HARQ Based Optimal Scheduling Strategy for Multi-Loop WNCS

This paper presents a Hybrid Automatic Repeat Request (HARQ) based scheduling scheme for a multi-loop Wireless Networked Control System (WNCS). For each single-loop system in the multi-loop system, it includes uplink transmission and downlink transmission. By considering a practical application scenario, we formulate a mathematical model wherein the downlink transmission can be assumed ideal, and the uplink transmission updates the new system status which is used to generate control commands. Due to the resource constraints, not all single-loop systems can update their status information in the same time slot. Meanwhile, using the HARQ mechanism can ensure a higher probability of successful transmission. To achieve the stability of the system, we propose a scheduling strategy to minimize the long-term average Mean Square Error (MSE) of the plant state. And we model the optimization problem as a Markov Decision Process (MDP) problem to obtain the optimal strategy. For the case that the channel error rates change rapidly, we propose the Lyapunov optimization strategy. And through further analysis, the Lyapunov optimization strategy is a suboptimal strategy, it can achieve the performance approach to the optimal strategy.