Distributed Secure Estimation Against Sparse False Data Injection Attacks

Distributed cyber–physical systems (CPSs) are with complex and interconnected framework to receive, process, and transmit data. However, they may suffer from adversarial false data injection attacks due to the more open attribute of their cyber layers, and the connections with neighbor agents could aggravate the disastrous consequences on the system performance degradation. In this article, we focus on investigating distributed secure estimation paradigms against sparse actuator and sensor corruptions by virtue of combinational optimization. First, the consensus-based static batch optimization and secure observer design problems are established, based on which the concepts of sparsity repairability and restricted eigenvalues under attacks are discussed. Then, both the distributed projected heavy-ball estimator and distributed projected Luenberger-like observer are designed, in terms of the intensified combinational vote locations and distributed implementation of projection operator, with strict convergence guarantees. Finally, two numerical examples are performed to verify the effectiveness of our theoretical derivation.