Synchronization for a Class of Uncertain Fractional Order Chaotic Systems with Unknown Parameters Using a Robust Adaptive Sliding Mode Controller

Yan Yan

doi:10.1155/2016/7404652

Abstract

This paper deals with the synchronization of a class of fractional order chaotic systems with unknown parameters and external disturbance. Based on the Lyapunov stability theory, a fractional order sliding mode is constructed and a controller is proposed to realize chaos synchronization. The presented method not only realizes the synchronization of the considered chaotic systems but also enhances the robustness of sliding mode synchronization. Finally, some simulation results demonstrate the effectiveness and robustness of the proposed method.

Highlights

IntroductionFractional calculus is as old as conventional calculus and with more than 300 years’ history, but its application to physics and engineering is in recent years
This paper deals with the synchronization of a class of fractional order chaotic systems with unknown parameters and external disturbance
Fractional calculus is as old as conventional calculus and with more than 300 years’ history, but its application to physics and engineering is in recent years

Summary

Introduction

Fractional calculus is as old as conventional calculus and with more than 300 years’ history, but its application to physics and engineering is in recent years. In recent years, sliding mode control method has been applied in the synchronization of fractional order chaotic systems. Based on the fractional order line systems’ stability theory, Wang et al [24] proposed an active sliding mode surface and design a controller to realize the modified projective synchronization for two different fractional order systems. In our previous work [25], a novel robust fractional order sliding mode approach for the synchronization of two fractional order chaotic systems in the presence of system parameter uncertain and external disturbance is proposed, but the unknown parameters were not considered.

Preliminary and System Description

Main Results

Simulation

Conclusions