Research On Stability And Synchronization Control For Neural Networks With Time-varying Delays

Delayed neural networks are important component of delayed systems,which have very abundant dynamic behaviors.In recent years,much attention on the dynamic behaviors of neural networks has been paid due to their extensive applications in signal and image processing,associative memories,pattern recognition,combinatorial optimization,automatic control and other areas.However,the existence of time delay cannot be ignored for the dynamic behaviors of neural networks,which may lead to oscillation,instability and even chaotic phenomenon.Therefore,the stability analysis and synchronization control of delayed neural networks have become two active topics of research.Many less conservative delaydependent stability criteria and synchronization control methods have been developed,but there is room for further investigation and improvement,for example,in the stability criteria,the matrices have high dimension and large computational burden;in the synchronization control methods,the obtained control gains may be too big to implement physically.This dissertation investigates the stability criteria and synchronization control for neural networks with time-varying delays,which not only improves the existing stability criteria but also develops the synchronization control methods.The main research results of this paper are as follows:(1)Stability criteria of neural networks with zero lower bound of time-varying delaysFor the stability analysis of neural networks with time-varying delays,some drawbacks existed in the study of using the information of delay neuron state derivative as a state vector set are pointed out,namely,the delay integral is shifted,and the dimension and computational burden of the matrices in the stability criteria are increased.A delay-dependent stability analysis method based on improved augmented Lyapunov-Krasovskii functional(LKF)is proposed.In the estimation of the derivative of the LKF,the information of delay neuron state derivative is disappeared such that the established delay-dependent stability criteria have less conservatism and lower computational burden.(2)Stability criterion of neural networks with nonzero lower bound of time-varying delaysFor the stability analysis of generalized neural networks with time-varying delays,the cases that the lower bound of time-varying delay is nonzero and the the lower bound of delay derivative is known are fully considered,new augmented LKF is constructed by employing the information on lower bounds of time-varying delays and neuron activation functions,a delay-dependent stability analysis method that depends on the new augmented LKF is derived.Based on the reciprocally convex combination inequality and bounded conditions on the slopeof neuron activation functions,the established delay-dependent stability criterion has much less conservatism and relatively low computational burden.(3)Finite-time synchronization of neural networks with time-varying delays based on a sliding mode control methodFor the finite-time synchronization problem of neural networks with time-varying delays,based on the drive-response concept and sliding mode control theory,the synchronization error is directly defined as a sliding manifold,a sliding mode control method is derived,which,compared with the existing linear state or delayed state feedback control methods,has the following advantages: there is no need to solve the unknown feedback control gain;the finite-time synchronization of delayed neural networks is guaranteed,and the synchronization time is shot.(4)Finite-time synchronization of neural networks with time-varying delays based on an integral sliding mode control methodFor the finite-time synchronization problem of neural networks with time-varying delays,some problems existed in the study of using integral sliding mode control method are pointed out,an integral sliding mode control method is proposed,which,compared with the existing integral sliding mode control methods,has the following advantages: the integral sliding manifold has simpler structure;there is no need to solve the unknown state feedback control gain matrix;the finite-time synchronization of delayed neural networks is guaranteed.(5)Adaptive synchronization of neural networks with time-varying delays based on an adaptive sliding mode control methodFor the adaptive synchronization problem of neural networks with time-varying delays,the case that the external constant input vectors of drive system and response system are mismatched is considered,an integral sliding manifold is constructed by employing the synchronization error,a suitable adaptive sliding mode controller and corresponding adaptive law are designed,an adaptive sliding mode control method is proposed,which can eliminate the affect caused by mismatched external constant input vectors.