On scheduling of deception attacks for discrete-time networked systems equipped with attack detectors

This paper is concerned with the attack scheduling of deception attacks for discrete-time systems with attack detection. Specifically, for a class of Kalman filters with χ2 detectors, an attacker with the given attack task needs to decide how many the maximum number is or how much the attack probability is for different kinds of attack scenarios (i.e. consecutive deception attacks or randomly launched deception attacks). Firstly, in light of the property of χ2 distribution, the predictions of detection probabilities under attacks are calculated in mean-square sense for these two attack scenarios. Then, in terms of predicted probabilities, the deception attack schemes are designed in the framework of Kalman filtering. For the case of consecutive attacks, the maximum number of attacks is determined via recursive Riccati-like difference equations. For the case of randomly launched deception attacks, the desired attack probability is obtained by solving a Riccati-like equation. Finally, a numerical example on target tracking is presented to demonstrate the effectiveness of the proposed suboptimal attack schemes.