Research On The Finite Time Control And Synchronization Of Fractional Order Chaotic Systems

The theory of fractional calculus can be regarded as the general form of calculus.Among the nonlinear systems,the fractional order chaotic system is the most complex,and the research of fractional order calculus related system should not be underestimated.Moreover,the research of fractional order chaotic systems has been further deepened in different directions of science and engineering.In practice,fractional order chaotic system is widely used in image encryption,power engineering,secure communication,medical and financial science.In control,there are more and more stability theories and synchronization methods related to fractional order chaotic systems,and each has its own characteristics and related applications.The finite time control theory is different from the traditional stability theory,and its control structure can be regarded as closed-loop feedback control.The complexity of finite time controller is relatively high,which is reflected in the anti-interference ability to the outside world and the robustness to the uncertainty of the system itself.At present,the research and application of anti synchronization control in practical engineering is not wide enough,so it is very meaningful to combine finite time control with anti synchronization.In this paper,starting from the integer order,the corresponding controllers are designed for the chaotic systems with different order according to the finite time anti synchronization problem.Finally,it is extended to practical application.The main contents are as follows:Firstly,the integral order and fractional order chaotic systems are analyzed,and the finite time anti synchronization is proved.A unified controller is designed to ensure the finite time anti synchronization of different order chaotic systems.Then,the results are applied to Lorenz chaotic systems with different orders.Simulink system model is used to simulate and verify the feasibility of the controller design.Secondly,based on Lyapunov stability theory and finite time control theory,a nonlinear controller with adjustable parameters is designed for fractional order chaotic system.The characteristic of the controller is that it has a settable parameter,which can affect the anti synchronization time.The fractional order Lorenz chaotic system is built by Simulink,and the finite time anti synchronization of the two systems under the action of the controller is realized.The effectiveness of adjusting the controller parameters on the finite time anti synchronization time is verified.Finally,for the fractional order chaotic system with unknown parameters,the adaptive control theory is used to identify the internal parameters of the system.The anti synchronization of fractional order chaotic system with parameter uncertainty is realized.An adaptive nonlinear controller is designed to ensure the finite time stability of the closed-loop control system.The parameter correction rate is calculated by Lyapunov function.This method improves the robustness of the system.The feasibility of this method is verified by the restoration of Simulink system.Finally,the research results are applied to the permanent magnet synchronous motor system.