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.

中文翻译：

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系统模型摄动的复杂动态网络弹性状态估计

本文研究了一类具有干扰的复杂网络的弹性估计问题。具体来说，系统矩阵和内部耦合同时存在不确定性，用高斯噪声或确定性范数界矩阵描述。对于每种不确定性，分别从“集中式”和“分布式”的角度设计了一类新颖的弹性估计算法。此处，“集中”是指每个节点都使用全局信息，而“分布式”是指在估计过程中仅使用每个节点自身及其邻居的本地信息。特别地，对于范数有限的不确定性，提出了一种扩展状态方法，其中引入了自适应系统矩阵以提高估计性能。推导每个节点的估计误差协方差的递归上限，以获得估计器增益。这样设计的估计算法避免求解线性矩阵不等式。此外，提供了仅关于系统矩阵的易于检查的条件，以保证估计算法在无限范围内的可行性。最后，通过几个数值例子证明了理论结果的有效性。