Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems
Authors: Gugat, Martin
Free Preview- Includes the most recent results on optimal control and stabilization of systems governed by hyperbolic PDEs
- Uses the wave, Korteweg-de Vries, and Burgers equations as typical examples to illustrate linear and nonlinear systems
- Suitable for use as a supplementary text in a graduate-level course or as a reference for post-graduates and researchers
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- About this book
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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.
- About the authors
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Martin Gugat is Professor in the Department of Mathematics at Friedrich-Alexander-University, Erlangen-Nürnberg, Germany.
- Reviews
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“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)
- Table of contents (7 chapters)
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Introduction
Pages 1-1
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Systems governed by the wave equation
Pages 3-28
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Exact Controllability
Pages 29-46
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Optimal Exact Control
Pages 47-67
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Boundary Stabilization
Pages 69-87
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Table of contents (7 chapters)
- Download Preface 1 PDF (25.5 KB)
- Download Sample pages 1 PDF (391.8 KB)
- Download Table of contents PDF (19.8 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems
- Authors
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- Martin Gugat
- Series Title
- SpringerBriefs in Control, Automation and Robotics
- Copyright
- 2015
- Publisher
- Birkhäuser Basel
- Copyright Holder
- The Author(s)
- eBook ISBN
- 978-3-319-18890-4
- DOI
- 10.1007/978-3-319-18890-4
- Softcover ISBN
- 978-3-319-18889-8
- Series ISSN
- 2192-6786
- Edition Number
- 1
- Number of Pages
- VIII, 140
- Number of Illustrations
- 1 b/w illustrations, 2 illustrations in colour
- Topics
