Optimal Denial-of-Service Attack Power Allocation Strategy for Remote State Estimation in CPSs With Two-Hop Networks

This paper concentrates on the optimal denial-of-service (DoS) attack power allocation strategy for remote state estimation in cyber-physical systems with two-hop networks. An intelligent relay with the assumption that it can conduct some simple recursive algorithms aims at transmitting the system process state across a vulnerable communication channel to the remote estimator, referred to as a cooperative system with the sensor. In the meantime, a malicious attacker disrupts the transmission on the channel strategically to deteriorate the performance of the system, but can do this under an energy budget constraint over an infinite time horizon. The symbol error rate is introduced to characterize the probability of the error-free packet reception, while the channel noise and the interference from another communication channel are incorporated into the communication model. We present the optimal attack power control problem as a Markov decision process (MDP) framework by the fact that there exists at least one deterministic stationary strategy. The optimal power control strategy is derived with a stochastic predictive control formulation, and then we propose the corresponding strategy for implementation by borrowing extensively a Q-learning algorithm. In addition, two quick time-saving and less computational sub-optimal attack power strategies are provided to disguise the attacker from detection. Finally, the theoretical results are illustrated by some numerical examples.