Synchronization Of Cohen-Grossberg Neural Networks With Time-varying Delays Via Saturated Impulsive Controller

Due to its benefits of lower control costs,increased control effectiveness,increased robustness,and ease of implementation in reality,impulsive control has been extensively applied in various fields such as engineering control and scientific technology.Examples include instantaneous switching in aerospace controllers,start-stop of vehicle ignition devices,periodic extermination of pests,heartbeats and blood circulation in living organisms.Meanwhile,in many areas of engineering practice and modern science,such as the swinging of a power arm and the motion control of robots,the motion trajectory is constrained by specific structures,spatial,energy,or other physical factors,thus affecting the entire motion process of the system.Therefore,to eliminate or reduce the impact of constraints,the design of system controllers should take into account the constraint conditions reasonably.Considering the prevalence of actuator saturation in impulsive control,this paper designs an impulsive controller that combines the characteristics of state saturation and investigates the related nonlinear systems,such as Cohen-Grossberg neural networks,using convex combination methods,Lyapunov stability theory,and impulsive control theory.The main research content and results are as follows:(1)The finite-time stability of nonlinear time-varying systems with saturated impulse input is investigated.Firstly,the proper mathematical model for this kind of system is built,and the saturation term in impulsive control is expressed as a series of convex combinations with feedback using the convex combination analysis method.Combining impulsive control and other relevant theories,the paper proposes sufficient conditions for achieving finite-time stability of the system.Secondly,based on this,sufficient conditions for finite-time contractive stability of the system are further obtained.In addition,the conclusions obtained are extended to the finite-time quasi-synchronization problem of chaotic neural networks,and the corresponding conditional results are obtained.Finally,the validity and feasibility of the conclusions are verified through simulation examples.(2)The synchronization issue of a class of time-varying-delay Cohen-Grossberg neural networks under saturated impulsive control is studied.Firstly,by constructing a novel Lyapunov-Krasovskii functional with a delay-dependent polynomial form,the saturation term in impulsive control is expanded into a convex combination,and the sufficient conditions for achieving synchronicity of the system are obtained by comprehensively applying impulsive control and other related theories.At the same time,an estimate of the attraction domain of the synchronization error system is also provided.Moreover,the synchronization problem of time-varying-delay Cohen-Grossberg neural networks with partial actuator saturation under impulsive control is further explored,as well as the synchronization problem of Hopfield neural networks under saturated impulsive control when the Cohen-Grossberg neural networks are simplified.Through these two derived conclusions,the synchronization problem of delay neural networks with saturated impulsive control is further investigated.Additionally,inspired by the saturated actuator,a special type of controller is designed in this paper to achieve finite-time synchronization of time-varying-delay Cohen-Grossberg neural networks.Finally,the effectiveness of the conclusions is verified through simulation results.