Dynamics Analysis Of Memristive Neural Networks And Its Applications

The researches about memristor and memristor-based neural networks have generated world wide interest since the successful development of TiO2-based memristor device by re-searchers of Hewlett-Packard company in 2008,especially for the memristive neural networks that build on the basis of VLSI circuit.In addition,considering its high storage,small size and non-volatile properties,which has shown wide applications.This paper considers the dynamic behaviors of memrisitve neural networks and then discusses its application in traffic network-s.The paper is divided into seven main chapters.The second chapter discusses the passive analysis of memrisitve neural network with probability time-varying delays.The third chapter considers the quasi-synchronization and synchronization control of memristive neural networks.In the fourth chapter,the finite-time and fixed-time stabilization control of memristive neural networks are studied.The fifth chapter analysis the state estimation of the memristor-based neural networks.The sixth chapter is the global robust exponential stability analysis of the discrete time neural network as well as the highway traffic system.The detaild conclusions are as follows:The second chapter studies the passivity analysis of memristive neural networks with prob-abilistic time-varying delays,by means of some reasonable hypothesis,the Lyapiunov function as well as linear matrix inequality(LMI)techniques,the corresponding sufficient condition-s that ensure the memristive neural network is passive is given.In which,considering the network of each weights are switching between two different constant values,therefore,the combination number of the possible form of the connection weight is 22n2.This approach fully consider the characteristics of each connection weights,which makes the conclusions derived in this chapter is more general.In addition,the derived criteria contain more variables,which have more flexibility and superiority.The third chapter considers the quasi-synchronization and synchronization control of memristive neural network.First,by means of a proper control strategy as well as the matrix measure method.The algebraic criterion to ensure the quasi-synchronization of the target model is given.Then,on the basis of the discontinuous control law,and a suitable Lyapunov function,sufficient conditions are presented to guarantee the drive-response system reach syn-chronization goal.What is different from the second chapter is that the robust analysis method is employed to tackle with the target model,i.e.,by introducing some measurable functions,the target model can be seen as a robust systems with uncertain parameters,and the this techniques can be used to deal with the corresponding dynamic behavior of the memristive neural networks,which also bring the new breakthrough to this kinds of system.In the fourth chapter,by means of the Lyapunov function method and the discontinuous control technique,the corresponding finite-time and fixed-time stabilization control strategy for delayed memristive neural networks were provided.It is worth noting that,the settling time of the finite-time stabilization heavily limited by the initial conditions of a system,which may constraint its widespread application,to overcome this shortcomings and make comparison with the fixed-time stabilization control method,the corresponding fixed-time stabilization criterion will be presented in the form of algebraic inequalities.Moreover,to guarantee a fast response,it is often reacquire the trajectories of the network states converge to some equilibrium point during a time interval,thus the upper bound of the settling time for stabilization is estimated.The fifth chapter analysis the state estimation of the memristive neural networks.By endowing the Lyapunov function,matrix analysis technique and a proper non-fragile state estimator,sufficient criteria for the stability findings are furnished.It is worth noting that,the state estimation of the continuous time system is first studied and then extended the derived conclusions to the discrete time case,which makes the results of this chapter be a continuation of the existing conclusions.The six chapter consider the sufficient conditions for the global robust exponential stability of the uncertain discrete-time system,and then the derived criterion is extended to freeway traffic system,which can be seen as a special case of uncertain discrete-time systeum.In the freeway traffic system,via the traffic flow of each cells and the definition of the uncongested equilibrium point,the corresponding conclusions are also reached,which can ensure the freeway system operating at an uncongested equilibrium state,achieving the goal of global robust exponential stability.These criteria are deeply reveal the dynamical mechanism of the discrete time neural networks as well as the freeway traffic systems.