H ∞ Control and Its Applications

Chen, Ben M.

doi:10.1007/978-1-84628-529-5

Cited by 38 publications

(21 citation statements)

References 68 publications

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“…For example, Petersen [15] has solved the problem for a class of one-block regular case. Scherer [17,18] has obtained a partial answer for state feedback problem for a larger class of systems by providing a computable candidate value together with algebraically verifiable conditions, and Chen and his co-workers [3,4] (see also [2]) have developed a noniterative procedures for computing the value of γ * for a class of systems (singular case) that satisfy certain geometric conditions. To be more specific, we introduce the following two geometric subspaces of linear systems: Given an n-th ii.…”

Section: Available Resultsmentioning

confidence: 99%

Problem 8.2 Non-iterative computation of optimal value in H∞ control

Chen¹

2009

Unsolved Problems in Mathematical Systems and Control Theory

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We consider an n-th order generalized linear system Σ characterized by the following state-space equations: Σ :where x is the state, u is the control input, w is the disturbance input, y is the measurement output, and h is the controlled output of Σ. For simplicity, we assume that D 11 = 0 and D 22 = 0. We also let Σ P be the subsystem characterized by the matrix quadruple (A, B, C 2 , D 2 ) and Σ Q be the subsystem characterized by (A, E, C 1 , D 1 ). The standard H ∞ optimal control problem is to find an internally stabilizing proper measurement feedback control law,such that when it is applied to the given plant (1), the H ∞ -norm of the resulting closed-loop transfer matrix function from w to h, say T hw (s), is minimized. We note that the H ∞ -norm of an asymptotically stable and proper continuous-time transfer matrix T hw (s) is defined aswhere w and h are, respectively, the input and output of T hw (s).

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Section: Available Resultsmentioning

confidence: 99%

Problem 8.2 Non-iterative computation of optimal value in H∞ control

Chen¹

2009

Unsolved Problems in Mathematical Systems and Control Theory

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“…by choosing a suitable δ to make the equality (14) hold when the residual and fault estimation belong to D 0 . Similarly, in (47), δ (or…”

Section: Performance Analysis Of the Adaptive Observermentioning

confidence: 99%

Robust fault diagnosis for a class of nonlinear systems

Wang

Zhang

2006

J. Control Theory Appl.

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Robust fault diagnosis based on adaptive observer is studied for a class of nonlinear systems up to output injection. Adaptive fault updating laws are designed to guarantee the stability of the diagnosis system. The upper bounds of the state estimation error and fault estimation error of the adaptive observer are given respectively and the effects of parameter in the adaptive updating laws on fault estimation accuracy are also discussed. Simulation example demonstrates the effectiveness of the proposed methods and the analysis results.

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“…The proposed solution, based on matrix pseudoinversion, is completed and made practically implementable by a nesting procedure for welding optimal subarcs that enables arbitrary enlargement of the control time interval. [17,18,4,22], and Soethoudt, Trentelman and Ran in [21,16]. Extension to cheap and singular problems is obtained by using matrix pencils or linear matrix inequalities.…”

Section: Introductionmentioning

confidence: 99%

“…In general, these new contributions concern the infinite-horizon problems, where optimality jointly with internal stability is required. The basic properties and algorithms referring to cheap and singular optimal control have been investigated by Arnold and Laub in [2], Van Dooren in [23], Ionescu, Oarȃ, and Weiss in [11,10,9], Geerts in [6], Saberi, Sannuti, Chen, and Stoorvogel in [17,18,4,22], and Soethoudt, Trentelman and Ran in [21,16]. Extension to cheap and singular problems is obtained by using matrix pencils or linear matrix inequalities.…”

Section: Introductionmentioning

confidence: 99%

A Nested Computational Approach to the Discrete-Time Finite-Horizon LQ Control Problem

Marro¹,

Prattichizzo²,

Zattoni³

2003

SIAM J. Control Optim.

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Abstract.A new algorithmic setting is proposed for the discrete-time finite-horizon linear quadratic (LQ) optimal control problem with constrained or unconstrained final state, no matter whether the problem is cheap, singular, or regular. The proposed solution, based on matrix pseudoinversion, is completed and made practically implementable by a nesting procedure for welding optimal subarcs that enables arbitrary enlargement of the control time interval. [17,18,4,22], and Soethoudt, Trentelman and Ran in [21,16]. Extension to cheap and singular problems is obtained by using matrix pencils or linear matrix inequalities.The above contributions mainly refer to continuous-or discrete-time infinitehorizon LQR problems. Conversely, this work focuses on the finite-horizon case for discrete-time systems. It applies to cheap, singular, or regular problems. Considering a sharp constraint on the final state, this paper extends the results given in [16], where the infinite-horizon case with asymptotic endpoint constraints is investigated. However, in the present paper, the requirement that the cost functions are positive semidefinite is still present, while in [16] it is not.From the algorithmic viewpoint, the present work differs from those of the abovementioned papers and is inspired by the system structure algorithm introduced by Silverman in his well-known contribution [20]; see also [19,8]. In the present work, the solution is achieved by the straightforward technique of pseudoinverting a particular system matrix as in [20], but the time interval considered can be arbitrarily

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H ∞ Control and Its Applications

Abstract: British Library Cataloguing in Publication Data Chen, Ben M., 1963-Hoo control and its applications. -(Lecture notes in control and information sciences ; 235) l.Control theory 2.Mathematical optimization l.Title 629.8'312 ISBN 978-1-85233-026-2 ISBN 978-1-84628-529-5 (eBook)

Cited by 38 publications

References 68 publications

Problem 8.2 Non-iterative computation of optimal value in H∞ control

Problem 8.2 Non-iterative computation of optimal value in H∞ control

Robust fault diagnosis for a class of nonlinear systems

A Nested Computational Approach to the Discrete-Time Finite-Horizon LQ Control Problem

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