Synchronization Analysis For Several Classes Of Neural Networks Based On Impulsive Hybrid Control

Impulsive control has become an important control method for complex nonlinear systems due to its low cost and easy implementation.It is widely used in rocket orbit correction,biological systems,stocks and financial markets.In actual engineering control,since the actuators of the physical control system are constrained by amplitude and energy due to problems such as components or bandwidth,actuator saturation will occur.Actuator saturation,as a common nonlinear constraint phenomenon,not only affects the performance of the physical control system,but also may seriously undermine the stability of the system.Therefore,in the nonlinear impulsive system,considering the saturated nonlinear factors has far-reaching practical significance and theoretical value.In this thesis,based on impulsive differential system theory,actuator saturation theory and Lyapunov stability theory,impulsive hybrid control is used to study the synchronization of several classes of complex neural networks with saturated input mechanism.The main contents and contributions of this paper are as follows :1.The synchronization problem of coupled stochastic reaction diffusion neural networks with multiple weights and delays under the control of pinning impulsive control is studied.Firstly,a new pinning impulsive control strategy is designed.This control strategy combines the characteristics of two control methods: fixed-time impulsive control and pinning control.Secondly,using the quadratic Lyapunov function with parameters,combined with mathematical induction,the local exponential stability criterion related to LMIs is obtained.In addition,by removing stochastic noise and multiple weights,the synchronization criteria of the reaction diffusion neural networks with pinning impulse control are obtained respectively.Finally,a numerical simulation verifies the validity of the theoretical results.2.The impulsive synchronization problem of coupled reaction diffusion neural networks based on intermittent control and actuator saturation is studied.First,fully considering the advantages and characteristics of saturation impulsive control and intermittent control,a new hybrid controller based on saturation impulsive control and intermittent control is proposed.Secondly,the polyhedral representation is used to deal with the saturation impulsive term in the established partial differential neural networks.By constructing a suitable Lyapunov function,combining Jensen's inequality,Lyapunov stability theory and comparison principle,etc.,the local exponential stability criterion of the drive-response error system,the design of the controller and the estimation of the attraction domain are obtained.In addition,the sector nonlinear model method is used to deal with the saturation impulsive term,and the assumption conditions of the dead zone nonlinear function are given,and the local exponential stability criterion of the system,the design of the controller and the estimation of the attraction domain are obtained.Finally,numerical simulations verify the validity of the theoretical results.3.The impulsive synchronization of chaotic neural networks based on hybrid control is studied.Firstly,a control strategy combining intermittent control and saturation impulsive control is considered.Secondly,the polyhedral representation is used to deal with the term of saturated nonlinear.By constructing a suitable Lyapunov-Krasovskii functional,combining Jensen's inequality,Wirtinger correlation inequality,Schur complement lemma,Lyapunov stability theory and comparison principle,the local stability conditions and the estimation of the region of attraction of the error system are obtained.In addition,the sector nonlinearity method is used to deal with the saturation nonlinearity,and the synchronization criterion can be obtained.Finally,numerical simulations verify the validity of the theoretical results.4.The impulsive synchronization problem of neural complex networks based on hybrid controller is studied.Firstly,two suitable hybrid controllers are established: impulsive saturation controller,hybrid controller combining saturation impulsive control and saturation feedback control.Secondly,by using polyhedral representation method and sector nonlinear model method,a suitable parameter quadratic Lyapunov function is constructed.By using comparison principle,Schur complement lemma,Jensen's inequality and so on,the exponential stability conditions and estimate of domain of attraction for the error system are obtained.In addition,considering the second controllers,the polyhedral representation method is used to obtain the synchronization criterion of the system and the estimate of domain of attraction.Finally,the correctness and effectiveness of the theoretical results are verified by numerical simulation.Finally,conclusions in the dissertation are collected,and future works are proposed.