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Optimization and Dynamical Systems

  • Uwe Helmke
  • John B. Moore

Part of the Communications and Control Engineering book series (CCE)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Uwe Helmke, John B. Moore
    Pages 1-42
  3. Uwe Helmke, John B. Moore
    Pages 43-80
  4. Uwe Helmke, John B. Moore
    Pages 81-100
  5. Uwe Helmke, John B. Moore
    Pages 101-124
  6. Uwe Helmke, John B. Moore
    Pages 125-161
  7. Uwe Helmke, John B. Moore
    Pages 163-200
  8. Uwe Helmke, John B. Moore
    Pages 201-227
  9. Uwe Helmke, John B. Moore
    Pages 229-267
  10. Uwe Helmke, John B. Moore
    Pages 269-309
  11. Back Matter
    Pages 311-403

About this book

Introduction

This work is aimed at mathematics and engineering graduate students and researchers in the areas of optimization, dynamical systems, control sys­ tems, signal processing, and linear algebra. The motivation for the results developed here arises from advanced engineering applications and the emer­ gence of highly parallel computing machines for tackling such applications. The problems solved are those of linear algebra and linear systems the­ ory, and include such topics as diagonalizing a symmetric matrix, singular value decomposition, balanced realizations, linear programming, sensitivity minimization, and eigenvalue assignment by feedback control. The tools are those, not only of linear algebra and systems theory, but also of differential geometry. The problems are solved via dynamical sys­ tems implementation, either in continuous time or discrete time , which is ideally suited to distributed parallel processing. The problems tackled are indirectly or directly concerned with dynamical systems themselves, so there is feedback in that dynamical systems are used to understand and optimize dynamical systems. One key to the new research results has been the recent discovery of rather deep existence and uniqueness results for the solution of certain matrix least squares optimization problems in geomet­ ric invariant theory. These problems, as well as many other optimization problems arising in linear algebra and systems theory, do not always admit solutions which can be found by algebraic methods.

Keywords

Dynamical System Dynamische Systeme Kontrolltheorie Lyapunov stability Numerische Lineare Algebra Optimisierung Signalverarbeitung control theory dynamical systems linear optimization numerical linear algebra optimization signal processing

Authors and affiliations

  • Uwe Helmke
    • 1
  • John B. Moore
    • 2
  1. 1.Department of MathematicsUniversity of WürzburgWürzburgGermany
  2. 2.Department of Systems Engineering and Cooperative Research Centre for Robust and Adaptive Systems, Research School of Information Sciences and EngineeringAustralian National UniversityCanberraAustralia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-3467-1
  • Copyright Information Springer-Verlag London 1994
  • Publisher Name Springer, London
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4471-3469-5
  • Online ISBN 978-1-4471-3467-1
  • Series Print ISSN 0178-5354
  • Buy this book on publisher's site