Optimal boundary control and boundary stabilization of hyperbolic systems [electronic resource] /
Gugat, Martin.author.
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.
Description based upon print version of record.
Includes bibliographical references and index.
Introduction -- Systems that are Governed by the Wave Equation -- Exact Controllability -- Optimal Exact Control -- Boundary Stabilization -- Nonlinear Systems -- Distributions -- Index.
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.
System theory.
Partial differential equations.
Calculus of variations.
Control engineering.
Mathematical optimization.
Systems Theory, Control.
Partial Differential Equations.
Calculus of Variations and Optimal Control; Optimization.
Control and Systems Theory.
Continuous Optimization.