Analytic programming in the task of evolutionary synthesis of a controller for high order oscillations stabilization of discrete chaotic systems

Abstract

This paper deals with the utilization of a symbolic regression tool, which is Analytic Programming (AP), together with two evolutionary algorithms, the Self-Organizing Migrating Algorithm (SOMA) and Differential Evolution (DE), for the synthesis of a new control law. This synthesized chaotic controller secures the stabilization of higher periodic orbits, which represent oscillations between several values of three selected discrete chaotic systems. Selected examples were: an artificially evolutionary synthesized system, logistic equation and Hénon map. The paper consists of the description of analytic programming as well as chaotic systems used, evolutionary techniques and the cost function. © 2013 Elsevier Ltd. All rights reserved.