Titlebook: Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems; Martin Gugat Book 2015 The Author(s) 2015 Boundary stabilizatio

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https://doi.org/10.1007/978-3-319-18890-4Boundary stabilization; Hyperbolic partial differential equations; Hyperbolic system; Optimal control p

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Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems978-3-319-18890-4Series ISSN 2191-8112 Series E-ISSN 2191-8120

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Exact Controllability,The question of exact controllability (see Lions, SIAM Rev. ., 1–68, 1988; Russell, J. Math. Anal. Appl. ., 542–560, 1967) is: Which states can be reached exactly at given control time . with a given set of control functions starting at time zero with an initial state from a prescribed set?

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Optimal Exact Control,ive function that models our preferences. This leads to an optimal control problem where the prescribed end conditions can be regarded as equality constraints. Often, the control costs that are given by the norm of the control function are an interesting objective function.

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Introduction,e for example Gugat et al., J. Optim. Theory Appl. ., 589–616, 2005; Work et al., Appl. Math. Res. Express ., 1–35, 2010). These models allow to study how control action influences the states in these systems.

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2191-8112 s, and Burgers equations as typical examples to illustrate l.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 us

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Nonlinear Systems,yperbolic system, the solution can loose a part of its regularity after a finite time. For example, classical solutions typically break down after finite time since there is a blow up in certain partial derivatives.