Optimal Finite Horizon Scheduling of Wireless Networked Control Systems

Control over networks is envisioned to be one of the driving applications of future mobile networks. Networked control systems contain sensors and controllers exchanging time-sensitive information to fulfill a particular control goal. In this work, we consider N heterogeneous feedback control loops closed over a wireless star network. A centralized scheduler located at the central node, i.e., base station (BS), determines the transmission schedule of sensor-to-BS and BS-to-controller communication links. We assume that each link can accommodate a single transmission at a time and is prone to data losses with time-varying probability. Moreover, each controller estimates the system state remotely based on available information. In such a setting, we formulate an optimization problem to minimize the network-induced estimation error at the controller. In particular, we determine the optimal transmission schedule on each link that leads to the minimum normalized mean squared error (nMSE) in a given finite horizon (FH). We compare the performance of our proposed FH scheduler to various schedulers from the existing literature. Our simulation results show that by solving the finite horizon problem optimally, we are able to reduce the nMSE by 10% when compared to the best performing scheduling policy among the selected policies from the state-of-the-art. Moreover, the linear-quadratic Gaussian (LQG) cost is reduced by more than 13% indicating a control performance improvement in the network.