Optimal Stealthy Attacks Against Remote State Estimation in Cyber-Physical Systems: A More Fine-Grained Stealthiness

This article studies the stealthy attack design problem on cyber-physical systems (cyber-physical system), where the ( $\epsilon $ , $\delta $ )-stealthiness, a more fine-grained quantification of the attack stealthiness, is considered. Under the ( $\epsilon $ , $\delta $ )-stealthy constraint, the optimization problem is nonconvex. By analysing the relationship between the two stealthy parameters, the nonconvex problem is transformed into the one with only equality constraints, which can be solved directly in one step with more simplified solution process. Furthermore, a general linear attack model is considered, and the optimal attack strategy is given analytically, which achieves greater attack performance but under a more stealthy level than the existing results. In addition, the constraint that the output matrix needs to have full rank rows in the existing works has been removed, and the completely analytical forms of the optimal attack parameters rather than numerical forms are presented. Finally, numerical simulations are given to show the effectiveness of the method and comparison results.