Distributed State Estimation For Complex Networks With Constrained Information

A complex network is a network composed of many nodes,among which there are certain connections.Examples of complex networks abound in everyday life,such as power grids,the World Wide Web（WWW）,airline networks,and disease transmission networks.The discovery of small-world networks and scale-free networks has made remarkable progress in the study of complex networks,and the synchronization and state estimation problems have aroused great interest of researchers.Since nodes in a complex network are usually distributed in different locations,it is necessary to utilize a communication network for data transmission.Various problems caused by data transmission（including sampling,network attacks）can cause nodes to sometimes fail to obtain accurate information about other nodes.Therefore,research on state estimation of complex networks with limited information is needed.In this thesis,the distributed state estimation problem of complex network systems is studied based on the classical Kalman filtering method under the limited information.The following researches are carried out:（1）For complex network systems in engineering practice,nonlinear uncertainty caused by external noise are inevitable.However,the extended Kalman filtering method proposed under the classical Kalman filtering framework can only deal with precisely known and differentiable nonlinearities.In order to deal with nonlinear uncertainty,the extended state method is proposed.On this basis,a distributed extended state method with less computation than the centralized method is proposed for complex network systems with nonlinear uncertainties.Firstly,a distributed state predictor is designed,and then a distributed state estimator is designed.Then,the optimal state estimator gain is designed and the upper bound of the prediction error covariance expressed by the recursive Riccati equation is obtained.Finally,a sufficient condition for the upper bound stability of the prediction error covariance is obtained by using vector-based iterative equations.Compared with the existing related literature,this condition is less conservative.（2）A reliable distributed state estimation method is designed for complex networks with multi-rate measurement sampling and random injection attack functions.Firstly,when the state update rate of the complex network is the same as the measurement sampling rate,the optimal local estimator at the state update point is obtained in a unified form,and the distributed estimator effectively solves the disturbance of the complex network.Then,the optimal upper bound of the state estimation error covariance and the optimal state estimator gain are derived based on mathematical induction.Compared with the existing traditional lifting methods,the newly proposed estimation algorithm can effectively solve the computational problems caused by nonlinear uncertainties.Finally,numerical simulation examples show that the designed distributed state estimation method is feasible.