TY - JOUR A1 - Krug, Richard A1 - Leugering, Günter A1 - Martin, Alexander A1 - Schmidt, Martin A1 - Weninger, Dieter T1 - Time-Domain Decomposition for Optimal Control Problems Governed by Semilinear Hyperbolic Systems with Mixed Two-Point Boundary Conditions JF - Control and Cybernetics N2 - In this article, we continue our work (Krug et al., 2021) on time-domain decomposition of optimal control problems for systems of semilinear hyperbolic equations in that we now consider mixed two-point boundary value problems and provide an in-depth well-posedness analysis. 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. KW - Time-domain decomposition KW - Optimal control KW - Semilinear hyperbolic systems KW - Convergence Y1 - 2021 ER - TY - JOUR A1 - Krug, Richard A1 - Leugering, Günter A1 - Martin, Alexander A1 - Schmidt, Martin A1 - Weninger, Dieter T1 - Time-Domain Decomposition for Optimal Control Problems Governed by Semilinear Hyperbolic Systems JF - SIAM Journal on Control and Optimization N2 - In this article, we extend the time-domain decomposition method described by Lagnese and Leugering (2003) to semilinear optimal control problems for hyperbolic balance laws with spatio-temporal varying coefficients. We provide the design of the iterative method applied to the global first-order optimality system, prove its convergence, and derive an a posteriori error estimate. The analysis is done entirely on the continuous level. A distinguishing feature of the method is that the decomposed optimality system can be interpreted as an optimality system of a local "virtual" optimal control problem. Thus, the iterative time-domain decomposition of the optimality system can be interpreted as an iterative parallel scheme for virtual optimal control problems on the subintervals. A typical example and further comments are given to show the range of potential applications. Moreover, we provide some numerical experiments to give a first interpretation of the role of the parameters involved in the iterative process. KW - Time-domain decomposition KW - Optimal control KW - Semilinear hyperbolic systems KW - Convergence KW - A posteriori error estimates Y1 - 2020 ER -