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Minimization, over selected convex sets, of a noncoercive cost functional for hyperbolic systems. (English) Zbl 0644.49003

We investigate the problem of optimal control of systems governed by second-order linear hyperbolic equations. We obtain a set of coupled differential equations and inequalities, whose unique solution will be the minimizing element of a noncoercive cost functional. We also study the regularity of the optimal control for a specific example.

MSC:

49J20 Existence theories for optimal control problems involving partial differential equations
35L10 Second-order hyperbolic equations
93C20 Control/observation systems governed by partial differential equations
35B37 PDE in connection with control problems (MSC2000)
93C05 Linear systems in control theory
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