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 <inline-formula> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula> in normal operation, where <inline-formula> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula> can be tuned to be arbitrarily small by means of a <italic>benchmark distribution</italic>. 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 <italic>stealthy</italic> attacks on open-loop stable systems—which perturb the system operation while producing false alarms consistent with the natural system noise—via a <italic>probabilistic</italic> reachable set. Tractable implementation is enabled via a linear optimization to compute the detection measure and a semidefinite program to bound the reachable set.

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