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Time-domain decomposition for optimal control problems governed by semilinear hyperbolic systems with mixed two-point boundary conditions

Krug Richard, Leugering Günter, Martin Alexander, Schmidt Martin, Weninger Dieter

Control and Cybernetics

2021

Vol. 50, No. 4

427--455

In this article, we study the time-domain decomposition of optimal control problems for systems of semilinear hyperbolic equations and provide an in-depth well-posedness analysis. This is a continuation of our work, Krug et al. (2021) in that we now consider mixed two-point boundary value problems. The more general boundary conditions significantly enlarge the scope of applications, e.g., to hyperbolic problems on metric graphs with cycles. We design an iterative method based on the optimality systems that can be interpreted as a decomposition method for the original optimal control problem into virtual control problems on smaller time domains.