Robust Adaptive Generalized Projective Synchronization of Chaotic Systems with Uncertain Disturbances

Zhen Jia,Guangming Deng

doi:10.1155/2012/362765

Abstract

The generalized projective synchronization (GPS) of chaotic systems with uncertain parameter noise and external disturbance is discussed. Based on the adaptive technique, a response system is constructed, and a novel adaptive controller is designed to guarantee the GPS between the drive‐response systems, and to eliminate the effect of external disturbance and parameters noise on GPS. The conclusion is proved theoretically, and corresponding numerical simulations are provided to verify the effectiveness of the proposed method.

Highlights

The concept of chaos synchronization was introduced in the first time by Pecora and Carroll and an effective synchronization method was proposed in 1990 1
In this paper, we further investigate the GPS of a class of chaotic or hyperchaotic systems with uncertain parameters’ noise and external disturbances
Many classical chaotic and hyperchaotic systems can be written in the form of 2.1

Summary

Introduction

The concept of chaos synchronization was introduced in the first time by Pecora and Carroll and an effective synchronization method was proposed in 1990 1. Many schemes of chaos synchronization have been developed and widely used in synchronization control of complex network, for example, linear coupling method, feedback approach, adaptive technique, and impulsive control 2–7. In authors introduced a generalized projective synchronization method for achieving the different variables of drive-response system synchronized up to different scaling factors. Suppression the effect of disturbance in synchronization process is very important in reality Motivated by this reason, in this paper, we further investigate the GPS of a class of chaotic or hyperchaotic systems with uncertain parameters’ noise and external disturbances. The approach proposed in our paper shows high robustness to the parameter noise and external disturbance.

Model Description and Preliminaries

Approach for the GPS and Noise Suppression

Numerical Simulations

Conclusion