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© 2015

Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems

Book

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

  1. 1.MathematikFriedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany

About the authors

Martin Gugat is Professor in the Department of Mathematics at Friedrich-Alexander-University, Erlangen-Nürnberg, Germany.

Bibliographic information

Industry Sectors
Electronics
Engineering
Finance, Business & Banking

Reviews

“The book presents the subject of controlling and stabilizing PDE systems in a didactic manner, detailing the computations. The book is very well organized … . This textbook will be useful for graduate and Ph.D. students in mathematics and engineering, interested in the subject … . In addition, the Bibliography contains some of the classical references in the literature regarding control and stabilization.” (Valéria N. Domingos Cavalcanti, Mathematical Reviews, August, 2016)

“The book under review treats optimal boundary control problems and stabilizability, where the system dynamics are governed by hyperbolic partial differential equations. … The book is written in an understandable style. The contents of the book, along with several exercises and references, make it an interesting and useful text for a wide group of mathematicians and engineers.” (Gheorghe Aniculăesei, zbMATH 1328.49001, 2016)