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arXiv · 2112.06535

Infinite Horizon Optimal Control Problems for a Class of Semilinear Parabolic Equations

Eduardo Casas·Karl Kunisch
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Abstract

Infinite horizon open loop optimal control problems for semilinear parabolic equations are investigated. The controls are subject to a cost-functional which promotes sparsity in time. The focus is put on deriving first order optimality conditions. This is achieved without relying on a well-defined control-to-state mapping in a neighborhood of minimizers. The technique of proof is based on the approximation of the original problem by a family of finite horizon problems. The optimality conditions allow to deduce sparsity properties of the optimal controls in time.

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Eduardo Casas, Karl Kunisch. 2021-12-13. Infinite Horizon Optimal Control Problems for a Class of Semilinear Parabolic Equations. https://arxiv.org/abs/2112.06535

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