Research On Robust Synchronization Of Fractional-order Chaotic Systems

The robust synchronization problem of fractional-order chaotic system, which is pre-sented along with the development of fractional-order theory and extensive use of chaotic synchronization, has attracted more and more attention of scholars. But at the same time, it is also a thorny problem in that chaotic system is particularly sensitive to parameter perturbation and external disturbance, and there is significant difference between the sta-bility of fractional-order chaotic system and integer order chaotic system.This dissertation focuses on the stability of fractional-order system and the robust synchronization method of fractional-order chaotic systems. Main contributions are given as follows:1. A robust synchronization control scheme for uncertain fractional-order chaotic sys-tems with external disturbances is designed based on the terminal sliding mode control theory. On the basis of fractional-order Lyapunov stability theory, a robust sliding mode control scheme, which is used to ensure the sliding mode motion occurs in limited time, is introduced to the fractional-order chaotic system. The proposed control scheme is applied to synchronize the fractional order Lorenz chaotic system and fractional-order Chen's cha-otic system with uncertainty and external disturbance parameters, simulation results show the applicability and efficiency of the proposed scheme. It should be pointed out in partic-ular that the introduced fractional-order terminal sliding mode controller is applicable for a large class of different uncertain fractional-order chaotic systems under external disturb-ances.2. Based on model approximation method, a new robust modified projective synchro-nization control scheme is presented for the fractional-order chaotic system which is global bounded for parameter uncertainty and external disturbances. Then the proposed method is used to the complete synchronization and revised projection synchronization of frac-tional-order Lorenz and Chen's chaotic systems with parameter uncertainty and external disturbances, simulation results show the robustness of the designed controller. It can also be concluded from the scheme's design process that the proposed scheme is effective for a large class of different uncertain fractional-order chaotic systems under external disturb-ances.3. By analyzing the stability of a time-varying fractional-order system, a stability the-orem is proposed for a time varying fractional-order system with order0<?<1. Then the presented stability theorem is used in the synchronization of the fractional-order Lii chaotic system, simulation results verify again that it is also effective when used in the process of controller design.4. First, a fractional-order mathematical model of permanent magnet synchronous motor (PMSM) is given. Then a fractional-order Lyapunov robust stability theorem and deduction, which makes it is more convenient to judge the stability of fractional-order system in time domain, are derived based on the fractional-order Lyapunov matrix differ-ential equation stability theory. Finally, different controllers which are designed respec-tively according to the proposed theorem and deduction are used to achieve the chaotic control and synchronization of the fractional-order PMSM system, numerical simulation curves show the effectiveness of the method.In conclusion, the main innovative achievements for fractional-order systems stability and fractional-order chaotic system robust synchronization in this paper are as follows:1. Based on the terminal sliding mode control scheme, fractional-order sliding mode surface and controller are designed to realize the robust synchronization of different un-certain fractional-order chaotic systems under external disturbances.2. Based on the upper bound of model approximation error method, a robust synchronization scheme is proposed for different uncertain fractional-order chaotic sys-tems under external disturbances.3. A stability theorem for time-varying fractional-order system is proposed and is successfully applied to the synchronization of fractional-order chaotic systems.4. A stability theorem for linear fractional-order system is proposed and is successfully applied to the synchronization of fractional-order PMSM chaotic system.