ADMM based Distributed State Observer Design under Sparse Sensor Attacks

This paper considers the design of a distributed state observer for discrete-time Linear Time Invariant (LTI) systems in the presence of sensor attacks. We assume there is a network of observer nodes, communicating with each other over an undirected graph, each with partial measurements of the output corrupted by some adversarial attack. We address the case of sparse attacks where the attacker targets a small subset of sensors. An algorithm based on Alternating Direction Method of Multipliers (ADMM) is developed which provides an update law for each observer that ensures convergence of each observer node to the actual state asymptotically.