An Optimal Periodic Attack Schedule Against Estimation Over Infinite-Time Horizon

The security issues of cyber-physical systems have received wide attentions in recent years. In this letter, we consider an offline periodic Denial of Service (DoS) attack scheduling problem against the transmission between sensor and estimator over infinite-time horizon. In order to handle offline infinite-time scheduling, different from existing methods which only solve online scheduling problem or provide implicit sub-optimal solutions, we propose a novel approach based on sub-schedules and sub-costs to describe the infinite-time schedule and its cost. Furthermore, an interesting property of periodic decline is discovered for the state distribution, thus we equivalently transform the primal scheduling problem into a finite-time one within a period with respect to the introduced sub-schedules. By analyzing the optimal state distributions within a period, we derive out the global optimal attack schedule in an analytical and explicit form. Numerical comparisons with other schedules (including the online one obtained by the state-of-the-art reinforcement learning-based method) validate the correctness and superiority of the proposed schedule and approach.