Optimal power schedule for distributed Kalman filtering under DoS attacks: a Stackelberg game strategy

This paper investigates the power schedule problem for a cyber-physical system under signal-to-interference-plus-noise ratio (SINR)-based denial-of-service (DoS) attacks. In contrast to the existing works where only a single channel or a multi-channel network with an estimation centre is considered, the interactive dynamic game process in a fully distributed wireless sensor network is concerned in this paper based on a distributed Kalman filtering framework. The aim of the sensors is to minimise the mean square error of the fusion filter from the perspective of infinite time domain power management. The attacker interferes the fusion channels to reach the opposite goal. The competitive relationship among the sensors and attacker is modelled as a general-sum deterministic game based on Stackelberg game. Taking into account the practical situation where each player does not have a good knowledge of the global information, a distributed reinforcement learning in groups algorithm based on Stackelberg strategy is proposed to learn the joint optimal strategy. In particular, we consider that the strategy space of each player is unknown to other players and can be infinitely expanded through the individual local observation information. Finally, the proposed results are verified by the simulation examples.