Estimate the States of Multiagent Systems Under Homologous Attacks by Optimization Approaches

This article revisits the problem of secure state estimation of multiagent systems under homologous attacks in [1]. We first characterize the condition on agents dynamics such that agents states can be uniquely solved from the attacked measurements of agents outputs. This condition implies that the conclusion in [1] that the attack signal and agents states can be uniquely reconstructed by adding longer time-windowed measurements is incomplete. Based on this condition, when the communication graph of agents is undirected, we propose two different distributed secure state estimators by reformulating the state reconstruction as optimization problems. The first estimator does not need agents to exchange with others their dynamics information, which is used by the second, but requires updating and exchanging more variables. Both estimators are much simpler and easier to understand than that proposed in [1]. Moreover, when the communication graph is directed and strongly connected, we also proposed two distributed state estimators, adjusted from the estimators for undirected graphs. Both of them require no global information of communication graphs but the network size. At last, we verify all the theoretical results with simulation examples.