Goal-oriented Transmission Scheduling for Energy-Efficient Wireless Networked Control in SAGIN: An AoI-thresholding Mechanism

Addressing the goal-oriented design for mission-critical services like remote control, stands as a pivotal challenge in the space-air-ground integrated network (SAGIN). This paper investigates an energy-efficient wireless networked control system with local and remote controllers in SAGIN. Frequent state transmission from sensor to remote controller would improve the quality of control (QoC) at the expense of nontrivial energy consumption. Nevertheless, such a tradeoff for the considered system has received little attention. In this sense, we propose a goal-oriented transmission scheduling design to balance QoC and energy consumption. In particular, we formulate an optimization problem on minimizing the weighted sum of control cost and power consumption by making decisions about whether to transmit the state or not. By formulating a Markov Decision Process framework, the optimal transmission scheduling policy is proven to have a threshold structure tied to the age of information (AoI). Then, the optimal AoI threshold is obtained by means of a discrete-time Markov chain. Equipped with this, we propose an AoI-thresholding mechanism that can provide insights into when to transmit the state in a computationally-efficient manner. Numerical results shed light on the advantages of the proposed policy over the periodical and greedy transmission policies for the considered system.