Optimal Scheduling of Multiple Sensors with Packet Length Constraint
For control systems with bandwidth-limited communication, this work provides a theoretical foundation for optimal sensor scheduling under packet length constraints.
This paper addresses the scheduling of multiple sensors with different packet lengths to minimize average estimation error covariance at a remote estimator, formulating it as an MDP and proving the existence of a deterministic stationary threshold policy.
This paper considers the problem of sensory data scheduling of multiple processes. There are $n$ independent linear time-invariant processes and a remote estimator monitoring all the processes. Each process is measured by a sensor, which sends its local state estimate to the remote estimator. The sizes of the packets are different due to different dimensions of each process, and thus it may take different lengths of time steps for the sensors to send their data. Because of bandwidth limitation, only a portion of all the sensors are allowed to transmit. Our goal is to minimize the average of estimation error covariance of the whole system at the remote estimator. The problem is formulated as a Markov decision process (MDP) with average cost over an infinite time horizon. We prove the existence of a deterministic and stationary policy for the problem. We also find that the optimal policy has a consistent behavior and threshold type structure. A numerical example is provided to illustrate our main results.