Optimal Control for Network of Coupled Oscillators

Abstract

This paper presents a nonlinear control framework for steering networks of coupled oscillators toward desired phase-locked configurations. Inspired by brain dynamics, where structured phase differences support cognitive functions, the focus is on achieving synchronization patterns beyond global coherence. The Kuramoto model, expressed in phase-difference coordinates, is used to describe the system dynamics. The control problem is formulated within the State-Dependent Riccati Equation (SDRE) framework, enabling the design of feedback laws through state-dependent factorisation. The unconstrained control formulation serves as a principled starting point for developing more general approaches that incorporate coupling constraints and actuation limits. Numerical simulations demonstrate that the proposed approach achieves robust phase-locking in both heterogeneous and large-scale oscillator networks, highlighting its potential applications in neuroscience, robotics, and distributed systems.