Distributed L1-state-and-fault estimation for Multi-agent systems

In this paper, we propose a distributed state-and-fault estimation scheme for multi-agent systems. The proposed estimator is based on an $\ell_1$-norm optimization problem, which is inspired by sparse signal recovery in the field of compressive sampling. Two theoretical results are given to analyze the correctness of the proposed approach. First, we provide a necessary and sufficient condition such that state and fault signals are correctly estimated. The result presents a fundamental limitation of the algorithm, which shows how many faulty nodes are allowed to ensure a correct estimation. Second, we provide a sufficient condition for the estimation error of fault signals when numerical errors of solving the optimization problem are present. An illustrative example is given to validate the effectiveness of the proposed approach.