Fixed Time Synchronization Of Chaotic Systems

In this thesis,we mainly consider the fixed-time control and synchronization of chaotic systems.It is well known that finite time synchronization of chaotic systems has more practical value than asymptotic synchronization.Fixed time synchronization is a special finite time synchronization.The convergence time is limited and independent of initial value condition,which overcomes the shartcoming that the convergence time of general finite time synchronization is related to the initial values.Compared with finite time synchronization,fixed time synchronization is more convenient and has more widespread application in practice.So it is of great theoretical and practical significance to study the fixed time synchronization of chaotic systems.This thesis firstly discusses the problem of fixed time synchronization of a class of order integer chaotic system,a new fixed time stability theory and a new saturation controller are proposed.The numerical simulation verifies the effectiveness and feasibility of the given method.Secondly,based on the unique advantages of the fractional derivative,in order to make the studied system more consistent with the actual situation,we discuss the fixed time synchronization of the fractional multi-layer chaotic network.A new fractional order fixed time stability theorem and some sufficient conditions of synchronization are proposed.This thesis has four chapters and the structure arrangement is as follows:In the first chapter,the relevant knowledge of chaology is introduced,such as the definition of chaos,the control and synchronization theory of chaotic system,the research status and significance.In the second chapter,the fixed time synchronization for a class of integer order chaotic systems under input saturation is considered.The saturation controllers is designed by using the backstepping control method and sufficient conditions for synchronization based on the Lyapunov stability theory.The numerical simulations verify the feasibility and effectiveness of the given method.Chapter 3 considers the fixed-time synchronization problem of fractional order multilayer chaotic networks.A new fractional order fixed time stability theorem is presented.Based on the proposed new fixed time stability theorem a new criterion to guarantee the fixed time synchronization of fractional order multilayer networks is given.The numerical simulations verify the correctness and feasibility of the given method.Chapter 4 reviews and summarizes the full paper in addition the research direction of future work is discussed.