Double Threshold Structure of Sensor Scheduling Policy Over a Finite-State Markov Channel

In this article, we consider the optimal sensor scheduling for remote state estimation in cyber-physical systems (CPSs). Different from the existing works concerning the time-invariant channel state in the wireless communication network, our work considers the time-varying channel state modeled by a finite-state Markov channel (FSMC). We focus on the problem of how to schedule the transmission of the sensor to minimize the estimation error at the remote side with less communication cost. Using the framework of the Markov decision process (MDP), the optimal scheduling policy is shown to be deterministic stationary (DS). We further derive its double threshold structure with respect to remote estimation errors and channel states. Moreover, a necessary and sufficient condition guaranteeing the mean-square stability of the remote estimator is given based on the structured scheduling policy. Numerical simulations are provided to verify the theoretical results.