Secure Distributed Observers for a Class of Linear Time Invariant Systems in the Presence of Byzantine Adversaries

We study the problem of distributed state estimation of a linear time-invariant system by a network of nodes, some of which are subject to adversarial attacks. We develop a secure distributed estimation strategy subject to an f-locally bounded Byzantine adversary model, where a compromised node can arbitrarily deviate from the rules of any prescribed algorithm. Under such a threat model, we provide sufficient conditions guaranteeing the success of our estimation strategy. Our method relies on the construction of a subgraph, which we call a Mode Estimation Directed Acyclic Graph (MEDAG), for each unstable and marginally stable eigenvalue of the plant. We provide a distributed algorithm for constructing a MEDAG and characterize graph topologies for which the construction algorithm is guaranteed to succeed. Our approach provides fundamental insights into the relationship between the dynamics of the system, the measurement structure of the nodes, and the underlying graph topology.