Finite-Time Synchronization And Control For Two Classes Of Nonlinear Hybrid Systems

Synchronization and control have important applications in many engineering fields,such as model recognition,image processing,secure communication,etc.Traditional syn-chronization control is to design appropriate control such that the coupled system achieve asymptotic synchronization or exponentially synchronization,i.e.,the synchronization is guaranteed only when time tends to infinity.However,in some practical applications,synchronization is often required to be realized in a relatively short time so as to improve the degree of security,working efficiency and reduce the control cost,etc.Therefore,it is necessary to study finite-time synchronization and control of nonlinear systems or even chaotic systems under various conditions.In addition,in the field of control,it is a very important research topic to design a simple but feasible controller that can re-duce the control cost to achieve the control purpose.Therefore,this paper studies the finite-time synchronization of two classes of nonlinear systems under the influence of com-plex factors such as proportional delay,uncertain parameters and stochastic disturbances.Some effective and easy to be implemented are designed and a series of finite-time syn-chronization criteria are obtained by referring to techniques such as functional analysis,nonsmooth analysis,matrix theory,stability theory,control theory,and mathematical in-duction method.Moreover,the finite settling time is estimated for every synchronization issue.Meanwhile,with the help of MATLAB,numerical simulations are given to verify the theoretical results.The main structure of this thesis is as follows:Chapter 1 introduces the importance of finite-time synchronization and control and discusses the research status of finite-time control in current literature.Particularly,existing results on finite-time control of memristive neural network are introduced and corresponding difficulties are discussed,and the issue of finite-time synchronization control for a class of hybrid continuous and discrete-time switched system is proposed.Chapter 2 considers the problem of finite-time drive-response synchronization of memristive neural network systems with proportional delay.By constructing a discontin-uous state feedback controller and using Lyapunov function method,a series of sufficient conditions for the synchronization are obtained in the framework of Filippov solution and 1-norm.The upper time-instant for the synchronization is given.Our results demonstrate that the memristive neural networks can achieve synchronization in the upper time-instant in spite of the proportional delay.After that,a special adaptive controller is designed to reduce the control gain for the finite-time synchronization.Chapter 3 investigates the finite-time synchronization problem for switched system composed of continuous subsystems and discrete subsystems.Both subsystems are af-fected by stochastic perturbations,which makes the model under consideration closer to reality.In order to save the channel resources and reduce the control cost as much as possible,a quantized intermittent controller which is only active for continuous-time sub-systems is designed.New analytical techniques and the mathematical induction method are used to obtain three criteria for the finite-time synchronization.Then,the synchro-nization time is estimated explicitly.