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 $\Gamma$.
| Subjects: | Analysis of PDEs (math.AP); Optimization and Control (math.OC) |
| Cite as: | arXiv:2504.19554 [math.AP] |
| (or arXiv:2504.19554v2 [math.AP] for this version) | |
| https://doi.org/10.48550/arXiv.2504.19554 arXiv-issued DOI via DataCite |
From: Olivier Ley [view email] [via CCSD proxy]
[v1]
Mon, 28 Apr 2025 08:00:07 UTC (59 KB)
[v2]
Fri, 22 May 2026 15:03:40 UTC (60 KB)
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