Study Of Finite Time Chaotic Synchronization For Fractional-Order Nonlinear Systems With Different Structures

Fractional order calculus as a fractional calculus on the order of any promotion,in recent years,increasingly perfect theory,application development,have emerged in the physical,chemical,biological,engineering,and many other practical system model.At the same time,chaos control and synchronization are two important methods in the practical application of chaos.Because of its potential application in secure communication and control processing,the synchronization of fractional-order chaotic systems has attracted wide attention from scholars.But most of the research on fractional order chaotic systems synchronization are research on infinite time domain,and with the deepening of the research on chaotic synchronization rate had the higher request,it enables the system to fractional order in finite time convergence is in limited time synchronization problems are becoming more and more meaningful,and chaotic synchronization in the practical application has been from a single system of synchronous gradually evolved into the different structure of the system synchronization,so for the finite time synchronization of fractional order different structure research is more meaningful.In this paper,combining with fractional calculus theory,the finite time stability theory of fractional order,sliding mode control theory and Lyapunov stability theory are used to study the finite time synchronization of fractional order chaotic systems with different structures.The main research contents are as follows:1.To analyze fractional order finite time stability theorem and its proof process is simplified,by simplified theory using nonlinear control design in view of the same dimension different structure and different dimension of two kinds of different structure of the finite time projection of synchronous controller.And through the example simulation verify the rationality and the effectiveness of the controller is simplified,and compared with the projective synchronization controller response finite time projective synchronization controller can effectively improve the synchronous speed.2.Considering that the uncertainties and external disturbances will affect the stability of the system under the actual situation,a new sliding mode surface is designed by combining the robustness of sliding mode control with fractional calculus and fractional order finite time stability theory,and the traditional terminal sliding mode controller is improved.The finite-time chaotic projective synchronization of the fractional-order chaotic systems of the same dimension and different structures with uncertainties and external disturbances and thefinite-time chaotic projective synchronization of the chaotic systems with different dimensions and different structures are realized.3.The theory of fractional-order finite time stability is introduced into the problem of external synchronization between two fractional-order complex networks with different topologies and dynamic nodes.Based on the fractional order finite time stability theory,combined with nonlinear control and two-way coupling method are designed in view of the different structure with the same topological structure between the network limited time synchronization and different structure with different topology network limited time synchronization between the two cases of a universal controller,the final realization of fractional order based on the thought of tracking control of brushless dc motor(BLDCM)chaos suppression problem.