Sliding Mode Synchronization Control Of Fractional Order Chaotic Systems

Nonlinear phenomena generally exist in engineering and real life.In recent years,fractional-order chaotic systems have become a hotspot in nonlinear science.The synchronization of fractional-order chaotic systems is a special control problem due to the potential applications of biology engineering and signal processing.Chaotic theory is widely used in the field of physics,engineering,biology and finance.Fractional-order differential theory provides a more accurate tool to model the complex systems,and they can reflect the dynamic characteristics of systems.Fractional-order chaotic systems have both the characteristics of fractional-order systems and chaotic systems.It can be widely used in secure communication.Therefore,it is very meaningful for the fractional-order chaotic systems.The synchronization of fractional chaotic systems and the stability analysis are studied using the fractional-order calculus theory,fractional-order stability theory and property and Lyapunov stability theory.The main contents of this paper are as follows:1.Chaotic systems,fractional-order differential theory and fractional-order chaotic systems are introduced in this paper.Then,sliding mode control is introduced.A sliding mode controller is designed using traditional sliding mode control method and fractional-order stability theory.Last,numerical simulation is carried out to prove the effectiveness of the method.2.Based on the fractional-order chaotic system theory and terminal sliding mode theory,a fractional-order non-singular terminal sliding surface is designed.Then,for the case that the unknown bounds of the uncertainties and external disturbances are assumed to be in advance,an adaptive control law is proposed to estimate the unknown bounds online,and force the trajectory of the synchronization error system onto the sliding surface.Last,the stability is proven by Lyapunov stability theory.In this paper,numerical simulation of the 3-D fractional Chen system is presented to show the efficiency and applicability of the proposed control strategy by using Matlab-simulink.A novel adaptive controller is designed to improve the complexity of the controller with retaining the nonlinear part,and the stability is proven.Finally,numerical simulation of the 4-D fractional-order Lorenz system is carried out to verify the effectiveness of the controller.3.The dynamical soft variable structure controller and the adaptive sliding mode controller are designed respectively for the linear part and the nonlinear part of the error system.Then,the stability of the controller is proven using the fractional-order stability theory and the Lyapunov stability theory.Finally,numerical simulation of fractional-order Chen system is verified the advantages and effectiveness of the soft variable structuresynchronization controller.