Schr\"{o}dinger Meets Kuramoto via Feynman-Kac: Minimum Effort Distribution Steering for Noisy Nonuniform Kuramoto Oscillators

TL;DR

This paper develops a novel stochastic optimal control framework for steering the probability distribution of noisy, nonuniform Kuramoto oscillators, combining measure-valued recursions and Feynman-Kac methods.

Contribution

It introduces a new approach to control distribution steering in noisy Kuramoto models using measure-valued recursions and Feynman-Kac path integrals, applicable to both first and second order models.

Findings

Successful numerical implementation demonstrated.

Effective control of oscillator distributions achieved.

Framework applicable to various networked oscillator systems.

Abstract

We formulate and solve the problem of finite horizon minimum control effort steering of the state probability distribution between prescribed endpoint joints for a finite population of networked noisy nonuniform Kuramoto oscillators. We consider both the first and second order stochastic Kuramoto models. For numerical solution of the associated stochastic optimal control, we propose combining certain measure-valued proximal recursions and the Feynman-Kac path integral computation. We illustrate the proposed framework via numerical examples.