Comparison of two cost functions for evolutionary synthesis of control law for higher periodic chaotic logistic equation

Abstract

This research deals with a synthesis of control law for chaotic logistic equation by means of analytic programming. The novelty of the approach is that a tool for symbolic regression - analytic programming - is used for the purpose of stabilization of higher periodic orbits - oscillations between several values of chaotic system. The paper consists of the descriptions of analytic programming as well as chaotic system and comparison between used two cost functions-black box type and standard type where the difference between required and actual state is calculated. For experimentation, Self-Organizing Migrating Algorithm (SOMA) with analytic programming and Differential evolution (DE) as second algorithm for meta-evolution were used. © 2011 IEEE.