Optimal Hybrid Intrusion Schedule Against State Estimation for Cyber-Physical Systems

The security issues of wireless cyber-physical systems (CPSs) have attracted widespread attentions in the decade. Existing research mainly focuses on the specific attack paradigm of a single attacker or eavesdropper. In this letter, we consider a smart intruder which has two options including eavesdropping and DoS attack. The intruder can switch between these two options based on the global cost function which is constructed as a trade-off between the intruder's estimation error, energy consumption, and estimation error at the estimator side. By modeling it as a Markov decision process (MDP), we give some structural properties of the optimal schedule analytically and explicitly. It can be theoretically proved that there remains a threshold structure for the optimal intrusion scheduling when the holding time of estimator is fixed. Further more, when intruder's holding time is fixed, the optimal strategy consists of two cases, both of which follow a threshold structure, and they exhibit opposing forms of the optimal solution. Numerical examples and comparisons with the state-of-art methods are presented to demonstrate the correctness and effectiveness of our proposed results.