Transmission Scheduling for Remote State Estimation in CPSs With Two-Hop Networks Subject to DoS Attacks

In this paper, a dynamic zero-sum game is formulated to describe the power decision-making process of the sensor/relay and the DoS attacker in cyber-physical systems. The sensor and the relay cooperate with each other to transmit the state estimation to the remote estimator, when the attacker, on the contrary, aims to disturb the wireless communication channels strategically for deterioration of the system performance but can do this taking into account its limited energy. Different from conventional battery-powered nodes, the sensor and the relay can harvest energy from the external environment and store it in their batteries for data transmission. We model the external environment state as a Markov chain to overcome the randomness of the harvested energy. In addition, to tackle the computation complexity of the Nash equilibrium (NE), we restrict our attention to a special case, i.e., the DoS attacker can only launch interference on one of the two communication channels over an infinite time horizon, and provide the corresponding NE strategy of the game using the Markov decision process and the multi-agent reinforcement learning algorithm. Finally, simulation examples are given to illustrate the theoretical findings of the paper.