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Static output feedback controller design for uncertain polynomial systems: an iterative sums of squares approach

IET CONTROL theory AND applications 2011年第9期5卷 1079-1084页

作者： Nguang, S. K. Saat, S. Krug, M. Univ Auckland Dept Elect & Comp Engn Auckland 1 New Zealand

This study examines the problem of designing a static output feedback controller for uncertain polynomial systems via an iterative sums of squares (SOS) approach. The derivation of the static output feedback controller is given in terms of the solvability conditions of state-dependent bilinear matrix inequalities (BMIs). An iterative algorithm based on the SOS decomposition is proposed to solve these state-dependent BMIs. Finally, numerical examples are provided at the end of the study as to demonstrate the validity of the proposed design technique.

关键词： state dependent bilinear matrix inequalities static output feedback controller design control system synthesis feedback linear algebra (numerical analysis) Control system analysis and synthesis methods uncertain polynomial systems: SOS decomposition polynomials Interpolation and function approximation (numerical analysis) uncertain systems linear matrix inequalities iterative methods iterative sums of squares approach

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Generalised minimum variance control state-space design

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IET CONTROL theory AND applications 2011年第15期5卷 1709-1715页

作者： Silveira, A. S. Coelho, A. A. R. Univ Fed Santa Catarina Dept Automat & Syst BR-88040900 Florianopolis SC Brazil

The main goal of this study is to propose a state-space design technique for the generalised minimum variance control. In this sense, the same results achieved in the transfer function design framework are granted by the state-space method. It simplifies the design procedure while avoiding the solution of the Diophantine equation. Instead, the minimum variance predictor is obtained by the direct feed-through of an estimated state vector using a Kalman filter designed directly from the state-space model and without the need to solve an algebraic Riccati difference equation. In this way, even when dealing with systems with long time delays, the design procedure requires only a small amount of work as compared to the classical Diophantine-dependent technique. The proof of equality between the transfer function and state-space methods is easily verified by simple linear algebra, showing that the Diophantine equation results are intrinsically embedded in the gains of the state-space predictor derived, which means that resultant polynomials of the Diophantine equation can also be obtained by construction with the new design method. Two simulation examples are given to demonstrate the proposed technique.

关键词： Signal processing theory minimum variance predictor Kalman filters transfer functions state-space methods linear algebra Diophantine equation control system synthesis state-space design technique Control system analysis and synthesis methods algebraic Riccati difference equation linear algebra (numerical analysis) delays estimated state vector transfer function design framework generalised minimum variance control time delays Riccati equations Distributed parameter control systems Kalman filter

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An extrapolated TSVD method for linear discrete ill-posed problems with Kronecker structure

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linear algebra AND ITS applications 2011年第7期434卷 1677-1688页

作者： Bouhamidi, A. Jbilou, K. Reichel, L. Sadok, H. Kent State Univ Dept Math Kent OH 44242 USA Univ Littoral Lab Math Pures & Appl Ctr Univ Mi Voix F-62228 Calais France

This paper describes a new numerical method for the solution of large linear discrete ill-posed problems, whose matrix is a Kronecker product. Problems of this kind arise, for instance, from the discretization of Fredholm integral equations of the first kind in two space-dimensions with a separable kernel. The available data (right-hand side) of many linear discrete ill-posed problems that arise in applications is contaminated by measurement errors. Straightforward solution of these problems generally is not meaningful because of severe error propagation. We discuss how to combine the truncated singular value decomposition (TSVD) with reduced rank vector extrapolation to determine computed approximate solutions that are fairly insensitive to the error in the data. Exploitation of the structure of the problem keeps the computational effort quite small. (C) 2010 Elsevier Inc. All rights reserved.

关键词： Ill-posed problem Kronecker product Truncated singular value decomposition Vector extrapolation Truncation criterion

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Using desktop computers to solve large-scale dense linear algebra problems

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JOURNAL OF SUPERCOMPUTING 2011年第2期58卷 145-150页

作者： Marques, M. Quintana-Orti, G. Quintana-Orti, E. S. van de Geijn, R. Univ Jaime I Depto Ingn & Ciencia Comp Castellon de La Plana 12071 Spain Univ Texas Austin Dept Comp Sci Austin TX 78712 USA

We provide experimental evidence that current desktop computers feature enough computational power to solve large-scale dense linear algebra problems. While the high computational cost of the numerical methods for solving these problems can be tackled by the multiple cores of current processors, we propose to use the disk to store the large data structures associated with these applications. Our results also show that the limited amount of RAM and the comparatively slow disk of the system pose no problem for the solution of very large dense linear systems and linear least-squares problems. Thus, current desktop computers are revealed as an appealing, cost-effective platform for research groups that have to deal with large dense linear algebra problems but have no direct access to large computing facilities.

关键词： Dense linear algebra Out-of-core algorithms LU factorization High-performance computing

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Asymptotic preconditioning of linear homogeneous systems of differential equations

Asymptotic preconditioning of linear homogeneous systems of ...

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conference on linear and numerical linear algebra - theory, methods and applications

作者： Trench, William F. Trinity Univ San Antonio TX 78212 USA

We consider the asymptotic behavior of solutions of a linear differential system x ' = A(t)x, where A is continuous on an interval la, DC)). We are interested in the situation where the system may not have a desirable asymptotic property such as stability, strict stability, uniform stability, or linear asymptotic equilibrium, but its solutions can be written as x = Pu, where P is continuously differentiable on la, infinity) and u is a solution of a system u ' = B(t)u that has the property in question. In this case we say that P preconditions the given system for the property in question. (C) 2010 Elsevier Inc. All rights reserved.

关键词： Asymptotic behavior linear differential system Llinear asymptotic equilibrium Strictly stable Uniformly stable

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Local feedback Pareto strategy for weakly coupled large-scale discrete-time stochastic systems

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IET CONTROL theory AND applications 2011年第17期5卷 2005-2014页

作者： Mukaidani, H. Hiroshima Univ Grad Sch Educ Higashihiroshima 7398524 Japan

In this study, the author discusses a Pareto strategy implemented via state and static output feedback for a class of weakly coupled large-scale discrete-time stochastic systems with state-and control-dependent noise. The asymptotic structure along with the uniqueness and positive semi-definiteness of the solutions of cross-coupled non-linear matrix equations (CNMEs) is newly established via the implicit function theorem. The main contribution of this study is the proposal of a parameter-independent local state and static output feedback Pareto strategy. Moreover, a computational approach for solving the CNMEs is also considered if the information about the small parameter is available. Particularly, a new iterative algorithm based on the linear matrix inequality is established to design a Pareto strategy. Finally, in order to demonstrate the effectiveness of the proposed design method, a numerical example is provided for practical aircraft control problems.

关键词： Pareto analysis parameter-independent static output feedback Other topics in statistics stochastic systems weakly coupled large-scale discrete-time stochastic systems state-dependent noise local feedback Pareto strategy cross-coupled nonlinear matrix equations Time-varying control systems control system synthesis linear matrix inequality LMI state feedback design method parameter-independent local state output feedback linear algebra (numerical analysis) Interpolation and function approximation (numerical analysis) asymptotic structure implicit function theorem linear matrix inequalities iterative methods Discrete control systems iterative algorithm practical aircraft control problems discrete time systems control-dependent noise

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H_∞ filtering for linear continuous-time systems subject to sensor non-linearities

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IET CONTROL theory AND applications 2011年第16期5卷 1925-1937页

作者： Zhou, B. Zheng, W. X. Fu, Y. -M. Duan, G. -R. Harbin Inst Technol Ctr Control Theory & Guidance Technol Harbin 150001 Peoples R China Univ Western Sydney Sch Comp & Math Penrith NSW 2751 Australia

In this study, the H-infinity filtering problem for linear continuous-time systems subject to sensor non-linearities is considered. First, the global H-infinity filtering is addressed by modelling the sensor non-linearities as sector non-linearities. The existence condition for an H-infinity filter is derived for such systems by using both the circle criterion theory and Popov criterion theory. In both cases, design methods for H-infinity filtering are proposed by means of linear matrix inequalities (LMIs)-based optimisation approach, which enables solutions to be found via efficient interior-point algorithms. To reduce the conservatism in the design of global H-infinity filters for linear systems with output saturation non-linearities, the local H-infinity filtering problem is considered. Local H-infinity filtering refers that the states are within some bounded set while a regional L-2 gain is guaranteed. An LMI-based approach is developed to calculate parameter matrices of the local H-infinity filter. numerical examples are given to demonstrate the usefulness of the proposed results.

关键词： H∞ control linear systems linear continuous time systems control system synthesis algebra Control system analysis and synthesis methods Nonlinear control systems Transducers and sensing devices nonlinear control systems sensor nonlinearities sensors Popov criterion theory control design H∞ filtering LMI based optimisation approach continuous time systems Optimal control linear matrix inequalities

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An extrapolated TSVD method for linear discrete ill-posed problems with Kronecker structure

An extrapolated TSVD method for linear discrete ill-posed pr...

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conference on linear and numerical linear algebra - theory, methods and applications

作者： Bouhamidi, A. Jbilou, K. Reichel, L. Sadok, H. Kent State Univ Dept Math Kent OH 44242 USA Univ Littoral Lab Math Pures & Appl Ctr Univ Mi Voix F-62228 Calais France

关键词： Ill-posed problem Kronecker product Truncated singular value decomposition Vector extrapolation Truncation criterion

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Stochastic Algorithms in linear algebra - beyond the Markov Chains and von Neumann - Ulam Scheme

Stochastic Algorithms in Linear Algebra - beyond the Markov ...

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International conference on numerical methods and applications

作者： Sabelfeld, Karl Inst Comp Math & Math Geoph Novosibirsk Novosibirsk 630090 Russia

ISBN: (纸本)9783642184659

Sparsified Randomization Monte Carlo (SRMC) algorithms for solving systems of linear algebraic equations introduced in our previous paper [34] are discussed here in a broader context. In particular. I present new randomized solvers for large systems of linear equations, randomized singular value (SVD) decomposition for large Matrices and their use for solving inverse problems, and stochastic simulation of random fields. Stochastic projection methods, which I call here "random row action" algorithms, are extended to problems which involve systems of equations and constrains in the form of systems of linear inequalities.

关键词： linear algebra

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The palindromic generalized eigenvalue problem A*x = λAx: numerical solution and applications

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linear algebra AND ITS applications 2011年第11期434卷 2269-2284页

作者： Li, Tiexiang Chiang, Chun-Yueh Chu, Eric King-wah Lin, Wen-Wei Southeast Univ Dept Math Nanjing 211189 Peoples R China Natl Formosa Univ Ctr Gen Educ Huwei 632 Taiwan Monash Univ Sch Math Sci Clayton Vic 3800 Australia Natl Chiao Tung Univ CMMSC Hsinchu 300 Taiwan Natl Chiao Tung Univ Dept Appl Math NCTS Hsinchu 300 Taiwan

In this paper, we propose the palindromic doubling algorithm (PDA) for the palindromic generalized eigenvalue problem (PGEP) A*x = lambda Ax. We establish a complete convergence theory of the PDA for PGEPs without unimodular eigenvalues, or with unimodular eigenvalues of partial multiplicities two (one or two for eigenvalue 1). Some important applications from the vibration analysis and the optimal control for singular descriptor linear systems will be presented to illustrate the feasibility and efficiency of the PDA. (C) 2009 Elsevier Inc. All rights reserved.

关键词： Palindromic generalized eigenvalue problem Doubling algorithm Singular descriptor system

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