Stealthy Attacks and Robust Detectors for Cyber-Physical Systems With Bounded Disturbances: A Zonotope Approach

This article investigates stealthy attacks on cyber-physical systems that are monitored by a parity-space-based detector and corrupted by bounded disturbances. Specifically, this work proposes a receding horizon attack strategy subject to strict and relaxed stealthiness constraints. Necessary and sufficient conditions for the existence of strictly stealthy attacks of arbitrary lengths are derived. On the defender's side, a robust detector is designed to detect malicious attacks utilizing zonotopes to handle bounded disturbances. A new recursive update method and a reduction operator are proposed to improve the accuracy and reduce the storage space of the detector. Unlike traditional parity-space-based detectors, it is proved that any attack that can completely bypass the robust detector must be bounded. Furthermore, two methods of determining the optimal gains of the proposed detector are provided. The effectiveness of the proposed methods is demonstrated through numerical examples.