Research On Synchronization Of Fractional Chaotic Systems With Disturbances

Fractional-order chaotic synchronization is an important subject in nonlinear field.Synchronization of chaotic fractional-order systems has attracted more and more attention due to its potential application in secure communication and control processing.However,due to the limitation of measurement technology in practice,there are many inevitable uncertainties due to the lack of relevant empirical theories.In addition,the external uncertainty disturbance of the system will often affect the performance of the system.Based on the theory of fractionalorder adaptive control,sliding mode control,finite time control and disturbance observer,a suitable controller is designed for the fractional-order chaotic system with various disturbances.Lyapunov stability theory is used to analyze the stability of the system.Firstly,aiming at chaotic synchronization problem with parameter perturbation,the adaptive rate of parameter estimation and feedback controller are designed for fractional-order hyperchaotic Lorenz system with the same structure,and the master-slave synchronization of hyperchaotic Lorenz system is successfully realized.Then the same structure is extended to the control of different structure,and the driving system is selected as fractional order Lorenz system,which is believed to be fractional order Lü system.The controller and adaptive rate are designed successfully to achieve heterostructure synchronization.The effect of parameter perturbation on fractional order mixing synchronization is eliminated successfully.Then,considering the problem of unknown external disturbances,a robust sliding mode control method is adopted to control fractional-order chaotic systems synchronously.A linear sliding mode surface is proposed to prove the convergence of the sliding mode surface.Then the adaptive sliding mode controller is designed to make the system state with external disturbance converge to the sliding mode surface.In view of the shortcomings of linear sliding mode,a non-singular terminal sliding mode surface,sliding mode controller and disturbance adaptive rate are designed by introducing fractional order terminal sliding mode control method.Finally,the chattering problem caused by discontinuity of sliding mode control is analyzed based on the theory of disturbance observer.A disturbance observer is designed,which can accurately and quickly estimate and compensate the uncertain disturbance.Combining with the disturbance observer and designing the feedback controller,the chattering of the system is reduced successfully when the control precision and control speed are notified.