Adaptive Tuning of Feedback Gain in Time-Delayed Feedback Control

TL;DR

This paper presents an adaptive method for tuning feedback gain in time-delayed feedback control, enhancing stabilization of unstable states in chaotic systems through a control theory-based algorithm.

Contribution

It introduces a novel adaptive tuning algorithm using the speed-gradient method, improving feedback control in systems with delays and noise.

Findings

Effective stabilization of fixed points and periodic orbits

Robustness to noise and initial conditions

Successful application to systems with multiple delays

Abstract

We demonstrate that time-delayed feedback control can be improved by adaptively tuning the feedback gain. This adaptive controller is applied to the stabilization of an unstable fixed point and an unstable periodic orbit embedded in a chaotic attractor. The adaptation algorithm is constructed using the speed-gradient method of control theory. Our computer simulations show that the adaptation algorithm can find an appropriate value of the feedback gain for single and multiple delays. Furthermore, we show that our method is robust to noise and different initial conditions.