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

With the rapid progress in the field of computer science and the deepening of the research on calculus theory,fractional calculus theory as an extension of integer calculus order has been continuously developed in the field of engineering and science.Chaotic systems have extremely complex nonlinear characteristics.In recent years,fractional-order chaotic systems have shown great value in the applications of image encryption,secure communication,physics,mathematics and biological engineering.In the field of control,there were many kinds of synchronization control methods for fractional order chaotic system,and some progress has been made.Compared with the non-finite time closed-loop control system,the finite-time closed-loop control system has better robustness and anti-disturbance performance,which can achieve more precise and flexible control.The main reason is that the finite-time controller has fractional power terms.At the present stage,most of the researches are on the finite time synchronization of integer order systems,but as far as fractional order systems are concerned,there are relatively few researches in related fields.Therefore,it is significant to study the finite time control and synchronization of fractional-order chaotic systems.In this paper,based on the fractional-order calculus theory,the fractional-order Lyapunov stability theory and the finite time control theory,combined with parameter identification and sliding mode control methods,different controllers were designed respectively to realize finite-time synchronization for the fractional order chaotic systems with unknown system parameters,load disturbances and uncertainty.The main contents were as follows:Firstly,the chaotic behavior of the studied system was judged by phase diagram and 0-1test method.A finite time controller was designed to realize the finite time synchronization of fractional-order Lorenz chaotic systems.Fractional-order Lorenz chaotic systems with unknown parameters were considered by discussing the concepts and basic principles of fractional-order calculus theory.According to Lyapunov stability theory,finite time control theory and parameter identification method,a new finite time controller and parameters correction rate were designed to realize finite time synchronization of fractional-order Lorenz chaotic systems with unknown parameters.In addition,unknown parameters of fractional order Lorenz chaotic systems were identified.Through Matlab simulation,the effectiveness of the finite-time synchronization control scheme was verified.Secondly,the finite-time synchronization control of fractional order chaotic systems with disturbances was studied.By using the designed finite-time controller,the fractional order chaotic systems with disturbances could realize synchronization in finite time,and the state variables of the error system were stable at zero value in finite time.Using Matlab numerical simulation,the finite time synchronization problem of fractional-order chaotic systems without disturbances was compared with that of fractional-order chaotic systems with disturbances,and the validity of the designed finite time synchronization method is verified.By adjusting the key parameters of the designed controller,the synchronization time of the finite time synchronization control of the controlled error system can be shortened and the estimation value of the finite time can be calculated.Finally,the sliding mode control theory method was applied to the finite time synchronization of fractional order chaotic systems,and the robust finite-time sliding mode synchronization control of a class of uncertain fractional-order chaotic systems was studied.A new fractional-order sliding mode surface was designed.Based on the finite time stability theory and Lyapunov stability theory,a robust finite time sliding mode controller is proposed.By changing the parameter values in the controller,the controller could satisfy the finite time control condition and the fixed time control condition respectively,so that the fractional order chaotic systems with uncertainties and random disturbances could realize the robust finite /fixed time sliding mode synchronization control.The effectiveness and superiority of the finite time synchronization control method were verified by Matlab simulation.