Impulsive Control Of Multi-Weighted Coupled Neural Network Dynamics

In recent years,coupled neural networks have attracted great attention of many researchers from different fields since they have been widely used in pattern recognition,signal processing,artificial intelligence,secure communications,robotics and other fields.As we all know,these applications rely heavily on some dynamical behaviors of coupled neural networks,particularly,the synchronization and passivity.In many existing literatures,neural networks achieve synchronization and passivity over the infinite time interval.In real life,since the life spans of machines and humans are limited,neural networks are expected to realize synchronization and passivity over a finite-time interval.In many existing results about the dynamical behaviors of coupled neural networks,the topology of networks is often single weighted.However,many networks in the real world should be described by multi-weighted networks.Therefore,it is of practical significance to investigate the dynamical behaviors of multi-weighted coupled neural networks.Neural networks are implemented by circuits,and the diffusion phenomenon of electrons in the non-uniform electromagnetic field is unavoidable.Then the dynamical behaviors of multi-weighted coupled neural networks with reaction-diffusion terms should also be discussed.Generally,it is difficult for coupled neural networks to achieve synchronization and passivity only by themselves,but such networks can obtain synchronization and passivity by using some control schemes.Compared with continuous control law,impulsive control reduces the amount of information transmitted and reduces the control cost.Thus,this dissertation considers the synchronization,passivity,finite-time synchronization,and finite-time passivity of multi-weighted coupled neural networks with and without reaction–diffusion terms under impulsive control,respectively.The main contributions are as follows:1 In Chapter Two,a class of neural networks with multiple state couplings and a class of neural networks with multiple time-delayed state couplings are proposed.Using Schur complement and designing suitable impulsive controller,the passivity,input strict passivity and output strict passivity of these two network models are studied,respectively.With the help of impulsive differential inequality and Lyapunov functionals,sufficient conditions to ensure the global exponential synchronization of the two network models are obtained.Finally,two numerical simulations verify the correctness of the theoretical results in this Chapter.2 In the third Chapter,a kind of multi-weighted coupled neural networks with and without uncertain parameters is proposed.By applying integration method,a finite-time boundedness criterion for such a network is established.Then,based on the impulsive control scheme,the finite-time passivity of multi-weighted coupled neural networks is discussed for the first time.In light of the Lyapunov functional method,this study is the first to obtain finite-time synchronization of the proposed network model via impulsive control.In addition,the uncertainty of the rate matrix and the weight matrix is also considered in the multi-weighted coupled neural networks.Sufficient conditions for ensuring the robust finite-time boundedness,robust finite-time passivity,and robust finite-time synchronization for such a network model are derived.3 Chapter Four presents a class of multi-weighted coupled reaction-diffusion neural network models with different dimensions of input and output.With the help of Wirtinger’s inequality,Schur complement,and integration method,the passivity,input strict passivity,and output strict passivity of such a network model under impulsive control are researched for the first time.Based on the impulsive control law,this Chapter also focuses on the synchronization of the proposed network model for the first time.Finally,the validity of the theoretical results is verified by two numerical simulations.4 A kind of neural networks with uncertain inner coupling matrices,multiple timedelayed state couplings,and reaction-diffusion terms is considered in the fifth Chapter.Applying Jensen’s inequality and Wirtinger’s inequality,a robust finite-time boundedness criterion for multi-weighted uncertain coupled reaction-diffusion neural networks is established.An impulsive controller is developed to obtain the robust finite-time passivity for the given network model.By utilizing Schur complement,this Chapter is the first to present a robust finite time synchronization criterion of such a network via impulsive control.