Research On Synchronization And Control Of Memristive Systems

Memristor was proposed for the first time by the Chinese professor Leon Chua who is a circuit theory expert.It was postulated as the missing fourth passive circuit element by Chua,which is associated with electricity and magnetic flux.Nearly forty years since it was put forward,there had been almost no breakthrough on the researches of the memristor.Not until 2008,did HP labs produce the first memristor device.Then memristor has attracted the attentions of many researchers,and has quickly become one of the most popular research interests in the field of automation and other related areas.Memristor has a distinctive memory function to the current or both ends of the voltage,as a result,the prospect of its application is very extensive in many areas,such as secure communication,memory,artificial intelligence computer.As per the existing literature,researches on memristor have mainly focused on two areas:(1)to investigate how to utilize the most cost-effective material to produce a device with characteristics of memristor in accordance with the research ideas of HP laboratory;(2)to study the dynamic behaviors of memristor-based systems and their applications according to Professor Chua's ideas.This dissertation continues to further investigate the dynamic behaviors and the applications of the memristive systems according to the ideas of Chua,including the synchronization and control of the memristive systems.The research objects involve the memristor-based neural networks,the memristor-based chaotic systems and so on reported in a flood of literature.The author considers combining memristive system and stochastic system,such as using an intermittent random perturbation to stabilize a memristor-based chaotic system,and combining memristor-based system and discontinuous system theory to further investigate dynamic properties of memristive system.Some basic tools in the theory of dynamical systems are utilized in the dissertation,such as Lyapunov stability theory,Hanalay inequality,impulsive theory and the modern control theory and method,as well as common methods in stochastic system theory,such as stochastic Lyapunov stability theories etc.Through the researches on the above problems and methods,the basic theoretical structure of the synchronization and control of the memristive system is established,and the progress of the research on the theory and application of the memristor is obtained.The main contributions of this dissertation are described as follows:1.The background,research significance and status of memristor are introduced,and then the research progresses of the memristive neural networks and the memristive chaotic systems are emphatically elaborated.Finally,the relevant theories and methods are introduced.2.A new type of double-compound synchronization,which is based on combinationcombination synchronization and compound synchronization of four chaotic systems,is investigated for six memristor-based Lorenz systems.By using Lyapunov stability theory and state feedback control control,some sufficient conditions are attained to ensure our conclusions hold.The corresponding theoretical proofs and numerical simulations are supplied to verify the effectiveness and feasibility of our synchronization design.Due to the complexity of our synchronization,it will be more secure to transmit and receive signals in application of communication.3.It is investigated that the problem of hybrid control of stochastic chaotic system based on memristive Lorenz system with discrete and distributed time-varying delays.First of all,the stochastic switched chaotic system is proposed based on Lorenz system modeled by piecewise linear memristor.Then,a novel hybrid controller is designed and the criteria are established to guarantee that the trivial solution of the corresponding stochastic system is exponentially stable in mean square.Furthermore,a novel technique is proposed to handle the problem of the difference,which can not be depicted directly by stochastic Newton-Leibniz formula,between two state values of different instants between which there may exist impulse instants.Finally,an example is given to illustrate the efficiency and feasibility of the presented method.4.The stabilization and destabilization of a given nonlinear system by an intermittent Brownian noise perturbation is considered.We give some novel criteria and get some new conclusions on stability and instability,which are relevant to the control period T and the noise width ?.These results are then exploited to examine stabilization and destabilization via intermittent stochastic perturbation and applied to the stabilization of a memristor-based chaotic system.Two numerical examples are presented to illustrate the theoretical results.5.The problem of exponential synchronization of stochastic time-delayed memristorbased neural networks via distributed impulsive control is studied.Based on the characteristics of memristor,the corresponding drive stochastic memristor-based neural networks and response stochastic memristor-based neural networks with distributed impulsive control input are established.Then the synchronization error system is obtained by using the concept of synchronization and stochastic differential inclusion theory.Through the generalized impulsive delay differential inequality technique,the criteria to guarantee that the error system is exponentially mean square stable,namely the drive system and the response system achieve the exponential synchronization are obtained.At last,the numerical simulation verify the effectiveness of the obtained theoretical results.Finally,the works of this dissertation are summarized,and the following research topics are forecasted.