Synchronization Research Of Neural Networks With Parameter Uncertainty

As a special class of dynamic systems,neural dynamical system can mimic neuro-biological architectures to some extent.It is widely used in biology,physics and economics.Since there are always unavoidable uncertainty in the model in real problems and could have some negative affect to the system,it is of great practical importance to study the synchronization of neural networks with uncertainty.In this article,several kinds of synchronization of neural networks with parameter uncertainties are studied.By using the method of fractional delay Mittag-Leffler function,comparison principle and matrix inequality technique,combined with the concrete neural network,the characteristics of the neural network with parameter uncertainty are analyzed,then the synchronization criterion of several kinds of neural networks is obtained.The article’s main contents include:The multiple quasi-synchronization problem for a class of fractional-order coupled neural networks with time delays and parameter uncertainty is discussed.In order to realize the multiple quasi-synchronization,a new pulse controller is established by using the check pulse control strategy.Using comparative principles and mathematical analysis,some criteria for multiple quasi-synchronization are established.The problem of lag synchronization for a class of neural networks with unmeasurable states and parameter uncertainties is investigated,due to the existence of parameter uncertainties and external environmental disturbances in the network,the information of some network states may be unmeasurable,based on this,it is necessary to design an appropriate impulse controller,and then discuss the problem of lag synchronization of the network.By using the transfer matrix method and linear matrix inequality technique,some sufficient conditions for the system to achieve lag synchronization are obtained.In addition,the number of measurable states under different conditions is analyzed,which shows that the results obtained are more general.The exponential synchronization problem of a class of delayed neural networks with parameter uncertainties and coupling delays is studied.Based on the quadratic Lyapunov function,a new event-triggered delayed impulsive control strategy is proposed.By using impulsive control theory and Lyapunov-Razumikhin technique,some less conservative sufficient conditions are given based on linear matrix inequalities,which show that the designed event-triggered delayed impulsive control can achieve exponential synchronization of the system and eliminate Zeno phenomenon.