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