Synchronization-based Topology Identification For Uncertain Complex Dynamic Networks

Complex network is a crucial research topic in the 21st century.In recent years,various aspects of complex networks,such as geometrical feature,function behavior,control and synchronization,have been widly investigated.Among all of them,the network control and synchronization is one of most important issue of complex networks with strong theoretical and practical value.It has a broad application prospects in different fields such as satellite navigation and positioning,chaos secure communication,multi-agent consensus.On the other hand,the topology structure plays an important role in the evolution of network functional behavior.Nevertheless,due to various reasons,the exact topology structure of complex networks is usually unknown or uncertain in practice.Therefore,it is of great necessity to gain the knowledge of the exact topology of the network.This dissertation studies the control and synchronization of complex dynamical networks and the synchronization-based topology identification of complex networks.The main contributions and innovations of this dissertation can be summarized as follows:(1)Based on the Lyapunov stability theory,we investigated the problerm of modified projective synchronization via aperiodically adaptive intermittent pinning control scheme.By adopting hybrid control technique,a new controller which combines aperiodically adaptive intermittent pinning control technique and nonlinear control technique is designed to realize modified projective synchronization between drive and response networks.Different from all current papers,the control scheme can deal with drive and response networks with different node dynamics,unknown system parameters and non-identical time-varying delays.In addition,the intermittent control period and control width of the proposed controller can be flexibly adjusted according to actual situations.These advantages make this scheme having a large application scope in practical engineering.(2)Based on Lyapunov stability theorem,we present a generalized lag synchronization based method to identify the exact topology of general uncertain complex dynamical networks with time delay and noise perturbation.A new controller is designed to realize generalized lag synchronization between drive and response systems.By adopting identification rules,the unknown topological structure of the network is identified simultaneously in the process of synchronization.Compared with existing works,the proposed scheme can realize synchronization and identification under the condition of non identical time-varying delay and noise pertuabation.Therefore,the scheme has strong anti-interference ability.Furthermore,when adopting this scheme,one can construct a complex dynamic network with simpler node dynamics to identify the unknown topology of complex networks whose node dynamics are much more complicated,which will reduce the control cost to a large degree.Besides,we discuss the effect of time delay as well as noise perturbation on identification results and verify that both of these two factors have positive effect on topology identification.According to our study,moderate noise and time delay can enhance the effect of identification and reduce the control cost to a certain degree.