Overview
- Discusses a wide range of applications, allowing readers to understand the concepts in whichever setting is most familiar to them
- Demonstrates how control boundary conditions may be defined for the most commonly used control devices
- Includes a detailed case study on the control of navigable rivers, using the Meuse River in Belgium, to illustrate the main technological features that may occur in real live applications of boundary feedback control
Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 88)
Part of the book sub series: PNLDE Subseries in Control (PNLDE-SC)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
About this book
The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis. Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones. They go on to show how the problem of boundary stabilization of systems of two balance laws by both full-state and dynamic output feedback in observer-controller form is solved by using a “backstepping” method, in which the gains of the feedback laws are solutions of an associated system of linear hyperbolic PDEs. The final chapter presents a case study on the control of navigable rivers to emphasize the main technological features that may occur in real live applications of boundary feedback control.
Stability and Boundary Stabilization of 1-D Hyperbolic Systems will be of interest to graduate students and researchers in applied mathematics and control engineering. The wide range of applications it discusses will help it to have as broad an appeal within these groups as possible.
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Authors and Affiliations
Bibliographic Information
Book Title: Stability and Boundary Stabilization of 1-D Hyperbolic Systems
Authors: Georges Bastin, Jean-Michel Coron
Series Title: Progress in Nonlinear Differential Equations and Their Applications
DOI: https://doi.org/10.1007/978-3-319-32062-5
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-32060-1Published: 09 August 2016
Softcover ISBN: 978-3-319-81185-7Published: 22 April 2018
eBook ISBN: 978-3-319-32062-5Published: 26 July 2016
Series ISSN: 1421-1750
Series E-ISSN: 2374-0280
Edition Number: 1
Number of Pages: XIV, 307
Number of Illustrations: 30 b/w illustrations, 31 illustrations in colour
Topics: Partial Differential Equations, Dynamical Systems and Ergodic Theory, Systems Theory, Control, Mathematical Applications in the Physical Sciences, Vibration, Dynamical Systems, Control