Probability-Based Stochastic Stealthy Attacks in Cyber-Physical Systems

This article focuses on the design of stochastic stealthy attacks in linear cyber-physical systems (CPSs), where the objective of attackers is to degrade the system's performance and maintain a delicate balance between detection and false alarm rates. In contrast to the commonly used stealthiness constraint defined using the Kullback–Leibler divergence, the $\varepsilon$ -stealthiness is established based on the detector's tolerance against the false alarm rate, providing an intuitive correlation between the attacker's stealthiness and the detection rate from a probabilistic perspective. Furthermore, we obtain an upper bound on the attack performance using the Schur–Horn theorem and devise a corresponding stealth attack strategy to ensure compliance with this bound. Finally, simulations with a three-tank system model are executed to corroborate the theoretical results.