Analysis And Control Of Complex-valued Stochastic Neural Network Systems With Time-varying Delays

It is well known that stochastic control system is widely used in the fields of economic system,network communication system and biological system.As the most important branch of modern artificial intelligence,neural network system has always been an important object studied by scholars.At present,a lot of achievements have been made in the research of deterministic neural network system in stability,dissipativity,synchronization and so on.However,most of the existing literature on neural networks focuses on the case of real-valued deterministic systems.In fact,because many industrial production projects involve complex variable signals,the state variables of the controlled system are extended from the real-valued domain to the complex-valued domain.At the same time,it is inevitable that the neural network system will be disturbed by various factors from the outside of the system,that is,adding the stochastic interference term to the system model can more accurately describe the actual situation of the system operation.Therefore,when the model of the actual system is established,the stochastic neural network system with the levy interference term is generally considered.This paper studies the dissipativity,Lagrange exponential stability and synchronization of complex-valued stochastic neural network systems with time-varying delay,the main works of this paper is as follows:1.The dissipativity of the complex-valued stochastic neural network systems driven by Brownian motion process is studied.By constructing Lyapunov function,applying Jensen inequality and stochastic analysis technique and linear matrix inequality method,several sufficient conditions of exponential dissipativity and(Q,S,R)-dissipativity of complex-valued stochastic neural network systems are obtained in the mean square sense.The validity and advancement of the results is illustrated by simulation results.2.The Lagrange expnential stability of complex-valued stochastic inertial neural network system driven by Brownian motion process is studied.The second order neural network system with inertial term is reduced to the first order differential form of the general neural network systems by replacing the intermediate variables.With the help of appropriate Lyapunov functions,Jensen inequalities,stochastic analysis techniques and LMI methods,several discriminant theorems for exponential stability of complex-valued stochastic inertial neural network systems in the mean square sense are obtained.The validity and advancement of the results are explained by simulation results.3.The synchronization control of complex-valued stochastic neural network systems driven by Brownian motion is studied.The Brownian motion process is used to describe the stochastic interference of the master and slave systems.By constructing appropriate Lyapunov function and controller,applying stochastic analysis technique and linear matrix inequality method,several sufficient conditions for the synchronization control of complex-valued stochastic neural network system are obtained.The validity and advancement of the results is demonstrated by simulation results.4.The synchronization control of complex-valued stochastic neural network systems driven by Brownian motion and Poisson jump composite process is studied.The stochastic interference which master system and slave system suffered are described by the Ito-levy type stochastic process.By constructing appropriate Lyapunov function and controller,applying Jensen inequality and stochastic analysis technique,and linear matrix inequality method,several sufficient conditions for the synchronization of complex-valued stochastic neural network system are obtained in the mean square sense.And the validity of the results is demonstrated by simulation results.