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Convex Optimization Problem (convex + optimization_problem)
Selected AbstractsRobust H, filtering for switched linear discrete-time systems with polytopic uncertaintiesINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 6 2006Lixian Zhang Abstract In this paper, the problem of robust H, filtering for switched linear discrete-time systems with polytopic uncertainties is investigated. Based on the mode-switching idea and parameter-dependent stability result, a robust switched linear filter is designed such that the corresponding filtering error system achieves robust asymptotic stability and guarantees a prescribed H, performance index for all admissible uncertainties. The existence condition of such filter is derived and formulated in terms of a set of linear matrix inequalities (LMIs) by the introduction of slack variables to eliminate the cross coupling of system matrices and Lyapunov matrices among different subsystems. The desired filter can be constructed by solving the corresponding convex optimization problem, which also provides an optimal H, noise-attenuation level bound for the resultant filtering error system. A numerical example is given to show the effectiveness and the potential of the proposed techniques. Copyright © 2006 John Wiley & Sons, Ltd. [source] New absolute stability criteria for time-delay Lur'e systems with sector-bounded nonlinearityINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 6 2010Xian Liu Abstract This paper is concerned with the problem of absolute stability of time-delay Lur'e systems with sector-bounded nonlinearity. Several novel criteria are presented by using a Lur'e,Postnikov function. For a general Lur'e system with known time delay, the absolute stability of it is analyzed by solving a set of linear matrix inequalities (LMIs). The maximum upper bound of the allowable time delay for a general Lur'e system is derived by solving a convex optimization problem. The feasibility of the LMIs implies some frequency-domain interpretations which are similar to the frequency-domain inequalities in the circle criterion and the Popov criterion. Copyright © 2009 John Wiley & Sons, Ltd. [source] On delay-dependent LMI-based guaranteed cost control of uncertain neutral systems with discrete and distributed time-varying delaysINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 12 2007Jenq-Der Chen Abstract In this paper, the problem of designing robust guaranteed cost control law for a class of uncertain neutral system with a given quadratic cost function is considered. Based on Lyapunov,Krasovskii functional theory, a delay-dependent criterion for the existence of guaranteed cost controller is expressed in the form of two linear matrix inequalities (LMIs), which can be solved by using effective LMI toolbox. Moreover, a convex optimization problem satisfying some LMI constraints is formulated to solve a guaranteed cost controller which achieves the minimization of the closed-loop guaranteed cost. An efficient approach is proposed to design the guaranteed cost control for uncertain neutral systems. Computer software Matlab can be used to solve all the proposed results. Finally, a numerical example is illustrated to show the usefulness of our obtained design method. Copyright © 2006 John Wiley & Sons, Ltd. [source] Support vector machines-based generalized predictive controlINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 17 2006S. Iplikci Abstract In this study, we propose a novel control methodology that introduces the use of support vector machines (SVMs) in the generalized predictive control (GPC) scheme. The SVM regression algorithms have extensively been used for modelling nonlinear systems due to their assurance of global solution, which is achieved by transforming the regression problem into a convex optimization problem in dual space, and also their higher generalization potential. These key features of the SVM structures lead us to the idea of employing a SVM model of an unknown plant within the GPC context. In particular, the SVM model can be employed to obtain gradient information and also it can predict future trajectory of the plant output, which are needed in the cost function minimization block. Simulations have confirmed that proposed SVM-based GPC scheme can provide a noticeably high control performance, in other words, an unknown nonlinear plant controlled by SVM-based GPC can accurately track the reference inputs with different shapes. Moreover, the proposed SVM-based GPC scheme maintains its control performance under noisy conditions. Copyright © 2006 John Wiley & Sons, Ltd. [source] A smoothing Newton's method for the construction of a damped vibrating system from noisy test eigendataNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2 2009Zheng-Jian Bai Abstract In this paper we consider an inverse problem for a damped vibration system from the noisy measured eigendata, where the mass, damping, and stiffness matrices are all symmetric positive-definite matrices with the mass matrix being diagonal and the damping and stiffness matrices being tridiagonal. To take into consideration the noise in the data, the problem is formulated as a convex optimization problem involving quadratic constraints on the unknown mass, damping, and stiffness parameters. Then we propose a smoothing Newton-type algorithm for the optimization problem, which improves a pre-existing estimate of a solution to the inverse problem. We show that the proposed method converges both globally and quadratically. Numerical examples are also given to demonstrate the efficiency of our method. Copyright © 2008 John Wiley & Sons, Ltd. [source] H, control of switched linear discrete-time systems with polytopic uncertaintiesOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 5 2006Lixian Zhang Abstract In this paper, the problem of designing H, state-feedback controllers for switched linear discrete-time systems with polytopic uncertainties is investigated. Two approaches on designing robust and parameter-dependent H, controllers are proposed and the existence conditions of the desired controllers are derived and formulated in terms of a set of linear matrix inequalities. By solving the corresponding convex optimization problem, the desired controllers are obtained, respectively, and different optimal H, noise-attenuation level bounds of corresponding closed-loop systems are given as well. The designed controllers have their own advantages and disadvantages regarding the conservatism and realization complexity. An illustrative example emerging in networked control systems (NCS) and numerical simulations are presented to show the applicability and effectiveness of the obtained theoretic results. Copyright © 2006 John Wiley & Sons, Ltd. [source] Observer-based non-fragile control against measurement disturbances and controller perturbations for discrete systems with state delay ,ASIAN JOURNAL OF CONTROL, Issue 3 2009Xiaosheng Fang Abstract This paper investigates the observer-based non-fragile control problem for a class of discrete time delay systems with measurement disturbances and controller perturbations. A simultaneous state and disturbance estimation technique is developed by designing a state observer for a descriptor system obtained from the original system. Based on this observer, the design method of a non-fragile controller is then formulated and the controller design problem is transformed to a convex optimization problem, which can be solved by a linear matrix inequality approach. In this design, the additive and multiplicative forms of uncertainties which perturb the gains of control and observer are both considered. The resultant non-fragile observer-based controller guarantees that the closed-loop system is asymptotically stable and can tolerate measurement disturbances and a certain degree of controller parameter perturbation. A numerical example is given to illustrate the effectiveness of the proposed design method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] Performance analysis of reset control systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 11 2010W. H. T. M. Aangenent Abstract In this paper we present a general linear matrix inequality-based analysis method to determine the performance of a SISO reset control system in both the ,2 gain and ,2 sense. In particular, we derive convex optimization problems in terms of LMIs to compute an upperbound on the ,2 gain performance and the ,2 norm, using dissipativity theory with piecewise quadratic Lyapunov functions. The results are applicable to for all LTI plants and linear-based reset controllers, thereby generalizing the available results in the literature. Furthermore, we provide simple though convincing examples to illustrate the accuracy of our proposed ,2 gain and ,2 norm calculations and show that, for an input constrained ,2 problem, reset control can outperform a linear controller designed by a common nonlinear optimization method. Copyright © 2009 John Wiley & Sons, Ltd. [source] Delay-dependent anti-windup strategy for linear systems with saturating inputs and delayed outputsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 7 2004S. Tarbouriech Abstract This paper addresses the problem of the determination of stability regions for linear systems with delayed outputs and subject to input saturation, through anti-windup strategies. A method for synthesizing anti-windup gains aiming at maximizing a region of admissible states, for which the closed-loop asymptotic stability and the given controlled output constraints are respected, is proposed. Based on the modelling of the closed-loop system resulting from the controller plus the anti-windup loop as a linear time-delay system with a dead-zone nonlinearity, constructive delay-dependent stability conditions are formulated by using both quadratic and Lure Lyapunov,Krasovskii functionals. Numerical procedures based on the solution of some convex optimization problems with LMI constraints are proposed for computing the anti-windup gain that leads to the maximization of an associated stability region. The effectiveness of the proposed technique is illustrated by some numerical examples. Copyright © 2004 John Wiley & Sons, Ltd. [source] | ||||||||||