Research On Finite Time And Fixed Time Synchronization Control Of Neural Networks With Time Delay

As is known to all,neural network is a mathematical model that can highly simulate the synaptic connection structure of human brain,and it has been widely used in signal processing,pattern recognition,parallel operation and optimization and other fields,attracting the attention of experts and scholars at home and abroad.Since this century,neural network has been widely used in many aspects.In artificial neural networks,chaotic synchronization of neural networks,as a special chaotic phenomenon,has been widely studied in control science and engineering.The concept of finite time and fixed time is introduced in synchronization because the practical application requires the realization of synchronization as fast as possible.In addition,time delay is widely existed in the transmission of the network,which will destroy the stability of the system and cause oscillation.Therefore,it is of great theoretical significance and practical value to study the finite time synchronization and fixed time synchronization of the neural network with time delay.In the light of the neural network with time-varying delay system,Supported by the stability theory of finite time and fixed time,this paper studies the finite time synchronization problem of neural network by intermittent sliding mode control,and studies the fixed time synchronization problem of neural network by intermittent control and adaptive control.The specific work is as follows:Firstly,the finite time synchronization problem of time-varying delay neural networks under intermittent control is studied.Because the intermittent control can save the control cost and the sliding mode control has the strong robustness,this paper combines the intermittent control and sliding mode control,and designs a non-periodic sliding mode controller.Combined with the finite time theory,the corresponding synchronization criterion and the calculation formula of transition time are obtained.The finite time synchronization of neural network is realized.Simulation results show the effectiveness of the proposed controller.Secondly,the fixed time synchronization problem of time-varying delay neural networks under intermittent control is studied.In previous literature,intermittent control is often used to realize progressive synchronization,exponential synchronization and finite time synchronization.In this paper,the intermittent control is applied to the fixed timesynchronization,and a periodic semi-intermittent controller is designed.Using the fixed time synchronization correlation lemma,the synchronization criterion of the drive response system is derived,the calculation formula of the transition time is given,and the influence of key parameters in the controller on the transition time is analyzed through simulation.Finally,the fixed time synchronization of time-varying delay neural networks under adaptive control is studied.Based on the theory of adaptive control,the delay-dependent adaptive controller was designed and the corresponding adaptive update rate,the suitable Lyapunov function is constructed,based on the fixed time synchronization lemma and the use of relevant mathematical inequality,deduce the calculation formula of transition time,obtained the driver response system of fixed time synchronization criterion.Compared with the general linear state feedback controller,the new controller reduces the transition time by Matlab simulation.