The Research On Fixed-time Synchronization Control Of Chaotic Systems With Different Dimensions

In recent years,with the discovery of chaos in many practical systems,chaos synchronization control has gradually become a research hot spot in various research fields,and has a wide range of practical applications in related fields,especially in secure communication,information processing and so on.However,the previous studies mostly considered the synchronization of the same dimension chaotic system.Because different dimensional chaotic systems(DDCSs)are also common in natural systems,more and more researchers begin to consider the synchronization problem of DDCSs,which has a wide application prospect in biology,physics and other disciplines.In this paper,the fixed-time synchronization control of DDCSs is studied.The main work is as follows:1.The global fixed-time synchronization of chaotic systems with different dimensions is studied.It is noted that parameters may not be accurately obtained in the actual system,so in this paper,the fixed-time synchronization problem of two DDCSs without unknown parameters and with unknown parameters is considered respectively,and new control protocols are proposed for the above situations.Based on the given control protocols and the theory of fixed-time stability of dynamic systems,the sufficient conditions for global fixed-time synchronization are derived,and the upper bound of convergence time which is only related to the system parameters but not to the initial conditions of the system is obtained,and the stability of the system is proved.Furthermore,the conclusions of two DDCSs are extended to more complex networked different dimension chaotic systems,and fixed time synchronization is also realized,which is of great significance for the study of neural network systems or complex network systems synchronization.Finally,the effectiveness of the proposed control strategy in different situations is verified by simulation.2.In this paper,the projective synchronization of time-varying matrix with unknown parameters is studied.Considering the known and unknown delays of DDCSs,two kinds of adaptive controllers are designed based on this.At the same time,in order to solve the parameter uncertainty,an adaptive parameter updating law is proposed.Based on the proposed adaptive control strategies,using the fixed-time stability theory and inequality theory,the sufficient conditions for projective synchronization of fixed-time time-varying matrix are derived,and the upper bound of convergence time is obtained,which does not change with the initial value of the system.It is worth noting that the realization of matrix time-varying matrix in matrix projective synchronization is more challenging than that of constant matrix.Finally,two simulation examples are given to verify the correctness of the conclusions.