Stochastic Synchronization Of Complex Network Systems

Synchronization has become one of the most prevalent topics in complex network research because of its universality and important practical significance.As is wellknown,finite time synchronization has a significant advantage in time cost.However,most of the existing investigations adopt both linear and finite time control protocols and ignore the influence of noise perturbation and time delay on complex network systems.In addition,compared with a large number of results for discrete-time stochastic systems,only a few results have appeared on the event-triggered control for continuous-time stochastic systems.This thesis focuses on the Kuramoto model,one of the most successful examples of complex networks for cluster synchronization,to explore the sufficient conditions for synchronization of the Kuramoto-oscillator network and the criterion for synchronization of the network with noise or time delay.The control protocol is further improved to solve the synchronization of the stochastic delay Kuramoto-oscillator network.The main work of this thesis is as follows:Firstly,time and energy costs for achieving synchronization of the Kuramotooscillator network are investigated.In order to achieve synchronization and optimize time and energy consumption,a novel switching controller is designed,which combines the advantages of both the linear feedback control method and the finite-time control technology.Sufficient conditions for achieving synchronization are established,and the estimates of time and energy costs are obtained mathematically as well.Particularly,the theoretical analysis and simulating calculation show that there exists a trade-off between time and energy costs.That is to say,energy consumption can be reduced by adjusting the control parameters,but the time cost will increase inevitably,and vice versa.Furthermore,we find that for fixed weights of time and energy costs of the performance index,the optimal values of parameters can be chosen to minimize the total cost.Secondly,time and energy costs for reaching synchronization of the stochastic Kuramoto-oscillator network are investigated.Based on previous work,noise perturbation is considered.By using the stability theory of stochastic differential equations and matrix analysis,sufficient conditions for synchronization are established,and the mathematical estimates of time and energy costs are given.To show the effectiveness of the proposed control strategies,several numerical examples are presented.Thirdly,time and energy costs for reaching synchronization of the delayed Kuramoto-oscillator network are investigated.In addition to noise,the time delay is another critical factor that affects the stabilization of the network.To solve the synchronization of the delayed Kuramoto-oscillator network,a proper switching control protocol is designed.At the same time,the upper bounds of time and energy costs for synchronization are estimated.The feasibility of the theoretical results is verified by several numerical simulations.Finally,the even-triggered control of the stochastic delay Kuramoto-oscillator network is investigated.Two even-triggered control schemes are proposed in which the sampling actions only occur at event-triggered instants.Sufficient conditions for meansquare phase agreement and frequency synchronization are derived based on the technology of stochastic analysis.Moreover,the lower bounds on the time interval between two consecutive event-triggered instants are obtained.Especially,there are no existing works on the event-triggered control strategy for stochastic Kuramoto-oscillator network with time-delay interaction.The results of this thesis establish the event-triggered control strategy for the stochastic delay Kuramoto-oscillator network for the first time.