Actor-Critic Algorithm for Optimal Synchronization of Kuramoto Oscillator

Abstract

This paper constructs a reinforcement learning (RL) based algorithm of Actor-Critic (AC) for the optimal synchronism of the Kuramoto oscillator. This is accomplished through the Ott-Antonsen ansatz framework for the dynamics of large interactive unit networks. Besides, this approach reduces the infinite-dimensional dynamics to phase space flow, i.e., low dimensional dynamics for certain systems of globally coupled phase oscillators. The resulting Hamiltonian-Jacobi-Bellman (HJB) expression is extremely difficult to solve in general, therefore this paper introduces the AC method for learning approximate optimal control laws for the Kuramoto oscillator model. RL has been contemplated as one of the efficient methods to solve optimal control of non-linear systems. For a collection of non-homogeneous oscillators, the states are elucidated as phase angles, which is the modification of the model for a coupled Kuramoto oscillator. An admissible initial control policy for the Kuramoto oscillator model is designed and solved using RL giving an approximate solution of the optimal control problem. Finally, local synchronism of the coupled Kuramoto oscillator model is supported through simulations analysis.