Stability And Synchronization Control For Delayed Discrete-time Recurrent Neural Networks

Over the past few decades,a lot of effort has been devoted to artificial neural networks owing to their wide applications in a variety of areas,such as pattern recognition,signal processing,associative memory,static image processing and combinatorial optimization.It is well known that stability of neural networks is a premise for above-mentioned engineering applications,while time delays,parameter uncertainties and stochastic disturbance are three main sources of neural networks' instability.The finite speed of information processing as well as parameter fluctuations of electronic components used in the large-scale integrated electronic circuits will lead to time-delays and parameter perturbation.In addition,stochastic disturbance is ubiquitous.Therefore,the stability analysis problem for stochastic neural networks with time delays and uncertainties is very significant.Over the last decade,the master-slave synchronization problem of neural networks with time delays has been well studied due to its potential applications in chemistry,biology,cryptogra-phy and secret communication.Up to now,many methods have been proposed to achieve the master-slave synchronization of neural networks with time delays,such as fuzzy control,impul-sive control,adaptive control,time-delay feedback control,sampled-data control and so on.The majority of the existing literatures have been concerned with models of master-slave system for continuous-time neural networks.In implementing and applications of neural networks,synchro-nization problem of discrete-time neural networks is more practical and significant owing to the extensive use of computer in today's digital era.This paper focuses on stability and synchronization control for discrete-time recurrent neural networks with time-varying delays.Time-delay feedback design method is adopted in design of synchronization controllerThe research results and innovations are summarised as follows:(1)Considering stochastic discrete-time recurrent neural networks with time-varying delay,a new Lyapunov-Krasovskii function is established to derive sufficient condition for asymptotical stability in mean square of the recurrent neural networks with stochastic disturbance by using lin-ear matrix inequality(LMI)and discrete Jensen inequality.As an extension,we further considered the stability analysis problem for the same neural networks with uncertainty.It is shown that the obtained result is less conservative than the existing ones when the described system is without dis-turbance and uncertainty.Meanwhile,the computational complexity is reduced since less variables are involved.(2)Considering discrete-time delayed recurrent neural networks with restricted disturbance and missing data,the problem of controller design is investigated to achieve synchronization of master-slave system.Compared with other literatures,this paper takes the constraints of distur-bance in error system model into account.The unreliable communication links between the neural networks,which are modeled as stochastic dropouts satisfying the Bernoulli distributions,are tak-en into account.By applying the Lyapunov-Krasovskii function,a sufficient condition is given in the form of linear matrix inequalities to achieve asymptotical stability of master-slave system's error.The error of master-slave system reached asymptotical stability in mean-square,and the master-slave system reached synchronization.The design method and result are also extended to the same master-slave system with model uncertainties.(3)Considering discrete-time recurrent neural networks with time-varying delay,the con-troller design problem for master-slave system synchronization is studied.During the course of design,we took the nonlinearity of controller into account,which is closer to practical application.The method is extended to the same master-slave system with model uncertainties.(4)Considering the master-slave system in Chapter 3,the design method of controller is im-proved.In Chapter 3,when ?(k)=0,then u(k)=0,which may result in the intense fluctuation of u(k)in some cases.In this Chapter,a feedback controller is designed based on a reuse mechanism,which avoids the fluctuation of the controller compared with the existing literature to ensure that the master-slave system with uncertainty is asymptotically synchronized in mean square.Genetic Algorithm(GA)algorithm is used to obtain the controller.