On Synchronization Control For Multi-networks With Connection Failure Between Different Networks

The synchronization is one of the most important research directions of complex network,which has gained more and more attention.In recent years,almost all complex network research has focused on the single isolated network.But in the real world,there exists the multi-network system constituted by several interacting networks,such as infrastructure network coupled by different infrastructure systems(supply system for food and water,power grid and traffic system),as well as the biological population network,etc.However,due to the interaction between different networks,it may appear the phenomenon of connection failure of nodes between networks;In addition,some network has strong ability to repair itself,and then,the failure of connection can be restored after a period of self-regulation,which can be called the recoverable connection failure.This kind of phenomenon will not only affect the network itself,but also destroy the normal work of the other connected network.Therefore,based on the case of recoverable connection failure of nodes between different networks,synchronization control problem of multi-networks is studied in this thesis,and the main work can be summarized as below:Firstly,considering the recoverable connection failure of coupled nodes between different networks,the synchronization problem of a multi-network is investigated.Bernoulli variable is used to describe the change between failure and recovery events.In order to be closer to reality,coupling terms in the same network and coupling terms between different networks are described separately in the mathematic model.The dimension-transformation matrix is used to deal with the mismatched node dimension.A pinning controller is designed,and the sufficient stability condition is given.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.Secondly,considering the case of recoverable connection failure of coupled nodes between different networks,the feedback controller is designed for a multi-network coupling system with coupled delay and random disturbance,and then the stability condition of the error system is given.Taking the multi-network system coupled by three networks as a simulation example,through comparing and analyzing the simulation results of normal connection and recoverable connection failure,the result shows that even in the case of recoverable connection failure,the network can realize the synchronization of nodes in each network.Again,the connection failure between nodes in different networks will lead to the change of network topology,and the change can be considered as the switch topology of network.Therefore,for the multi-network with switching topology,the globally exponentially synchronization condition is given by using the average dwell time method.Then,taking the multi-network including networks which can't realize self-synchronization as a simulation example,the result shows that the global exponential synchronization of the network can be achieved by controlling the synchronization time of the self-synchronized sub-networks.Finally,the main work of this thesis is summarized and some future research directions are put forward.