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H-Optimal Control and Related

Minimax Design Problems

  • Tamer Başar
  • Pierre Bernhard

Part of the Systems & Control: Foundations & Applications book series (SCFA)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Tamer Başar, Pierre Bernhard
    Pages 1-12
  3. Tamer Başar, Pierre Bernhard
    Pages 13-27
  4. Tamer Başar, Pierre Bernhard
    Pages 72-113
  5. Tamer Başar, Pierre Bernhard
    Pages 114-150
  6. Tamer Başar, Pierre Bernhard
    Pages 151-179
  7. Tamer Başar, Pierre Bernhard
    Pages 180-193
  8. Tamer Başar, Pierre Bernhard
    Pages 194-207
  9. Tamer Başar, Pierre Bernhard
    Pages 208-212
  10. Tamer Başar, Pierre Bernhard
    Pages 213-220
  11. Back Matter
    Pages 221-225

About this book

Introduction

One of the major concentrated activities of the past decade in control theory has been the development of the so-called "HOO-optimal control theory," which addresses the issue of worst-case controller design for linear plants subject to unknown additive disturbances, including problems of disturbance attenuation, model matching, and tracking. The mathematical OO symbol "H " stands for the Hardy space of all complex-valued functions of a complex variable, which are analytic and bounded in the open right­ half complex plane. For a linear (continuous-time, time-invariant) plant, oo the H norm of the transfer matrix is the maximum of its largest singular value over all frequencies. OO Controller design problems where the H norm plays an important role were initially formulated by George Zames in the early 1980's, in the context of sensitivity reduction in linear plants, with the design problem posed as a mathematical optimization problem using an (HOO) operator norm. Thus formulated originally in the frequency domain, the main tools used during the early phases of research on this class of problems have been operator and approximation theory, spectral factorization, and (Youla) parametrization, leading initially to rather complicated (high-dimensional) OO optimal or near-optimal (under the H norm) controllers.

Keywords

control control theory Mathematica measurement optimal control optimization Tracking

Authors and affiliations

  • Tamer Başar
    • 1
  • Pierre Bernhard
    • 2
  1. 1.Coordinated Science LaboratoryUniversity of IllinoisUrbanaUSA
  2. 2.InriaUnité de Recherche Sophia-AntipolisValbone CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4899-3561-8
  • Copyright Information Birkhäuser Boston 1991
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4899-3563-2
  • Online ISBN 978-1-4899-3561-8
  • Series Print ISSN 2324-9749
  • Series Online ISSN 2324-9757
  • Buy this book on publisher's site