Adapting Predictive Feedback Chaos Control for Optimal Convergence Speed

TL;DR

This paper introduces an adaptive predictive feedback chaos control method that optimizes convergence speed when stabilizing unstable periodic orbits in chaotic systems, with proven linear convergence and practical applicability.

Contribution

It presents a novel adaptive control scheme that dynamically adjusts control parameters for faster stabilization of chaotic orbits, supported by analytical and numerical analysis.

Findings

Converges at least linearly to an optimal spectral radius.

Proven analytically and numerically.

Easy to implement algorithmically.

Abstract

Stabilizing unstable periodic orbits in a chaotic invariant set not only reveals information about its structure but also leads to various interesting applications. For the successful application of a chaos control scheme, convergence speed is of crucial importance. Here we present a predictive feedback chaos control method that adapts a control parameter online to yield optimal asymptotic convergence speed. We study the adaptive control map both analytically and numerically and prove that it converges at least linearly to a value determined by the spectral radius of the control map at the periodic orbit to be stabilized. The method is easy to implement algorithmically and may find applications for adaptive online control of biological and engineering systems.