Designing resilient control strategies for mitigating stealthy attacks is a crucial task in emerging cyber-physical systems. In the design of anomaly detectors, it is common to assume Gaussian noise models to maintain tractability; however, this assumption can lead the actual false alarm rate to be significantly higher than expected. We propose a distributionally robust anomaly detector for noise distributions in moment-based ambiguity sets. We design a detection threshold that guarantees that the actual false alarm rate is upper bounded by the desired one by using generalized Chebyshev inequalities. Furthermore, we highlight an important trade-off between the worst-case false alarm rate and the potential impact of a stealthy attacker by efficiently computing an outer ellipsoidal bound for the attack-reachable states corresponding to the distributionally robust detector threshold. We illustrate this trade-off with a numerical example and compare the proposed approach with a traditional chi-squared detector.
@article{arxiv.1909.12506,
title = {Distributionally Robust Tuning of Anomaly Detectors in Cyber-Physical Systems with Stealthy Attacks},
author = {Venkatraman Renganathan and Navid Hashemi and Justin Ruths and Tyler H. Summers},
journal= {arXiv preprint arXiv:1909.12506},
year = {2019}
}