An Alternate Iterative Differential Evolution Algorithm for Parameter Identification of Chaotic Systems

Wanli Xiang,Xuelei Meng,Meiqing An

doi:10.1155/2015/740721

Abstract

Parameter estimation of chaotic systems plays a key role for control and synchronization of chaotic systems. At first, the parameter estimation of chaotic systems is mathematically formulated as a global continuous optimization problem. Then through integrating two differential mutation strategies, an improved greedy selection mechanism and a population diversity balance scheme, an alternate iterative differential algorithm, called AIDE, is presented to solve the problem in this paper. Subsequently, experiments are tested on a set of cases of parameter estimation of chaotic systems and the results show that AIDE is better than or at least equal to DE/rand/1/bin, DE/best/1/bin, and other four well-known algorithms in all cases.

Highlights

In 1963, Lorenz first found the classical chaotic attractor during the process of simulating the change of atmosphere through a three-dimensional autonomous system [1]
Dai et al [19] transformed the problem of parameter estimation of chaotic systems into a global optimization problem through designing a suitable objective function and solved the optimization problem using genetic algorithm
He et al [16] employed particle swarm optimization (PSO) algorithm for solving the problem of parameter estimation of Lorenz system and found that PSO is better than genetic algorithm (GA)

Summary

Introduction

In 1963, Lorenz first found the classical chaotic attractor during the process of simulating the change of atmosphere through a three-dimensional autonomous system [1]. Chang [4] proposed an improved differential evolution algorithm to estimate the unknown parameters of Chen and Lusystems. He et al [16] employed particle swarm optimization (PSO) algorithm for solving the problem of parameter estimation of Lorenz system and found that PSO is better than genetic algorithm (GA). In order to further improve the accuracy of the parameter estimation of chaotic systems, inspired by the existence of a few big evolution eras and small evolution eras in nature, we propose an alternate iterative differential evolution algorithm, in which two mutation strategies with different search abilities (exploration and exploitation) are employed to imitate the evolutionary behaviour of big evolution era and small evolution era, respectively.

Problem Description

Canonical Differential Evolution

Alternate Iterative Differential Evolution

Experimental Study and Discussion