Robust Adaptive Sliding Mode Control for Generalized Function Projective Synchronization of Different Chaotic Systems with Unknown Parameters

Xiuchun Li,Wei Xu,Jianhua Gu

doi:10.1155/2013/407436

Abstract

When the parameters of both drive and response systems are all unknown, an adaptive sliding mode controller, strongly robust to exotic perturbations, is designed for realizing generalized function projective synchronization. Sliding mode surface is given and the controlled system is asymptotically stable on this surface with the passage of time. Based on the adaptation laws and Lyapunov stability theory, an adaptive sliding controller is designed to ensure the occurrence of the sliding motion. Finally, numerical simulations are presented to verify the effectiveness and robustness of the proposed method even when both drive and response systems are perturbed with external disturbances.

Highlights

Chaos synchronization has been a hot topic since the pioneering work of Pecora and Carroll [1]
Numerical simulations are presented to verify the effectiveness and robustness of the proposed method even when both drive and response systems are perturbed with external disturbances
Amongst all kinds of chaos synchronization, projective synchronization (PS), which was first reported by Mainieri and Rehacek [10], has been extensively investigated in the recent years because it can obtain faster communication with its proportional feature. this means that the drive and response systems can synchronize up to a scaling factor

Summary

Introduction

Chaos synchronization has been a hot topic since the pioneering work of Pecora and Carroll [1]. Xiang and Chen [15] and Aghababa and Akbari [16] have all proposed sliding mode control method to synchronize two different chaotic systems with disturbances. They [15, 16] only realize complete synchronization, and the parameters of the system in [14,15,16] are all known. Two different chaotic systems are illustrated to verify the effectiveness of the proposed method, and it can be found that the designed controller has stronger robustness when both drive and response systems are all perturbed with external disturbances

Description of Chaotic System

Design of the Adaptive Sliding Mode Controller

Numerical Simulations

Conclusions