Finite-Time Synchronous Control Of Stochastic Memristive Neural Networks

Memristor is a new type of passive device.For its unique characteristics similar to biological synapses,it can be used to simulate synapses in constructing large-scale neural network called memristive neural networks;On the other hand,stochastic perturbations and time-delay exist widely in real networks,and the system's finite-time synchronization has the best convergence time,better robustness and anti-jamming capability.Therefore,this paper will focus on stochastic memristive neural networks to study the finite-time synchronization and fixed-time synchronization.The main results are as follows:First,the finite-time anti-synchronization of stochastic time-delay memristive neural networks under the switching control method is studied.By constructing an appropriate Lyapunov function and designing a switching controller,Based on the weak infinitesimal operator,differential inclusion theory,stochastic Layapunov stability theory,and the matrix inequality analysis method,the sufficient criterion corresponding the finite-time synchronization of stochastic time-delayed memristive neural network is obtained with designing a switching controller.Compared with the traditional control method,it is found that using the switching control method has a shorter anti-synchronization convergence time.Secondly,the finite-time synchronization of time-delay memristor-based neural networks with parameter uncertainty and noise interference is studied under the given adaptive control law.By constructing a Lyapunov function and applying the finite time adaptive control principle,the adaptive update rate of uncertain parameters is obtained,and the corresponding controller design law is given,which ensures that the neural network can achieve synchronization within a limited time.It is found that the designed adaptive controller can effectively overcome the damage caused by the interference to the system synchronization.Finally,the fixed-time anti-synchronization of stochastic memristive neural networks with mixed delays is studied.Using a polynomial feedback control strategy,the sufficient criterion for realizing the anti-synchronization of fixed time is presented by using strict infinite mathematic operator,differential inclusion theory,stochastic Layapunov stability theory and other rigorous mathematical methods.Meanwhile,the upper bound of convergence time of anti-synchronization is also given.This control method solves the problem that the anti-synchronization convergence time of stochastic mixed delay neural network is affected by the initial state.