Optimal Downlink-Uplink Scheduling of Wireless Networked Control for Industrial IoT
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This paper 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 mode, i.e., can simultaneously receive the sensor's information and transmit its own command to the actuator. In this work, we consider a practical half-duplex controller, which introduces a novel transmission-scheduling problem for WNCSs. A frequent schedule of the sensor's transmission results in a better estimation of the plant states at the controller and thus a higher quality of the control command, but it leads to a less frequent/timely control of the plant. Therefore, considering the overall control performance of the plant, i.e., the average-cost function of the plant, there exists a fundamental tradeoff between the sensor's and controller's transmission. We formulate a new problem to optimize the transmission-scheduling policy that minimizes 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 reliability 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.
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