Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems

✍ Scribed by Martin Gugat

• Publisher: Birkhäuser Basel
• Year: 2015
• Tongue: English
• Leaves: 143
• Series: SpringerBriefs in Electrical and Computer Engineering
• Edition: 1st
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-viii
Introduction....Pages 1-1
Systems governed by the wave equation....Pages 3-28
Exact Controllability....Pages 29-46
Optimal Exact Control....Pages 47-67
Boundary Stabilization....Pages 69-87
Nonlinear Systems....Pages 89-125
Distributions....Pages 127-133
Back Matter....Pages 135-140

✦ Subjects

Systems Theory, Control; Partial Differential Equations; Calculus of Variations and Optimal Control; Optimization; Control; Continuous Optimization