An Optimal Hybrid Fake-Acknowledgment Attack Strategy on State Estimation With Energy Constraint

Security issues of cyber-physical systems have attracted more and more attentions these years. In this letter, we investigate an energy-constrained optimal hybrid fake-acknowledge attack strategy on state estimation over infinite-time domain, where an attacker will choose certain time instants to generate or block (denoted as Phase I and Phase II, respectively) the feedback flag-acknowledgment (ACK) signals based on a given sensory transmission schedule (STS). We first provide an explicit threshold form of the optimal STS under power constraint. Based on this, the optimal attack strategy for Phase I is presented and proved to satisfy a threshold form. We continue to discuss the optimal state distribution at the threshold, which contributes as a bridge to link these two phases, and consequently derive out the optimal attack strategy for Phase II. Moreover, the condition of convergence is also analytically provided. Comparisons with other feasible schedules are accomplished to verify the correctness and effectiveness of our proposed results.