Advanced Targeting Cost Function Design for Evolutionary Optimization of Control of Logistic Equation

Abstract

This research deals with the optimization of the control of chaos by means of evolutionary algorithms. This work is aimed on an explanation of how to use evolutionary algorithms (EAs) and how to properly define the advanced targeting cost function (CF) securing very fast and precise stabilization of desired state for any initial conditions. 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. For each version, repeated simulations were conducted to outline the effectiveness and robustness of used method and targeting CF.