Approximation of an optimal control problem on a network with a perturbed problem in the whole space
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| author | Camar-Eddine, Mohamed Chuberre, Mériadec Haddou, Mounir Ley, Olivier |
| author_facet | Camar-Eddine, Mohamed Chuberre, Mériadec Haddou, Mounir Ley, Olivier |
| contents | A classical optimal control problem posed in the whole space R^2 is perturbed by a singular term of magnitude $ε$^{-1} aimed at driving the trajectories to a prescribed network $Γ$. We are interested in the link between the limit problem, as $ε$ $\rightarrow$ 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 $Γ$. 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 $Γ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19554 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximation of an optimal control problem on a network with a perturbed problem in the whole space Camar-Eddine, Mohamed Chuberre, Mériadec Haddou, Mounir Ley, Olivier Analysis of PDEs Optimization and Control A classical optimal control problem posed in the whole space R^2 is perturbed by a singular term of magnitude $ε$^{-1} aimed at driving the trajectories to a prescribed network $Γ$. We are interested in the link between the limit problem, as $ε$ $\rightarrow$ 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 $Γ$. 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 $Γ$. |
| title | Approximation of an optimal control problem on a network with a perturbed problem in the whole space |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2504.19554 |