A Multi-Channel Transmission Schedule in CPSs With the Energy Harvesting Defender Subject to DoS Attacks

Abstract

This paper investigates the optimal power scheduling for accurate remote state estimation in cyber-physical systems (CPSs) subject to denial-of-service attacks. A critical scenario is examined where sensor data is transmitted to a remote estimator over a multi-channel network that is vulnerable to a malicious attacker. At each time step, the sensor—equipped with an energy harvester—is to select a channel for transmitting data packets with the objective of minimizing the expected estimation error at the remote estimator. Concurrently, the attacker needs to decide which channel to target in order to maximize the expected estimation error, under constraints imposed by limited energy resources. To model the interactive decision-making process between the sensor and the attacker, a two-player Markov game framework is employed, capturing the conflicting objectives of the two players. Furthermore, an adaptive reinforcement learning algorithm named Q-learning algorithm is proposed to address the complexity of finding Nash equilibrium. Finally, simulation results demonstrate the effectiveness of the proposed approach.