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Reliable H_∞ control of uncertain descriptor systems with multiple time delays

IEE PROCEEDINGS-CONTROL theory AND applications 2003年第6期150卷 557-564页

作者： Yue, D Lam, J Ho, DWC Nanjing Normal Univ Dept Control Sci & Engn Nanjing 210042 Jiangsu Peoples R China Univ Hong Kong Dept Mech Engn Hong Kong Hong Kong Peoples R China City Univ Hong Kong Dept Math Hong Kong Hong Kong Peoples R China

The reliable H-infinity controller design problem for uncertain descriptor systems with actuator failures and multiple time delays is investigated. Sufficient conditions to guarantee that the unforced system is regular, impulse-free and exponentially stable are derived. The derived conditions are expressed in terms of a set of linear matrix inequalities, which can be effectively solved by using well known algorithms. Then, based on these results, a reliable H-infinity controller is proposed such that, for all admissible uncertainties and actuator failures occurring among the prescribed subset of faulty actuators, the resulting closed-loop system is regular, impulse-free and exponentially stable with an H-infinity norm bound constraint. The effectiveness of the proposed method is demonstrated by a numerical example.

关键词： sufficient conditions asymptotic stability delays numerical example linear matrix inequalities stability criteria H∞ control memoryless systems time-varying norm-bounded parameter uncertainties Optimal control multiple time delays regular impulse-free unforced system algebra reliable H∞ controller design problem control system synthesis exponential stability linear memoryless controller closed loop systems Control system analysis and synthesis methods uncertain systems uncertain descriptor systems actuator failures time-varying systems closed-loop system Stability in control theory Time-varying control systems H∞ norm bound constraint

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Parallel newton two-stage multisplitting iterative methods for nonlinear systems

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BIT numerical MATHEMATICS 2003年第5期43卷 849-861页

作者： Arnal, J Migallón, V Penadés, J Univ Alicante Dept Ciencia Computac & Inteligencia Artificial E-03071 Alicante Spain

Parallel Newton two-stage iterative methods to solve nonlinear systems are studied. These algorithms are based on both the multisplitting technique and the two-stage iterative methods. Convergence properties of these methods are studied when the Jacobian matrix is either monotone or an H-matrix. Furthermore, in order to illustrate the performance of the algorithms studied, computational results about these methods on a distributed memory multiprocessor are discussed.

关键词： parallel and distributed algorithms nonlinear systems numerical methods multisplitting methods two-stage methods distributed memory

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theory of inexact Krylov subspace methods and applications to scientific computing

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2003年第2期25卷 454-477页

作者： Simoncini, V Szyld, DB Univ Bologna Dipartimento Matemat I-40126 Bologna Italy CNR Ist Matemat Applicata & Tecnol Informat I-27100 Pavia Italy Temple Univ 038 16 Dept Math Philadelphia PA 19122 USA

We provide a general framework for the understanding of inexact Krylov subspace methods for the solution of symmetric and nonsymmetric linear systems of equations, as well as for certain eigenvalue calculations. This framework allows us to explain the empirical results reported in a series of CERFACS technical reports by Bouras, Fraysse, and Giraud in 2000. Furthermore, assuming exact arithmetic, our analysis can be used to produce computable criteria to bound the inexactness of the matrix-vector multiplication in such a way as to maintain the convergence of the Krylov subspace method. The theory developed is applied to several problems including the solution of Schur complement systems, linear systems which depend on a parameter, and eigenvalue problems. numerical experiments for some of these scientific applications are reported.

关键词： inexact matrix-vector multiplies Krylov subspace methods inexact preconditioning inner-outer methods iterative nonsymmetric solver

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theory of inexact Krylov subspace methods and applications to scientific computing

Theory of inexact Krylov subspace methods and applications t...

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7th Annual Copper Mountain conference on Iterative methods

关键词： inexact matrix-vector multiplies Krylov subspace methods inexact preconditioning inner-outer methods iterative nonsymmetric solver

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The adventures of a simple algorithm

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linear algebra AND ITS applications 2003年 361卷 41-61页

作者： Dax, A Hydrol Serv IL-91360 Jerusalem Israel

This paper presents, analyzes, and tests a row-action method for solving the regularized linear programming problem: minimize 1/2parallel toxparallel to(2)(2) + alphac(T)x subject to Ax greater than or equal to b, where a is a given positive constant. The proposed method is based on the observation that the dual of this problem has the form: maximize b(T)y - 1/2parallel to A(T) y - alphacparallel to(2)(2) subject to y greater than or equal to 0. and if y(alpha) solves the dual then the point x(alpha) A(T)y(alpha) - alphac provides the unique solution of the primal. Maximizing the dual objective function by changing one variable at a time results in an effective row-action method which is suitable for solving large sparse problems. One aim of this paper is to clarify the convergence properties of the proposed scheme. Let Y-k denote the estimated dual solution at the end of the kth iteration, and let X-k = A(T) y(k) - alphac denote the corresponding primal estimate. It is proved that the sequence {x(k)} converges to x(alpha), while the sequence {y(k)} converges to a point y(alpha) that solves the dual. The only assumption which is needed in order to establish these claims is that the feasible region is not empty. Yet perhaps the more striking features of the algorithm are related to temporary situations in which it attempts to solve an inconsistent system. In such cases the sequence {y(k)} obeys the rule: y(k) = u(k) + kv. where {u(k)} is a fastly converging sequence and v is a fixed vector that satisfies A(T)v = 0 and b(T)v > 0. So the sequence {X-k} is almost unchanged for many iterations, The paper ends with numerical experiments that illustrate the effects of this phenomenon and the close links with Kaczmarz's SOR method. (C) 2002 Elsevier Science Inc. All rights reserved.

关键词： regularized linear programming row-action methods constrained SOR methods

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2nd International conference on Symbolic and numerical Scientific Computation, SNSC 2001

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2nd International conference on Symbolic and numerical Scientific Computation, SNSC 2001

ISBN: (纸本)3540405542

The proceedings contain 19 papers. The special focus in this conference is on Symbolics and Numerics of Differential Equations. The topics include: Notes on triangular sets and triangulation-decomposition algorithms I;notes on triangular sets and triangulation-decomposition algorithms II;passive complete orthonomic systems of PDEs and involutive bases of polynomial modules;symmetries of second- and third-order ordinary differential equations;symbolic methods for the equivalence problem for systems of implicit ordinary differential equations;on the numerical analysis of overdetermined linear partial differential systems;dynamical aspects of involutive bases computations;congestion and almost invariant sets in dynamical systems;datagraphs in algebraic geometry and K3 surfaces;resultants and neighborhoods of a polynomial;multi-variate polynomials and Newton-Puiseux expansions;wavelets with scale dependent properties;accurate numerical fourier transform in d-dimensions;exact real computation in computer algebra;symbolic methods for the element preconditioning technique;solving symbolic and numerical problems in the theory of shells with mathematica;a symbolic procedure for the diagonalization of linear PDEs in accelerated computational engineering;computer algebra approach to an analysis and nonlinear periodic waves in shallow water.

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On the stabilizability of control constrained linear systems

On the stabilizability of control constrained linear systems

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5th International conference on numerical methods and Application

作者： Krastanov, M Veliov, V Bulgarian Acad Sci Inst Math & Informat BU-1113 Sofia Bulgaria Vienna Univ Technol Inst Econometr Operat Res & Syst Theory A-1040 Vienna Austria

ISBN: (纸本)3540006087

We study the problem of stabilization of time-invariant linear systems with controls which are constrained in a cone. Under small-time local controllability conditions we propose a simple construction of a Lipschitz piecewise linear stabilizing feedback. Moreover, we show that the stabilizing feedback can be chosen in such a way that the number of switchings from one linear form to another, that may occur along a trajectory of the closed-loop system, is uniformly bounded.

关键词： Feedback

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Pole placement preconditioning

Pole placement preconditioning

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作者： Calvetti, D. Reichel, L. Department of Mathematics Case Western Reserve University Cleveland OH 44106 United States Department of Mathematical Sciences Kent State University Kent OH 44242 United States

The partial pole placement problem has received considerable attention in Control theory, where it is applied to stabilize time-invariant linear control systems. This paper discusses application of the partial pole placement problem to the construction of preconditioners for linear systems of equations. numerical examples show that these preconditioners can improve the rate of convergence of the restarted GMRES methods significantly. © 2003 Elsevier Science Inc.

关键词： Arnoldi process Implicitly restarted Arnoldi method Iterative method Nonsymmetric linear system Partial eigenvalue assignment problem Preconditioner

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The adventures of a simple algorithm

The adventures of a simple algorithm

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9th conference of the International-linear-algebra-Society

作者： Dax, A Hydrol Serv IL-91360 Jerusalem Israel

关键词： regularized linear programming row-action methods constrained SOR methods

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5th International conference on numerical methods and applications, NMA 2002

5th International Conference on Numerical Methods and Applic...

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5th International conference on numerical methods and applications, NMA 2002

ISBN: (纸本)3540006087

The proceedings contain 64 papers. The special focus in this conference is on Quasi-Monte Carlo methods, Robust Iterative Solution methods, Control and Uncertain Systems. The topics include: An introduction to the theory of plausible and paradoxical reasoning;comparison of ten methods for the solution of large and sparse linear algebraic systems;variable-coefficient difference schemes for quasilinear evolution problems;additive schemes for systems of time-dependent equations of mathematical physics;geometry of polynomials and numerical analysis;hybrid Monte Carlo methods for matrix computation;a new efficient algorithm for generating the scrambled sobol’ sequence;generating and testing the modified halton sequences;parallel importance separation and adaptive Monte Carlo algorithms for multiple integrals;Monte Carlo and quasi-Monte Carlo algorithms for the barker-ferry equation with low complexity;on some weight Monte Carlo methods for investigating the asymptotical behavior of solution of the transfer equation;a Monte Carlo approach for finding more than one eigenpair;a new class of grid-free Monte Carlo algorithms for elliptic boundary value problems;Monte-Carlo integration using cryptographically secure pseudo-random generator;galerkin and control volume finite element methods for large scale air pollution simulations;robust preconditioners for saddle point problems;on a multigrid adaptive refinement solver for saturated non-Newtonian flow in porous media;on a multigrid eigensolver for linear elasticity problems;discrete methods for optimal control problems and numerical schemes of higher order for a class of nonlinear control systems.

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