Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems
Nonfiction, Science & Nature, Mathematics, Differential Equations, Science, Other Sciences, System Theory, Reference & Language, Reference
| Author: | Martin Gugat | ISBN: | 9783319188904 |
| Publisher: | Springer International Publishing | Publication: | July 15, 2015 |
| Imprint: | Birkhäuser | Language: | English |
| Author: | Martin Gugat |
| ISBN: | 9783319188904 |
| Publisher: | Springer International Publishing |
| Publication: | July 15, 2015 |
| Imprint: | Birkhäuser |
| Language: | English |
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.
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.
