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Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems

  • Martin Gugat

Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)

Also part of the SpringerBriefs in Control, Automation and Robotics book sub series (BRIEFSCONTROL)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Martin Gugat
    Pages 1-1
  3. Martin Gugat
    Pages 3-28
  4. Martin Gugat
    Pages 29-46
  5. Martin Gugat
    Pages 47-67
  6. Martin Gugat
    Pages 69-87
  7. Martin Gugat
    Pages 89-125
  8. Martin Gugat
    Pages 127-133
  9. Back Matter
    Pages 135-140

About this book

Introduction

This brief considers recent results on optimal control and stabilization of systems governed by hyperbolic partial differential equations, specifically those in which the control action takes place at the boundary.  The wave equation is used as a typical example of a linear system, through which the author explores initial boundary value problems, concepts of exact controllability, optimal exact control, and boundary stabilization.  Nonlinear systems are also covered, with the Korteweg-de Vries and Burgers Equations serving as standard examples.  To keep the presentation as accessible as possible, the author uses the case of a system with a state that is defined on a finite space interval, so that there are only two boundary points where the system can be controlled.  Graduate and post-graduate students as well as researchers in the field will find this to be an accessible introduction to problems of optimal control and stabilization.

Keywords

Boundary stabilization Hyperbolic partial differential equations Hyperbolic system Optimal control problem Wave equation

Authors and affiliations

  • Martin Gugat
    • 1
  1. 1.MathematikFriedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-18890-4
  • Copyright Information The Author(s) 2015
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-18889-8
  • Online ISBN 978-3-319-18890-4
  • Series Print ISSN 2191-8112
  • Series Online ISSN 2191-8120
  • Buy this book on publisher's site
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