Optimal Stealthy Deception Attack Against Cyber-Physical Systems

This paper studies the problem of designing the optimal deception attack to maximize a utility function with the Kullback-Leibler divergence adopted as a detection constraint. The utility function reflects the goal of pulling the state away from the origin, increasing the cost of the controller and decreasing the cost of the attacker. To analyze the stealthiness of the attack, the attack signal is decomposed into two parts, one of which is strict stealthy. The necessary and sufficient condition is derived for the case that the strict stealthy attack cannot lead to an unbounded benefit. In this case, the linear transformation of the optimal attack is proved to be a Gaussian distribution. With the mean value and covariance of the Gaussian distribution as variables, the original problem is transformed into a new problem which may not be convex. A suboptimal attack policy is provided and the upper bound for the loss of benefit when using the suboptimal attack is also given. A numerical example of unmanned ground vehicle is illustrated to verify the effectiveness of the proposed attack policy.