Optimal Stealthy Linear-Attack Schedules on Remote State Estimation

Abstract

In this paper, we address optimal schedule issue of a linear attacker without being detected by $\chi ^2$ detector. Due to limited energy, the attacker needs to decide whether to launch attacks at each step and design optimal attack strategy over a finite-time horizon. To address it, we take average error (AE) and terminal error (TE) as indices. After analyzing AEs under three special types of schedules and studying monotonic property of TE with respect to attack time instants, the optimal attack schedules for AE and TE are respectively determined theoretically. Besides, we further investigate optimal attack schedule for multiple subsystems. The accomplished results well extend the existing work in false data attacks without optimal structure and promote the linear-attack in dynamical systems to the optimal schedule issue. Illustrative examples are also given to validate our theoretical results.