Research On Some Problems Of Impulsive Synchronization In Chaotic Systems With Actuator Saturation

In recent years,chaos control has become one of the hot spots in the international research because of the complex dynamic characteristics and wide application prospects of chaotic systems.Synchronization control of chaotic systems has been paid more and more attention in the field of natural science and engineering applications.Impulsive control has been widely concerned by the scholars due to its significant control advantages,and has achieved remarkable application results in many fields.The impulsive control method only needs to transmit the information at the impulsive time,which can greatly reduce the information redundancy in the communication process and improve the performance of the system significantly.In the actual control system,the actuator fault and saturation phenomenon will lead to the degradation of the system control performance,and even cause the stability of the stable closed-loop system.In view of this,this thesis studies several problems of impulsive synchronization of chaotic systems under the influence of actuator saturation.By constructing discontinuous Lyapunov function and using linear matrix inequality(LMI)method,it studies a more flexible,more effective and more consistent impulsive control algorithm.The main research contents of this thesis include the following aspects:Firstly,a set of improved impulsive control methods for a class of time-delay chaotic systems with actuator saturation are proposed.Based on impulsive differential equation and Lyapunov stability theorem,sufficient conditions to ensure synchronization of time-delay chaotic neural networks are obtained.The impulsive control method in this thesis has no strict requirements on the delay size and actuator saturation domain,and is more flexible and practical in practical systems compared with the existing research results.The results obtained can be applied to a wider range of nonlinear time-delay systems.Secondly,considering the inevitable noise interference in information communication,the impulsive synchronization control of chaotic system under stochastic disturbance is studied.An appropriate impulsive controller is designed,and the inequalities between the eigenvalues of the saturated impulsive function,the disturbance parameters and the impulsive gain are obtained by combining Lyapunov stability theory.Thirdly,based on the theory of impulsive differential systems,Lyapunov stability and finite time control technology,the finite time and fixed time synchronization of chaotic systems are studied by using the impulsive control method,and the sufficient conditions for the finite time and fixed time synchronization of chaotic systems are obtained.Different from the existing finite time and fixed time synchronization methods,this thesis adopts an effective impulsive control strategy,which has faster convergence rate and less state information transmission.