Optimal Control for Kuramoto Model: from Many-Particle Liouville Equation to Diffusive Mean-Field Problem
Year: 2025
Type: preprint
Abstract: In this paper, we investigate the mean-field optimal control problem of a swarm of Kuramoto oscillators. Using the notion of wrapped distribution, we explain the connection between the stochastic particle system and the mean-field PDE on the periodic domain. In the limit of an infinite number of oscillators the collective dynamics of the agents' density is described by a diffusive mean-field model in the form of a non-local PDE, where the non-locality arises from the synchronization mechanism. We prove the existence of the optimal control of the mean-field model by using $Γ$-convergence strategy of the cost functional corresponding to the Liouville equation on the particle level. In the discussion of propagation of chaos for fixed control functions we complete the relative entropy estimate by using large deviation estimate given by \cite{MR3858403}.
Source: arXiv (Cornell University)
Authors: Chen, Li, Wang, Yucheng, Zhidkova, Valeriia
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W6979337090
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