Optimal Downlink–Uplink Scheduling of Wireless Networked Control for Industrial IoT

This article considers a wireless networked control system (WNCS) consisting of a dynamic system to be controlled (i.e., a plant), a sensor, an actuator, and a remote controller for mission-critical Industrial Internet of Things (IIoT) applications. A WNCS has two types of wireless transmissions, i.e., the sensor's measurement transmission to the controller and the controller's command transmission to the actuator. In the literature of WNCSs, the controllers are commonly assumed to work in a full-duplex (FD) mode by default, i.e., being able to simultaneously receive the sensor's information and transmit its own command to the actuator. In this article, we consider a practical half-duplex (HD) controller, which introduces a novel transmission-scheduling problem for WNCSs. A frequent scheduling of sensor's transmission results in a better estimation of plant states at the controller and thus a higher quality of control command, but it leads to a less frequent/timely control of the plant. Therefore, considering the overall control performance of the plant in terms of its average cost function, there exists a fundamental tradeoff between the sensor's and the controller's transmissions. We formulate a new problem to optimize the transmission-scheduling policy for minimizing the long-term average cost function. We derive the necessary and sufficient condition of the existence of a stationary and deterministic optimal policy that results in a bounded average cost in terms of the transmission reliabilities of the sensor-to-controller and controller-to-actuator channels. Also, we derive an easy-to-compute suboptimal policy, which notably reduces the average cost of the plant compared to a naive alternative-scheduling policy.