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Time-domain decomposition of optimal control problems for the wave equation. (English) Zbl 1134.49313
Summary: We consider the problem of boundary optimal control of a wave equation with boundary dissipation by the way of time-domain decomposition of the corresponding optimality system. We develop an iterative algorithm which shows that the decomposed optimality system corresponds to local-in-time optimal control problems which can be treated in parallel. We show convergence of the algorithm. Finally, we provide a time discretization which is reminiscent of an instantaneous control scheme. We thereby also contribute to the problem of convergence of such schemes.

49M27Decomposition methods in calculus of variations
35L05Wave equation (hyperbolic PDE)
49K20Optimal control problems with PDE (optimality conditions)
93C20Control systems governed by PDE
Full Text: DOI
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