Research On Intermittent Control For Finite-time Synchronization Of Complex Systems

As it is well known,complex networks or neural networks have been paid more and more attention by experts and scholars due to its wide application in many fields.Many problems in real life can be described and visualized through models of complex systems,such as the World Wide Web,food chain,pattern recognition,social science and so on.Among them,the synchronization of complex systems is the basis for the known dynamical systems to identify the unknown dynamical systems,because it usually indicates that the state trajectories of two systems are consistent with each other over time.Synchronization behavior is a very interesting collective activity in a complex dynamic network,which is already a considerable number of research topics.Based on previous studies,this dissertation discusses how to design appropriate controllers to synchronize complex systems within a finite time.The main work is as follows:Most scholars tend to explore asymptotic stability or exponential stability.That is,only when the time tends to infinity,the system can reach synchronization.Usually in various fields,the network needs to be able to be synchronized in the shortest possible time.In order to improve the convergence speed of the network,the expert introduced a more useful way to make the system fast synchronization,namely finite time synchronization.The main research content of this dissertation is to realize finite time synchronization of complex systems under adaptive periodically intermittent control.By designing intermittent control scheme,based on linear matrix inequality and Lyapunov stability theory,the synchronization criterion for complex networks with delay in finite time is obtained after rigorous theoretical consideration.Due to the limitation of signal transmission in practical application,delay can inevitably lead to oscillation or instability of the system.This dissertation mainly considers the general transmission delay,distributed delay and time-varying delay.Chapter two mainly aims at the complex network with distributed delay to achieve the finite-time hybrid projective synchronization.Chapter three mainly aims at the inertial neural network with time-varying delay to achieve the finite-time synchronization.The second-order inertial systems can be transformed into two first-order differential systems by selecting the appropriate variable substitution.The system is adjusted by designing the adaptive periodically intermittent controller.At the same time,with several linear matrix inequality and finite time stable theory.So as to construct a Lyapunov function,the complex system finite-time synchronization criterion was deduced in this dissertation.Finally,the feasibility solution is solved by the LMI toolbox,Numerical example are given to illustrate the effectiveness of the proposed method.