Stability Of Delayed Recurrent Neural Networks With Noise Based On Dynamic Delay Interval Method

In the past few decades,the theory and the application of neural network algo-rithm have become a focus in academia.In the typical neural network model,from input layer to hidden layer and output layer,all layers are connected while the nodes in each layer are not.So there is no information feedback,which leads to a limited applications range.Recurrent neural network is a model that the net can memorize the previous information then apply it into current output calculation.That is to say,in the hidden layer of recurrent neural network nodes are connected,and the input information is composed of the input layer' s output and the last output of itself.Recurrent neural network has abundant dynamic characteristics,which is widely applied in pattern recognition,associative memory,parallel computing,and combinatorial optimization,etc.In order to realize optimal control effectively by the dynamic characteristics of recurrent neural network,it' s vital to determine the stability of the network,which is whether the net,work has and only has an stable equilibrium point.Because the unstable equilibrium point leads to a divergent opti-mization result and multiple equilibrium points lead to a suboptimal result.How to waken the unstable factors in neural network in order to build an optimal recurrent neural network and how to define stability in the network are the primary focus in this research.Of all the unstable factors,the pivotal two are the time delay by the limitation of signal velocity and the random noise from the environment disturbance.In order to investigate the stability of a,recurrent neural network with time delays,first,a new method,which is called the dynamic delayed interval method,is provided to analyze the stability of a recurrent neural network with time-varying delays.Second,considering computational amount,based on convex functional inequality,a criterion about stability of a recurrent neural network with time-varying delays is provided.Third,the stability of a random recurrent neural network with white noise and with generalized noise are analyzed separately.Last,numerical simulations are provided to illustrate the effectiveness of this method and its result.The main contents and contributions are listed as follows:(1)For the stability of a recurrent neural network,the dynamic delayed interval(DDI)method is proposed,whose linear matrix inequality results the can be applied to stability analysis of the multi or additive delayed recurrent neural network.This method reduces the conservatism resulting from the inequality techniques in stability analysis of the multi or additive delayed recurrent neural network.Based on this theory,when the parameters in the dynamic delayed interval get effective optimization,the allowed maximal upper bound of time-varying delay will be significantly enlarged and the conservatism of stable condition will be significantly reduced.At the same time,the optimization of parameters in the dynamic delayed interval method is provided.(2)Based on DDI,the stability of neural network with time-varying delays can be studied,and an optimal result of stability criterion can be obtained.The original Lyapunov function for analyzing systems with multiple time-delays is improved to a Lyapunov function with a flexible range of integration.Then according to this improved Lyapunov function,stability of concerned systems with multiple time varying delays can be analyzed,and the corresponding theorem can be concluded.(3)For the global asymptotic stability of systems with multiple time varying de-lays is discussed,taken Cohen-Grossbcrg neural network as an example,con-sidering the calculation amount of the method which is based on the number of free weight in a matrix,a stability analysis based on the generalized convex matrix inequality is provided.First,the mathematical induction is used to prove the generalized convex matrix inequality.Then,based on this convex matrix inequality,a criterion in the form of linear matrix inequality is provided for stability of the recurrent neural network with multiple time varying delays.(4)For the stochastic neural network with time delays under white noise,a method that judging stability of a stochastic neural network with time delays based on white noise model is provided,in which Brownian movement and parame-ter uncertainty are described as the uncertainty of neural network.Based on DDI,an improved Lyapunov function is proposed and then the value of the function with the derivation of system can be analyzed.Based on general-ized Finsler theorem,an improved criterion judging stability of the stochastic neural network with time delays is proposed.(5)For the random recurrent neural network with time delays under nonwhite noise,a stability analysis modeling by generalized noise is provided.A new kind of noise(generalized noise)is proposed and modeled,and then the stabil-ity characteristics of neural network with nonwhite noise is discussed.First,the existence and uniqueness of equilibrium point in random recurrent neural network with generalized noise is proved.Second,based on the provided lem-ma about random stability,the stability criterion of recurrent neural network in the form of LMI can be derived.Last,the conservatism of stability analysis in a random neural network is discussed.