| Abstract: |
| 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 their density is described by a diffusive mean-field model in the form of a nonlocal PDE, where the nonlocal term arises from the synchronization mechanism. We prove that the macroscopic optimal control problem admits a solution by using $\Gamma$-convergence strategy of the cost functional corresponding to the Liouville equation on the particle level. |
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