Synchronization Control Of Neural Networks With Piecewise Constant Arguments

In recent ten years,neural networks with piecewise constant argument of generalized type have been widely investigated by many researchers.Distinct from the traditional neural networks,this neural network belongs to hybrid neural network because of the deviating function.That is,in the course of evolution,this neural network is not only advanced but also delayed.Judging from the appearance of this kind of neural network,its deviation function affects the evolution of the whole network,so before analyzing the dynamical characteristics of this neural network,the most important link is to find out the relationship between the deviating argument item and the current term,so as to measure the deviating argument item.And this is the key to solve the problems related to neural networks with piecewise constant argument.This paper is dedicated to discuss the impulsive synchronization,fixed deviation synchronization and finite-time fixed deviation synchronization for generalized type neural networks with piecewise constant argument.By using Lyapunov stability theory and linear approximation method,a sufficient condition for synchronization of two uniform non-directional neural networks under impulsive control is obtained.Moreover,based on fixed deviation stability theory,finite-time control of nonlinear system and matrix inequality theory,by constructing the appropriate Lyapunov function under the discontinuous controller consisting of a linear state feedback term and a symbol function term,theoretical criterion to ensure that two identical nondirectional neural networks achieve fixed deviation synchronization and finite-time fixed deviation synchronization.As a whole,in this paper,impulsive control and discontinuous state feedback control are used to act on neural networks with piecewise constant argument,so that the synchronization of this kind of neural network can be realized.However,there are many ways of synchronization,the use of different control laws will lead to different synchronization results.In addition,there will also be time delay,environment noise and other phenomena in the neural network.Therefore,other control rules may be used to study the synchronization characteristics in relation to generalized type neural networks with piecewise constant argument in the future.