Resilient state estimation for complex dynamic networks with system model perturbation

This article investigates the resilient estimation problem for a class of complex networks with disturbances. Specifically, there exist uncertainties in system matrices and inner coupling simultaneously, described by Gaussian noise or deterministic norm-bounded matrices. For each kind of uncertainty, a novel class of resilient estimation algorithms is designed from 'centralized' and 'distributed' perspectives, respectively. Here, 'centralized' means that global information is utilized by each node while 'distributed' indicates that only the local information of each node's own and its neighbors is used in the estimation process. Particularly, for norm-bounded uncertainties, an extended-state method is proposed, where adaptive system matrices are introduced to improve the estimation performance. A recursive upper bound of the estimation error covariance for each node is derived to obtain the estimator gains. Such designed estimation algorithms avoid solving linear matrix inequalities. Furthermore, an easy-to-check condition only about the system matrices is provided to guarantee the feasibility of the estimation algorithms on the infinite horizon. Finally, the effectiveness of the theoretical results is demonstrated by several numerical examples.