Modification of delayed feedback control using ergodicity of chaotic systems

Abstract

We devise a modified delayed feedback control algorithm that allows one to stabilize unstable target states of chaotic systems for any initial conditions placed on a strange attractor. The algorithm is based on ergodicity of chaotic systems. We first let the chaotic system to evolve unperturbed until it approaches the neighbourhood of the target state. Then we activate the controller that stabilizes that target state. We propose a special algorithm that evaluates the closeness of the current state of the system to the target state. For continuous-time systems, this algorithm can be implemented by simple low-pass filters. We demonstrate the efficacy of our algorithm with numerical computations of statistics of successful stabilizations. Keywords: chaos, dynamical systems, delayed feedback control, ergodicity