells is analyzed based on the overflow metabolism model. Due to overflow metabolism, often attributed to limited oxygen capacity, lactate and ammonia are formed when the substrate concentrations (glucose and glutamine) are above a critical value, which results in a decrease in biomass productivity. Optimal feeding rate, on the one hand, for a single feed stream containing both glucose and glutamine and, on the other hand, for two separate feed streams of glucose and glutamine are determined using a Nelder-Mead simplex optimization algorithm. The optimal multi exponential feed rate trajectory improves the biomass productivity by 10 % as compared to the optimal single exponential feed rate. Moreover, this result is validated by the one obtained with the analytical approach in which glucose and glutamine are fed to the culture so as to control the hybridoma cells at the critical metabolic state, which allows maximizing the biomass productivity. The robustness analysis of optimal feeding profiles obtained with different optimization strategies is considered, first, with respect to parameter uncertainties and, finally, to model structure errors.
周川; 何俊伟; 陈庆伟
2013-01-01
Considering the problem of congestion control for the time-varying and uncertain TCP/IP network, we proposed a novel discrete-time robust active queue management (AQM) scheme based on H-infinity feedback control for the TCP flow model with link capacity disturbance and parameter uncertainties simultaneously. In this method, the bandwidth occupied by short-lived connections is treated as the external disturbances, and the effect of both delay and parameter uncertainties is taken into account for the TCP/AQM system model. By using Lyapunov stability theory and LMI techniques, we propose a discrete-time robust H-infinity AQM controller to guarantee the asymptotic stability and robustness of the queue length response of a router queues. Finally the NS-2 simulation results demonstrate effectiveness of the proposed method.%针对TCP/IP网络存在参数时变和不确定性下的拥塞控制问题,提出一种新的基于H∞状态反馈控制的离散鲁棒主动列队管理算法(AQM).该方法针对不确定TCP流模型,将短期突发流所占据的带宽作为系统的外部干扰,同时考虑时滞和参数不确定性因素,基于Lyapunov稳定性理论和线性矩阵不等式技术,设计了离散鲁棒状态反馈控制器以保证路由器队列响应的稳定性和鲁棒性.最后,通过NS-2仿真验证了本文方法的有效性.