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Robust H_∞ dynamic output feedback control for linear time-varying uncertain systems via switching-type controllers

IET CONTROL theory AND applications 2010年第1期4卷 89-99页

作者： Yang, G. -H. Ye, D. Northeastern Univ Coll Informat Sci & Engn Shenyang 110004 Peoples R China Northeastern Univ Key Lab Integrated Automat Proc Ind Minist Educ Shenyang 110004 Peoples R China

The problem of designing robust H-infinity switching-type controllers via dynamic output feedback for uncertain linear systems is studied. The uncertainties are assumed to be time varying, unknown, but bounded, which appear affinely in the matrices of system model. Here, a switching mechanism is introduced to construct a novel robust H-infinity controller with time-varying gains and to reduce the conservativeness inherent in traditional robust H-infinity controllers with fixed gains. The proposed controller gains are switching between a number of fixed gains automatically, which depend on the bounds of uncertain parameters. New sufficient conditions with less conservativeness than those for designing traditional robust controllers with fixed gains are also derived to guarantee the stability and H-infinity performances of the closed-loop systems, and a two-step linear matrix inequality (LMI)-based procedure is proposed for designing switching controllers. A numerical example is given to illustrate the effectiveness of the proposed method.

关键词： H∞ control two-step linear matrix inequality robust H∞ switching-type controllers time-varying systems time-varying gains Time-varying control systems Stability in control theory control system synthesis robust H∞ dynamic output feedback control Control system analysis and synthesis methods closed-loop systems closed loop systems linear systems robust control linear time-varying uncertain systems feedback linear algebra (numerical analysis) uncertain systems linear matrix inequalities Optimal control

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Robust iterative learning control design for uncertain time-delay systems based on a performance index

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IET CONTROL theory AND applications 2010年第5期4卷 759-772页

作者： Meng, D. Jia, Y. Du, J. Yu, F. Beihang Univ BUAA Res Div 7 Beijing 100191 Peoples R China Beihang Univ BUAA SMSS Minist Educ Key Lab Math Informat & Behav Semant LMIB Beijing 100191 Peoples R China Beijing Univ Posts & Telecommun Sch Comp Sci & Technol Beijing Key Lab Intelligent Telecommun Software & Beijing 100876 Peoples R China Henan Polytech Univ Sch Elect Engn & Automat Jiaozuo 454000 Henan Peoples R China

Here the authors concerned with robust iterative learning control (ILC) for uncertain time-delay systems. They demonstrate that the design of a robust ILC is straightforward based on a performance index for the error system. The ILC algorithms under consideration are rather simple. They show that after the two-dimensional analysis of ILC, a Lyapunov-like approach can be used to directly obtain a stable algorithm that achieves monotonic convergence of the control input error. Sufficient stability conditions are provided in terms of linear matrix inequalities, which can determine learning gains as well. They also show that the Lyapunov-like approach can be applied to design robust ILC for uncertain systems with time-varying delay or multiple time delays. numerical simulation results are presented to illustrate the effectiveness of the proposed ILC approach.

关键词： performance index two-dimensional analysis adaptive control error system ILC algorithms Lyapunov-like approach Stability in control theory control system synthesis Control system analysis and synthesis methods robust control linear algebra (numerical analysis) delays Lyapunov methods learning systems Self-adjusting control systems uncertain time-delay systems Interpolation and function approximation (numerical analysis) uncertain systems linear matrix inequalities iterative methods control input error robust iterative learning control design monotonic convergence Distributed parameter control systems

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H_∞ stabilisation of non-linear stochastic active fault-tolerant control systems: fuzzy-interpolation approach

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IET CONTROL theory AND applications 2010年第10期4卷 2003-2017页

作者： Lin, Z. Lin, Y. Zhang, W. Beijing Univ Aeronaut & Astronaut Sch Automat Beijing 100191 Peoples R China Shandong Univ Sci & Technol Coll Informat & Elect Engn Qingdao 266510 Peoples R China

This study addresses the H-infinity control design problem systematically for a class of non-linear stochastic active fault-tolerant control systems with Markovian parameters. A sufficient condition for the non-linear stochastic fault-tolerant H-infinity control u(1)(x(t), eta(t)) is given in terms of a set of coupled Hamilton-Jacobi inequalities (HJIs). Then, a fuzzy-interpolation approach is developed to conquer the difficulty in solving the coupled HJIs, which sustains a fault-tolerant H-infinity fuzzy control u(2)(x(t), eta(t)) by solving linear matrix inequalities, instead of HJIs. A simulation example is presented to illustrate the effectiveness of the proposed design method.

关键词： H∞ control Markovian parameters stochastic systems Combinatorial mathematics Time-varying control systems stability control system synthesis Stability in control theory Control system analysis and synthesis methods Nonlinear control systems nonlinear stochastic system H∞ stabilisation H∞ control design interpolation algebra fault tolerance nonlinear control systems Interpolation and function approximation (numerical analysis) Optimal control linear matrix inequalities fuzzy-interpolation approach active fault-tolerant control systems Markov processes Hamilton-Jacobi inequalities fuzzy set theory

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New stability criteria for continuous-time systems with interval time-varying delay

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IET CONTROL theory AND applications 2010年第6期4卷 1101-1107页

作者： Zhu, X. -L. Wang, Y. Yang, G. -H. Zhengzhou Univ Light Ind Sch Comp Sci & Commun Engn Zhengzhou 450002 Henan Peoples R China Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore Northeastern Univ Coll Informat Sci & Engn Shenyang 110004 Liaoning Peoples R China Northeastern Univ Minist Educ Key Lab Integrated Automat Proc Ind Shenyang 110004 Liaoning Peoples R China

The authors investigate the stability for continuous-time systems with interval time-varying delay. To deal with the non-linear time-varying coefficients derived from Jensen's integral inequality, a well-known feature of the sum of these coefficients is utilised. Combining with a delay partition method, the upper bound of the derivative of the Lyapunov functional can be estimated more tightly and expressed as a convex combination with respect to the reciprocal of the delay rather than the delay. New less conservative stability criteria are derived in terms of linear matrix inequalities. numerical examples are given to illustrate the effectiveness of the proposed results.

关键词： delay partition method stability criteria nonlinear systems Lyapunov functional continuous-time systems stability nonlinear time-varying coefficients Time-varying control systems Stability in control theory linear algebra (numerical analysis) delays Lyapunov methods Nonlinear control systems Distributed parameter control systems interval time-varying delay continuous time systems linear matrix inequalities time-varying systems

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Simultaneous optimisation of the low-pass filter and state-feedback controller in a robust repetitive-control system

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IET CONTROL theory AND applications 2010年第8期4卷 1366-1376页

作者： She, J. -H. Wu, M. Lan, Y. -H. He, Y. Tokyo Univ Technol Sch Comp Sci Tokyo 1920982 Japan Cent S Univ Sch Informat Sci & Engn Changsha 410083 Hunan Peoples R China

A low-pass filter is inserted in a repetitive controller to guarantee the stability of the modified repetitive-control system. The control precision strongly depends on the parameter of the filter. This study presents a method of simultaneously optimising the parameters of the low-pass filter and state feedback of a modified repetitive-control system in which the plant contains a class of uncertainties. First, the relationship between the control precision of a repetitive-control system and a low-pass filter is explained. Next, a linear matrix inequality (LMI)-based robust-stability condition is derived for fixed state-feedback gains. This condition is transformed into a generalised eigenvalue problem and is used to calculate the maximum cut-off angular frequency of the low-pass filter. Then, another LMI-based robust-stability condition is derived for a fixed low-pass filter, and is employed to find H-infinity static-state-feedback gains. Moreover, an iterative algorithm that combines these two robust-stability conditions is designed that yields the largest bandwidth while guaranteeing closed-loop robust stability. The conservativeness of the result produced by the algorithm is the same as that of the less conservative of the two robust-stability conditions. Finally, two numerical examples demonstrate the validity of the method.

关键词： H∞ control Signal processing theory Optimisation techniques robust repetitive control system eigenvalue problem H∞ static state feedback gains time-varying systems Stability in control theory control system synthesis parameter optimisation linear matrix inequality Control system analysis and synthesis methods LMI low-pass filters state feedback closed loop systems robust control eigenvalues and eigenfunctions linear algebra (numerical analysis) cut-off angular frequency Interpolation and function approximation (numerical analysis) Optimal control linear matrix inequalities iterative methods iterative algorithm state feedback controller closed loop robust stability optimisation low pass filter

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Unified bound on the order of controllers using matrix pencil characterisation

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IET CONTROL theory AND applications 2010年第1期4卷 140-150页

作者： Xin, X. Okayama Prefectural Univ Fac Comp Sci & Syst Engn Okayama 7191197 Japan

This study concerns the existence and design of reduced-order controllers for a rather general class of continuous-and discrete-time control design problems which can be characterised by the linear matrix inequality (LMI) framework. From a matrix pencil perspective, this paper presents a unified bound on the order of controllers in terms of the minimal rank of two matrix pencils valued at their generalised eigenvalues at infinity and in the unstable region (the closed right-half plane for continuous-time systems and the region excluding the open unit circle for discrete-time systems) . When full-order controllers exist, such matrix pencil characterisation-based bound reveals the existence of reduced-order controllers if one of two subsystems of the generalised plant has infinite zeros or unstable invariant zeros. A numerical example of obtaining reduced-order controllers for the covariance upper bound control problem is given. This study provides a more complete view of the role of infinite zeros or unstable invariant zeros in feedback systems.

关键词： H∞ control feedback system infinite zeros Stability in control theory control system synthesis continuous-time control design linear matrix inequality Control system analysis and synthesis methods unstable invariant zeros discrete-time control design matrix pencil characterisation robust control linear quadratic Gaussian control eigenvalues and eigenfunctions feedback continuous-time systems algebra reduced-order controller design poles and zeros generalised eigenvalues continuous time systems reduced order systems linear matrix inequalities covariance upper bound control problem Discrete control systems Optimal control discrete-time systems discrete time systems

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Improved approach to delay-dependent stability analysis of discrete-time systems with time-varying delay

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IET CONTROL theory AND applications 2010年第10期4卷 2152-2159页

作者： Huang, H. Feng, G. Soochow Univ Sch Elect Informat Suzhou 215006 Peoples R China City Univ Hong Kong Dept Mfg Engn & Engn Management Hong Kong Hong Kong Peoples R China

This study focuses on studying the asymptotical stability analysis problem for discrete-time systems with time-varying delay. By utilising the S-procedure and an inequality technique, a novel delay-dependent stability criterion is derived in terms of two linear matrix inequalities. Since no slack variable is introduced, less decision variables are involved in the stability condition and the burden of numerical computation is thus reduced. It is also rigorously proved that the authors' result is less conservative than some recent ones. Furthermore, the developed approach is extended to address the stability analysis problem of delayed discrete-time systems with norm-bounded uncertainties. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed results.

关键词： time-varying systems control system analysis Time-varying control systems Stability in control theory Control system analysis and synthesis methods delay dependent stability analysis S-procedure asymptotical stability analysis inequality technique norm bounded uncertainties time varying delay delayed discrete time system algebra delays Discrete control systems linear matrix inequalities Distributed parameter control systems discrete time systems asymptotic stability

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The tree and forest spaces with applications to initial-value problem methods

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BIT numerical MATHEMATICS 2010年第4期50卷 713-728页

作者： Butcher, J. C. Chan, T. M. H. Natl Taichung Inst Technol Dept Informat Accounting Taichung Taiwan Univ Auckland Dept Math Auckland New Zealand

Tree and forest spaces, which are at the heart of the theory of Runge-Kutta methods, are formulated recursively, and it is shown that the forest space is an algebra. To obtain order conditions in a systematic manner, Banach algebras are introduced to generate both the elementary weights for a general Runge-Kutta method and the corresponding quantities based on the Picard integral. To connect these two concepts, the Picard integral is written as the limiting case of an s-stage Runge-Kutta method, equivalent to s steps of the Euler method, as s tends to infinity. This approach makes it possible to make direct use of the tree space without going over to the dual space. By choosing linear combinations of trees, appropriate to a particular application, it is shown how to obtain alternative ways of writing the order conditions. This leads to a simpler and more direct derivation of particular methods.

关键词： The Picard integral High derivative operators Banach algebra The forest space The tree space

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Preconditioning Schur Complement Systems of Highly-Indefinite linear Systems for a Parallel Hybrid Solver

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numerical Mathematics(theory,methods and applications) 2010年第3期3卷 352-366页

作者： I.Yamazaki E.G.Ng Lawrence Berkeley National Laboratory BerkeleyCaliforniaUSA

A parallel hybrid linear solver based on the Schur complement method has the potential to balance the robustness of direct solvers with the efficiency of preconditioned iterative ***,when solving large-scale highly-indefinite linear systems,this hybrid solver often suffers from either slow convergence or large memory requirements to solve the Schur complement *** overcome this challenge,we in this paper discuss techniques to preprocess the Schur complement systems in parallel. numerical results of solving large-scale highly-indefinite linear systems from various applications demonstrate that these techniques improve the reliability and performance of the hybrid solver and enable efficient solutions of these linear systems on hundreds of processors,which was previously infeasible using existing state-of-the-art solvers.

关键词： Schur complement method preconditioning matrix preprocessing.

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Multi-step-ahead Multivariate Predictors: a Comparative Analysis 49

Multi-step-ahead Multivariate Predictors: a Comparative Anal...

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49th IEEE conference on Decision and Control (CDC)

作者： Cescon, Marzia Johansson, Rolf Lund Univ Dept Automat Control SE-22100 Lund Sweden

ISBN: (纸本)9781424477463

The focus of this article is to undertake a comparative analysis of multi-step-ahead linear multivariate predictors. The approach considered for the estimation will be based on geometrically reliable linear algebra tools, resorting to subspace identification methods. A crucial issue is quantification of both bias error and variance affecting the estimate of the prediction for increasing values of the look ahead when only a small number of samples is available. No complete theory is available so far, nor sufficient numerical experience. Therefore, the analysis of this paper aims at shading some lights on the topic providing some insights and help to develop some intuitions.

关键词： linear algebra

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