Feedback Control of Coupled Nonlinear Oscillators with Uncertain Parameters

The effective control of synchronization patterns in an oscillator ensemble is essential for optimal functioning of natural and engineered systems, with applications across diverse domains, including power systems, robotics, and medical device development. In this work, we address the problem of designing a feedback law to establish a desired synchronization structure in a pair of oscillators with model uncertainties. These oscillators are modeled using phase models with uncertainties in their phase response curves and oscillation frequencies. Our principle idea is to design a switching input by utilizing the periodicity of system dynamics. The input parameters for this switching strategy are determined by solving a simple convex quadratic program with inequality constraints. In addition, we derive analytic expressions of feedback inputs for anti-phase and in-phase synchronization of a pair of sinusoidal and SNIPER phase oscillators. The effectiveness of the proposed approach is demonstrated on both phase models and complex biophysical models of spiking neurons.