Research On The Soft Control For Synchronization Of Fractional Order Chaotic Systems

In recent years,fractional order systems have attracted considerable attentions.Fractional order generalized the classical integer order integration and differentiation non-integer order,which giving a more accurate modeling to describe real world.Fractional order chaos synchronization has been developed extensively as an important topic in nonlinear science.It has been investigated by scientists working in fields as different as secure communications,financial,chemical,physical,and biological systems.There are some progress about the kinds of effective controller to the synchronization of fractional order chaotic systems.Soft variable structure control(SVSC)is another branch in the development of variable structure control,which achieve a high regulation rate and optimal control effect.Many soft variable structure control methods have been developed to the real world.Based on soft variable structure control,many studies have been successfully extended to the stability control of fractional order systems.Further it enrich and perfect the stable control of fractional order linear systems.However,there was still a lot of room for the study of synchronization of fractional order nonlinear systems,and the research result of fractional order chaos synchronization was rarely in the soft variable structure control.The synchronization of fractional chaotic systems which using the adaptive control and soft variable structure control in the control constraints and finite-time control were studied on the premise of the fractional-order calculus theory and the Lyapunov stability theory.The main contents of this thesis were roughly as follows:1.The research background and significance of the soft synchronization control for fractional-order chaotic systems were introduced.The research status and development of fractional-order control,chaotic synchronization control and soft variable structure control were summarized in detail.It provided a background for the application of soft variable structure control to the synchronization control of fractional chaotic systems.Then,the definition property of fractional calculus,the definition and control method of fractional order chaotic systems were introduced.It was mainly showed the development of soft variable structure control,the basic theory and the design method.The theoretical basis were proposed for the paper.2.It is a soft adaptive controller designed for a sufficient condition.Fractional order differential theory was introduced in this paper.In order to solve the problem of synchronization between two fractional-order chaotic systems,a new soft adaptive controller was proposed by applying the indirect Lyapunov approach.By the way,A novel sufficient condition for asymptotic stability of the synchronization between two fractional-order chaotic systems with the order ?(0(27)?(27)1)was presented.Next,the controller with different control parameters was compared with traditional feedback controller.A numerical example was provided to demonstrate the effectiveness of the proposed methods.3.It is a soft structure controller designed for a sufficient condition in control constraints.Based on the new adaptive control,we studied the designing method of the soft structure controller in control constraints for synchronization between two fractional-order chaotic systems.The linear adaptive controller was designed for the synchronization between fractional-order chaotic systems.Then we improved the controller by the soft structure control.A novel sufficient condition for asymptotic stability of the synchronized system was presented in the control constraints.The advantage between the two controllers have be analyzed.The final example was provided to demonstrate the effectiveness of the proposed methods.And the adaptive soft structure controller achieved a high regulation rate to the synchronization in the control constrains.4.The soft structure control for finite synchronization time were introduced.Based on the adaptive soft structure control with control constraints,we studied the designing method of the soft structure controller in the finite time synchronization of fractional-order chaotic systems.A new soft structure controller was proposed for the generalized finite time projective synchronization of two fractional order linear systems with control constraints by applying the direct Lyapunov approach.Then the controller have be extended to get the synchronization of fractional-order chaotic systems.At the same time,the relation between the control parameters and synchronization time was proved.The simulation showed the shorter time by the different control parameters.