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arXiv · 2504.19554

Approximation of an optimal control problem on a network with a perturbed problem in the whole space

Mohamed Camar-Eddine·Mériadec Chuberre·Mounir Haddou·Olivier Ley
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Abstract

A classical optimal control problem posed in the whole space R^2 is perturbed by a singular term of magnitude $\epsilon$^{-1} aimed at driving the trajectories to a prescribed network $\Gamma$. We are interested in the link between the limit problem, as $\epsilon$ $\rightarrow$ 0, and some optimal control problems on networks studied in the literature. We prove that the sequence of trajectories admits a subsequential limit evolving on $\Gamma$. Moreover, in the case of the Eikonal equation, we show that the sequence of value functions associated with the perturbed optimal control problems converges to a limit which, in particular, coincides with the value function of the expected optimal control problem set on the network $\Gamma$.

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Mohamed Camar-Eddine, Mériadec Chuberre, Mounir Haddou, Olivier Ley. 2025-04-28. Approximation of an optimal control problem on a network with a perturbed problem in the whole space. https://arxiv.org/abs/2504.19554

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