Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems
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 typ
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Martin Gugat
Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems 123
SpringerBriefs in Electrical and Computer Engineering Control, Automation and Robotics
Series editors Tamer Ba¸sar, Urbana, USA Antonio Bicchi, Pisa, Italy Miroslav Krstic, La Jolla, USA
More information about this series at http://www.springer.com/series/10059
Martin Gugat
Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems
Martin Gugat Mathematik Friedrich-Alexander-Universität Erlangen-Nürnberg Erlangen, Germany
ISSN 2191-8112 ISSN 2191-8120 (electronic) SpringerBriefs in Electrical and Computer Engineering ISBN 978-3-319-18889-8 ISBN 978-3-319-18890-4 (eBook) DOI 10.1007/978-3-319-18890-4 Library of Congress Control Number: 2015939419 Mathematics Subject Classification (2010): 93C20, 93D15, 49J20 Springer Cham Heidelberg New York Dordrecht London © The Author(s) 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www. springer.com)
Preface
For many systems in engineering, control action does not take place everywhere in the system but only at certain points, for example at the boundary. In this SpringerBrief we consider systems of this type, where the system dynamics are governed by hyperbolic partial differential equations. As a typical example we consider the wave equation, and in the chapter about nonlinear systems also the Korteweg-de Vries and Burgers equations. The aim is to familiarize the reader with the problems of optimal boundary control and stabilization that appear in this framework. We also introduce the notion of exact controllability, which is an essential concept in this context. To keep the presentation as accessible as possible, we consider the case of systems with a state that is defined on a space interval. In the case of a finite interval that is also relevant for many applications, there are two boundary po
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