High-Confidence Attack Detection via Wasserstein-Metric Computations

This letter considers a sensor attack and fault detection problem for linear cyber-physical systems, which are subject to system noise that can obey an unknown light-tailed distribution. We propose a new threshold-based detection mechanism that employs the Wasserstein metric, and which guarantees system performance with high confidence with a finite number of measurements. The proposed detector may generate false alarms with a rate Δ in normal operation, where Δ can be tuned to be arbitrarily small by means of a benchmark distribution. Thus, the proposed detector is sensitive to sensor attacks and faults which have a statistical behavior that is different from that of the system noise. We quantify the impact of stealthy attacks on open-loop stable systems-which perturb the system operation while producing false alarms consistent with the natural system noise-via a probabilistic reachable set. Tractable implementation is enabled via a linear optimization to compute the detection measure and a semidefinite program to bound the reachable set.