Evolutionary techniques for deterministic chaos control

Abstract

This work deals with optimization of the control of chaos by means of evolutionary algorithms. The main aim of this paper is to show that powerful optimizing tools like evolutionary algorithms can be in reality used for the optimization of deterministic chaos control. This work is aimed on explanation of how to use evolutionary algorithms (EAs) and how to properly define the cost function (CF). It is also focused on selection of control method and the explanation of all possible problems with optimization which comes together in such a difficult task, which is chaos control. Five new approaches for constructing the cost functions leading to satisfactory results are presented here. These cost functions secure fast and precise stabilization of chaotic system. As a model of deterministic chaotic system, the one dimensional logistic equation was used. The evolutionary algorithm Self-Organizing Migrating Algorithm (SOMA) was used in four versions. At the end, the brief overview of most important results is also presented.