An Online Kullback–Leibler Divergence-Based Stealthy Attack Against Cyber-Physical Systems

This article investigates the design of online stealthy attacks with the aim of moving the system's state to the desired target. Different from the design of offline attacks, which is only based on the system's model, to design the online attack, the attacker also estimates the system's state with the intercepted data at each instant and computes the optimal attack accordingly. To ensure stealthiness, the Kullback–Leibler divergence between the innovations with and without attacks at each instant should be smaller than a threshold. We show that the attacker should solve a convex optimization problem at each instant to compute the mean and covariance of the attack. The feasibility of the attack policy is also discussed. Furthermore, for the strictly stealthy case with zero threshold, the analytical expression of the unique optimal attack is given. Finally, a numerical example of the longitudinal flight control system is adopted to illustrate the effectiveness of the proposed attack.