Topology Identification For Complex Dynamical Networks Considering Time Delays And Incomplete Measurements

In a complex network model,vertices and edges are used to represent dynamical individuals and complicated relations between these independent systems.The topological structure functions vitally in a complex dynamical network.It plays a crucial part that connects every independent system into a network and realizes the information sharing from different individuals.If one is going to explore a complex dynamical network,the prior knowledge needed to acquire is the topological structure.When a serious malfunction occurs in a large-scale network,it is primary to quickly identify the fault location before trouble removal.However,the topological structure is barely known or observable exactly in most practical situations.Therefore,growing attentions have been paid on topology identification for complex dynamical networks.Caused by physical constraints or technological restrictions,many unreliable or uncertain factors exist widely,which should be considered seriously during the identification process,such as time delays,stochastic perturbations,uncertain system parameters,incomplete measurements of transmitted signals,etc.Long-distance communication,information congestion and such disturbing factors may result in time delays during transmitting the information of node states between the drive and response networks built for topology identification,as well as stochastically incomplete measurements of information interfered by non-ideal communication channel(like signal attenuation effect and signal shielding effect,etc.).There is little attention has been focused on the topology identification with incomplete measurements of transmitted drive states,which could affect the network synchronization and topology identification seriously.Motivated by the above discussion,we investigate the topology identification for complex dynamical networks with chaotic node dynamics considering multiple disturbing factors that exist widely and simultaneously in real-world information transmission,such as different types of inevitable time delays,stochastically incomplete measurements of information.We propose appropriate topology identification schemes to efficiently deal with the negative effects caused by communication disturbing factors that exist simultaneously,and conduct the real-time monitoring and fault diagnosis for the topological structure.The proposed schemes can improve the performance and enhance the stability of the established topology identification systems.The main contributions in four parts are listed as follows:(1)Considering that node states are affected by the non-ideal channel environment in the process of information transmission,such as the occurrence of signal attenuation or shielding,etc.,the state-coupling information in the drive network and the information of node states received by the respond network are too disturbed to be completely measured compared with which were sent at the beginning.Treating the situation that the incomplete measurements of information occur randomly,we use the received but interfered information to construct the drive and response network.Resorting to Lyapunov stability theory and stochastic process analysis,we raise a new method for identifying the topology that handles well with the excessive deviation in operating identification controllers due to the incomplete measurements.We ensure the error dynamical network from the drive-response system to be stabilized applying proper feedback gains on the controllers,so that we recover the topological structure of the original network and monitor it in real time.The strict derivation and proof process are shown,and the correctness of the raised method is verified in the simulation.(2)Two unreliable factors,the coupling time delay and incomplete measurements of information,existing in the communication channel at the same time,are considered in the topology identification of complex dynamical networks.The original network is regarded as the drive network,and the response network is established with the same node dynamics of the drive network in order to reconstruct its topological structure.In this case,the coupling information in the drive network is disturbed: it is delayed to some extent.Also,the information transmitted in the drive network or between the drive and response networks has an amplitude decrease along with the situation that some time series are missing under the influence of the unstable channel environment.Based on Lyapunov stability theory,stochastic process analysis and La Salle’s invariance principle,a novel scheme of topological identification is proposed in order to break the limitation on the node dynamics which existed in previous schemes.According to the measured but disturbed information,a proper error compensation scheme is designed to reduce or even eliminate the influence of the above two interference on the information,so that the identification controller could be stabilized in a normal state.Identifying the topological structure of the original network could be achieved by synchronizing the response network with the drive network.The relevant theoretical analysis and derivation are provided,and numerical simulations are carried out to verify the effectiveness of the designed scheme.(3)The topology identification and fault diagnosis problems for the multi-layer complex dynamical network model are considered in ideal and non-ideal communication environments respectively.Based on the classical single-layer complex dynamical network model,a new network model with two-layer structure is constructed considering the existence of information coupling delay and incomplete measurements in the original network and communication channel.Combined with Lyapunov stability theory and stochastic process analysis,the role of interlayer coupling connections playing in the topology identification is analyzed.Instead of building another integrated two-layer response network,we treat one layer of the multi-layer structure as the drive network,the other layer as the response network.Based on the basic principles of generalized synchronization between networks with different structures,we are able to identify the topology of the drive network and make real-time monitor on topology changes,which provides solutions for network troubleshooting.The detailed theoretical analysis and proof process are given.The complex dynamic network with chaotic node dynamics is selected to conduct simulations in order to show that the proposed scheme is accurate and effective.