Authors:
- Opens a wide research subject by incorporating the study of synchronization into the field of control
- Introduces a complete theory for treating the exact and approximate boundary synchronizations for a coupled system of wave equations
- Outlines the solutions not only for exact boundary synchronization, but also for situations where there is further lack of boundary controls for approximate boundary synchronization
Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 94)
Part of the book sub series: PNLDE Subseries in Control (PNLDE-SC)
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Table of contents (32 chapters)
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Front Matter
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Synchronization for a Coupled System of Wave Equations with Dirichlet Boundary Controls: Exact Boundary Synchronization
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Front Matter
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Synchronization for a Coupled System of Wave Equations with Dirichlet Boundary Controls: Approximate Boundary Synchronization
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Front Matter
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Synchronization for a Coupled System of Wave Equations with Neumann Boundary Controls: Exact Boundary Synchronization
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Front Matter
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Synchronization for a Coupled System of Wave Equations with Neumann Boundary Controls: Approximate Boundary Synchronization
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Front Matter
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About this book
Within this carefully presented monograph, the authors extend the universal phenomenon of synchronization from finite-dimensional dynamical systems of ordinary differential equations (ODEs) to infinite-dimensional dynamical systems of partial differential equations (PDEs). By combining synchronization with controllability, they introduce the study of synchronization to the field of control and add new perspectives to the investigation of synchronization for systems of PDEs. With a focus on synchronization for a coupled system of wave equations, the text is divided into three parts corresponding to Dirichlet, Neumann, and coupled Robin boundary controls. Each part is then subdivided into chapters detailing exact boundary synchronization and approximate boundary synchronization, respectively. The core intention is to give artificial intervention to the evolution of state variables through appropriate boundary controls for realizing the synchronization in a finite time, creatinga novel viewpoint into the investigation of synchronization for systems of partial differential equations, and revealing some essentially dissimilar characteristics from systems of ordinary differential equations.
Primarily aimed at researchers and graduate students of applied mathematics and applied sciences, this text will particularly appeal to those interested in applied PDEs and control theory for distributed parameter systems.
Reviews
“The book is well organized and presents the most important notions of boundary synchronization for hyperbolic systems. The book is suitable for senior undergraduate and graduate students as well as practical engineers, scientist and researchers interested in boundary synchronization for hyperbolic systems.” (Seenith Sivasundaram, zbMATH 1443.93002, 2020)
Authors and Affiliations
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School of Mathematical Sciences, Fudan University, Shanghai, China
Tatsien Li
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Institut de Recherche Mathématique Avancée, Université de Strasbourg, Strasbourg, France
Bopeng Rao
Bibliographic Information
Book Title: Boundary Synchronization for Hyperbolic Systems
Authors: Tatsien Li, Bopeng Rao
Series Title: Progress in Nonlinear Differential Equations and Their Applications
DOI: https://doi.org/10.1007/978-3-030-32849-8
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-32848-1Published: 19 December 2019
Softcover ISBN: 978-3-030-32851-1Published: 19 December 2020
eBook ISBN: 978-3-030-32849-8Published: 02 December 2019
Series ISSN: 1421-1750
Series E-ISSN: 2374-0280
Edition Number: 1
Number of Pages: X, 333
Number of Illustrations: 1 b/w illustrations, 1 illustrations in colour
Topics: Systems Theory, Control, Partial Differential Equations, Ordinary Differential Equations, Control and Systems Theory