Distributed Resilient Interval Observers for Bounded-Error LTI Systems Subject to False Data Injection Attacks

This paper proposes a novel distributed interval-valued simultaneous state and input observer for linear time-invariant (LTI) systems that are subject to attacks or unknown inputs, injected both on their sensors and actuators. Each agent in the network leverages a singular value decomposition (SVD) based transformation to decompose its observations into two components, one of them unaffected by the attack signal, which helps to obtain local interval estimates of the state and unknown input and then uses intersection to compute the best interval estimate among neighboring nodes. We show that the computed intervals are guaranteed to contain the true state and input trajectories, and we provide conditions under which the observer is stable. Furthermore, we provide a method for designing stabilizing gains that minimize an upper bound on the worst-case steady-state observer error. We demonstrate our algorithm on an IEEE 14-bus power system.