High-Confidence Attack Detection via Wasserstein-Metric Computations
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This paper considers a sensor attack and fault detection problem for linear cyber-physical systems, which are subject to possibly non-Gaussian noise that can have 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. 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 which is part of our mechanism. Thus, the proposed detector is sensitive to sensor attacks and faults which have a statistical behavior that is different from that of the system's noise. We quantify the impact of stealthy attacks—which aim to perturb the system operation while producing false alarms that are consistent with the natural system's noise—via a probabilistic reachable set. To enable tractable implementation of our methods, we propose a linear optimization problem that computes the proposed detection measure and a semidefinite program that produces the proposed reachable set.
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