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DOI: 10.23952/cot.2026.41
Received June 4, 2025; Accepted September 27, 2025; Published online May 22, 2026
Abstract. We present a new algorithmic approach for the computational solution of optimal control problems with hybrid nature governed by linear parabolic partial differential equations (PDEs) featuring state-dependent switches. We propose a stepwise reformulation of the initial model by methods from disjunctive programming (DP) and a time transformation method. Under a transversality asssumption, we first remove the state-dependent switching rule by introduction of explicit switching variables and vanishing constraints (VCs). Subsequently, we reformulate the obtained optimization task as a mathematical problem with equilibrium constraints (MPEC). Afterwards, the combination of the previous reformulation steps with a regularization of the state equation and Moreau-Yosida type penalization yields a surrogate model with only finite dimensional constraints. Ultimately, this approach allows us to derive necessary first-order optimality conditions to filter candidates for optimality. After detailed discussion of each reformulation step, we introduce the algorithmic framework based on the semismooth Newton method. Finally, we report on promising computational results within the presented framework.
How to Cite this Article:
F.M. Hante, C. Kuchler, An algorithmic framework for optimal control of hybrid dynamical systems with parabolic PDEs, Commun. Optim. Theory 2026 (2026) 41.