Estimation Of The Domain Of Attraction Of Discrete-time Cohen-grossberg Neural Networks With Actuator Saturation

In recent years,the researches of artificial neural networks have attracted more attention.Among many neural network models,the development of the Cohen-Grossberg neural networks proposed by Cohen and Grossberg is particularly prominent.Due to their unique characteristics,they are widely used in pattern recognition,computer vision,associative memory,optimization control and other fields.Moreover,the impulse phenomenon is common in many engineering systems.Impulsive control has become an important measure for maintaining system stability,because of its unique advantages of easy implementation and low cost.And also,in practical engineering,actuator saturation is an unavoidable problem.Due to the non-smooth nature of actuator saturation phenomenon,it will not only affect the operating performance of the systems,but also cause the instability of the system.However,the research on impulse input neural networks with actuator saturation is in its infancy.Therefore,it is significant to study such control systems in depth.Of course,due to the highly nonlinear nature of the Cohen-Grossberg neural networks,global stabilization may still not be achieved after the anti-saturation impulsive control is added.Therefore,it is necessary to consider the local asymptotic stability of the systems as well as the global stability of the systems.And when the systems are local asymptotic stability,the domain of attraction of the equilibrium points represents the Cohen-Grossberg neural networks' error correction and optimization capabilities.Therefore,this paper focus on the estimation of the domain of attraction of discrete-time CohenGrossberg neural networks with impulsive input with actuator saturation,including the following:Firstly,the stability and domain of attraction of the discrete-time linear system with impulsive input with actuator saturation are studied.When the original discrete linear system shows a divergence or convergence trend,the system can be globally stabilized by adding the impulse controller with actuator saturation;when the original system can only reach local stability,the system's equilibrium point attraction domain is estimated by means of ellipsoid invariant sets.Secondly,the discrete Cohen-Grossberg neural networks with impulsive input with actuator saturation are studied,the saturation nonlinear term is processed by the convex hull representation method and the Lyapunov function is constructed,and obtained the system global stability criterion.When the system is locally asymptotically stable,the estimates of the domain of attraction are obtained,and the optimization results are attempted to obtain the maximum estimates.