Synchronization And Control For Memristive Neural Networks

The research on memristor has been increasing when the first real memristor device was confirmed by the researchers of Hewlett-Packard in 2008.Because of the superior performances,such as nanoscale,low energy dissipation,large storage capacity,strong fault tolerance and memory ability,the memristor is a perfect candidate for synapses in the circuit implementation of neural networks.Artificial neural network is a mathematical model that simulates the processing mechanism of complex information in human brain.It has a wide application prospect in signal processing,optimal combination,pattern recognition and other fields.In addition,artificial intelligence is achieved via the in-depth learning of neural networks,which is one of reasons why neural networks have attracted much attention.Synchronization is applied to many fields,such as image encryption and secure communication.The structure of memristive neural network is more complex due to its multi-valued and nonlinear properties.It is easy to produce complex dynamical behaviors such as chaos,which can improve the security performance of secure communication.In this paper,we adopt some theoretical tools,such as differential inclusion,nonsmooth analysis,Lyapunov stability theory,graph theory,and combine some inequality techniques,such as Gronwall inequality,geometric inequality,Halanay inequality,to analyse the synchronization problems of several kinds of memristive neural networks.This paper consists of four chapters.The details are as follows:In Chapter 1,the development backgrounds of neural network,synchronization and memristor are briefly described.At the same time,the writing motivation and research significance of this paper are also revealed.In Chapter 2,some required theoretical results are provided,such as Filippov solution,generalized directional derivative,generalized gradient,Laplace matrix.In Chapter 3,the global exponential synchronization problems of memristive inertial neural network,memristive competitive neural network and T-S fuzzy memristive neural network are studied.In the study of memristive inertial neural network,an appropriate variable substitution is introduced to transform the delayed inertial memristiv neural network into the first order differential equations.Then,by designing a nonlinear controller with sign function term,based on generalized Lyapunov method and some inequality techniques,sufficient conditions for global exponential synchronization in algebraic form and matrix form are obtained,respectively.In the study of memristive competitive neural network,some delay-dependent and delay-independent synchronization criteria are obtained under a new controller,respectively.In the study of T-S fuzzy memristive neural network,the finite-time synchronization for T-S fuzzy memristive neural networks is considered under a proper fuzzy controller.In Chapter 4,the synchronization problem of the coupled memristive neural networks is analysed.First,a variable substitution is introduced to reduce the order of the coupled memristive inertial neural network.Then,based on generalized Lyapunov method,graph theory and inequality technique,the coupling structure characteristics and synchronization criteria are obtained.Finally,the finite-time synchronization and fixed-time synchronization of coupled memristive neural networks are studied under a unified control framework,respectively.Meanwhile,the settling time is accurately estimated.In this chapter,our discussion is leaderless synchronization,which is different from leader-follower synchronization in previous studies.