Flocking Of Cucker-Smale Systems And Synchronization Of Complex Networks

Complex systems often exhibit consistent and ordered collective behavior,for example,flocks of flying birds,schools of moving fish swarms,clusters of robots in coordinated motion and so on.Therefore,the investigation of collective behavior of complex systems is of great significance and has attracted widespread attention from scholars at home and abroad.The Cucker-Smale system is a typical model for describing the collective behavior of complex systems,however,existing research has focused more on asymptotical flocking problem in the Cucker-Smale system.In this thesis,we consider the convergence time of the Cucker-Smale system and the effect of disturbances such as stochastic noise on the Cucker-Smale system flocking behavior.At the same time,the reach methods are extended to the study of cooperative control of complex networks.The main elements of this thesis are as follows:First,the finite-time and fixed-time flocking problems of the Cucker-Smale system with pinning control are investigated.For the Cucker-Smale system,pinning controllers are designed by combining finite-time and fixed-time control techniques.Based on the finite-time stability theory,sufficient conditions for the Cucker-Smale system to reach the finite-time and fixed-time flocking with pinning control are obtained and estimates of the upper bound of time to realize flocking are given.In addition,it is shown that the controllers can guarantee that no collision occurs between particles during flocking and sufficient conditions for collision avoidance between particles are given.Finally,the effect of network size and control parameters on the system flocking speed was analysed by numerical simulations.Secondly,the finite-time and fixed-time flocking problems of stochastic CuckerSmale systems are investigated.The interference of stochastic noise is introduced into the classical Cucker-Smale model to construct a stochastic pinning control model,which considers the effect of noise on the convergence speed of the Cucker-Smale system.The models are analysed for stochastic stability based on a suitable Lyapunov function.The conditions required for the stochastic Cucker-Smale system to reach flocking are obtained and estimates of the upper bound on flocking time are given.Finally,the effect of controller parameters and noise intensity on the flocking speed is analysed using simulations.Finally,the problems of finite-time stochastic cluster synchronization for complex networks is investigated.For complex networks,the finite-time stochastic cluster synchronization problems with pinning control and without pinning control are investigated.For each of the two cases,finite-time controllers with noise terms are designed.By means of stochastic process theory and stability theory of stochastic differential equation,the stochastic stability of the proposed protocol is analyzed and sufficient conditions for achieving clustering synchronization are established.Finally,the theoretical results obtained are analysed by simulations.