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Optimal Boundary Control of Hyperbolic Balance Laws with State Constraints

  • In this paper we analyze the optimal control of initial-boundary value problems for entropy solutions of scalar hyperbolic balance laws with pointwise state constraints. Hereby, we suppose that the initial and the boundary data switch between different C¹-functions at certain switching points, where the C¹ -functions and the switching points are considered as the control. For a class of cost functionals, we prove first order necessary optimality conditions for the corresponding optimal control problem with state constraints. Furthermore, we use a Moreau-Yosida type regularization to approximate the optimal control problem with state constraints. We derive optimality conditions for the regularized problems and finally prove convergence to the solution of the optimal control problem with state constraints.
Author:Johann Michael Schmitt, Stefan Ulbrich
Document Type:Preprint
Date of Publication (online):2019/11/01
Date of first Publication:2021/02/01
Release Date:2017/11/21
Institutes:Technische Universität Darmstadt