Age of Loop for Wireless Networked Control System in the Finite Blocklength Regime: Average, Variance and Outage Probability

Age of information (AoI) is an effective measure of the information freshness for wireless networked control systems (WNCSs). However, the AoI performance for a closed loop of WNCS with two-way delays has remained unexplored, especially in the finite blocklength (FBL) regime. In this paper, we investigate the peak age of loop (PAoL) performances, including the average, variance and outage probability of PAoL, for WNCSs with FBL over fading channels. Their closed-form expressions are respectively derived regarding the blocklength and the maximum number of allowable transmissions. We prove that the average PAoL is less than the sum of the average peak AoI in uplink (UL) and downlink (DL) due to the coupling between UL and DL. We also show that there is a tradeoff between the average PAoL and the variance/outage probability of PAoL. Based on the comprehensive performance analysis, we study a PAoL-oriented communication and control co-design with an adaptation scheme for transmission power, blocklength and the maximum number of allowable transmissions. Simulation results verify the correctness of the analytical results and show that the proposed PAoL-oriented scheme significantly outperforms the UL only and DL only optimization schemes, with an up to 8-fold reduction in the average control cost.