On Synchronization Control For Multi-network With Inter-network Coupling Fault And Random Disturbance

Complex networks are presently significant tools and methods to describe and understand the complex system.Complex networks have been used widely in different scientific fields,such as sociology,biological sciences,computer sciences and so on,which have become a brilliant research topic of complexity science field.In recent years,almost all complex network research has focused on the single network.But there exists the multi-network system constituted by several interacting networks.Therefore it is significant to study synchronization control problem for multi-network in the real world.In this thesis,the synchronization of multi-network is investigated by combining the nonlinear system theory,Kronecker product technique.The main work can be summarized as follows:Firstly,considering the permanent fault of coupled nodes among different networks,coupling terms in the same network and coupling terms among different networks are described separately in the mathematic model in order to be clear to explain multi-network.The dimension-transformation matrix is used to deal with the mismatched nodes dimension in the different networks.A synchronization controller is designed with pinning control scheme.Based on linear matrix inequalities and Lyapunov stability theory,a sufficient stability condition and a pinning control scheme are given by which the nodes in the same network can achieve synchronization.Taking the multi-network system coupled by two networks as a simulation example,numerical simulation results show that the proposed controller can achieve synchronization for the multi-network system.In addition,it shows that the specifically pinning scheme is more effective than the randomly pinning scheme.Secondly,considering the permanent fault and the recoverable fault of coupled nodes among different networks,Bernoulli variable is used to describe the change between failure and recovery events.A pinning controller is designed and the sufficient stability condition is given.Control is applied to some nodes so that each network is internally synchronized.Taking the multi-network system coupled by three networks as a simulation example,the result shows that even in the case of the permanent fault and the recoverable fault among different networks,the multi-network can achieve the synchronization of nodes in each network.Thirdly,considering random disturbance for the discrete-time multi-network system,where the noise perturbation is scalar Brownian motion.Based on the Lyapunov theory,the sufficient conditions for network synchronization are obtained.Then,the multi-network is synchronized by applying a pinning controller to some nodes.Taking the discrete-time multi-network system coupled by two networks as a simulation example,the result shows that even in the case of random disturbance,the proposed controller can achieve synchronization for the discrete-time multi-network system.Finally,the main work of this thesis is summarized and some future research directions are put forward.