Sliding Mode Control Research Of Fractional-order Complex Chaotic Systems On Complex Networks

Control and synchronization in nonlinear systems is a hot topic in dynamic behavior research in recent years.For two nonlinear systems that are doing chaotic motion,how to synchronize them is a very meaningful work.On the other hand,with the continuous development of fractional differentials and the deep exploration of differential theory,more research shows that fractional differentials can more effectively describe the physical phenomena and dynamic behaviors in the real world.Therefore,how to synchronize the fractional-order nonlinear systems that do chaotic motion is undoubtedly worth studying.However,in practical applications,system uncertainty and external disturbances are inevitable,and this factor makes the ideal model unable to accurately describe the actual system.How to effectively estimate the model of an unknown system is also very interesting and very meaningful work.Based on the above background,this paper first summarizes the chaotic system and complex networks,including the origin,research status and classical methods of chaos control and synchronization research.Then,a brief description of the existing results of the fractional complex chaotic system is given.Then an effective solution is proposed to reduce the chattering of the independent fractional complex chaotic systems.An active sliding mode controller with fractional sliding surface is designed to complete synchronization between two fractional-order complex chaotic systems.Furthermore,an effective solution to how to better estimate the unknown nonlinear part of the system is proposed,and the mode synchronization of the fractional-order complex chaotic system is realized.This article will study from the following two aspects:1.Based on active control and sliding mode control,the control and synchronization of fractional complex chaotic systems are studied.In the paper,two main problems to be solved are considered in the study of the synchronization process of fractional complex chaotic systems.First,considering that in the real world,chaotic systems will have uncertain parts and external environmental disturbances.Second,how to design an effective sliding mode controller,the most important work is how to effectively combine the active control idea and sliding mode control,design a dynamic sliding mode controller with a novel fractional sliding surface,and finally complete Synchronization between two fractional complex chaotic systems.Finally,a series of theoretical proofs and simulation experiments were carried out to verify the reliability and feasibility of the designed controller.2.Combining RBF neural network and sliding mode control,the control and synchronization in module space and phase space(module-phase synchronization)of fractional-order complex chaotic systems are studied.In this paper,we mainly analyze and study the problem from two aspects.First,how to use the RBF neural network to approximate the unknown nonlinear function in the fractional-order chaotic system;Second,how to control the sliding mode effectively combined with the RBF neural network,a neural sliding mode controller is designed,which finally realizes the synchronization in module space and phase space of the fractional-order complex chaotic system(module-phase synchronization).And the corresponding theoretical verification and experimental analysis were carried out.