Data-driven phase control for limit-cycle oscillators under partial observation

TL;DR

This paper introduces an autoencoder-based approach for real-time phase estimation of limit-cycle oscillators from partial observations, enabling improved control of synchronization in complex rhythmic systems.

Contribution

It presents a novel phase estimation method using delay embedding and autoencoders, enhancing control strategies for oscillators with unknown dynamics under limited observation.

Findings

The method accurately estimates phase errors under weak inputs.

Effective phase-reduction-based feedback control achieved in numerical simulations.

Applicable to different oscillator models like Stuart-Landau and Hodgkin-Huxley.

Abstract

Controlling rhythmic systems, typically modeled as limit-cycle oscillators, is an important subject in real-world problems. Phase reduction theory, which simplifies the multidimensional oscillator state under weak input to a single phase variable, is useful for analyzing the oscillator dynamics. In the control of limit-cycle oscillators with unknown dynamics, the oscillator phase should be estimated from time series under partial observation in real time. In this study, we present an autoencoder-based method for estimating the oscillator phase using delay embedding of observed state variables. We evaluate the order of the phase estimation error under weak inputs and apply the method to phase-reduction-based feedback control of mutual synchronization of two oscillators under partial observation. The effectiveness of our method is illustrated by numerical examples using two types of limit-cycle oscillators, the Stuart-Landau and Hodgkin-Huxley models.