Age of Loop Oriented Wireless Networked Control System: Communication and Control Co-Design in the FBL Regime

In this paper, age of loop (AoL) is investigated for communication and control co-design in wireless networked control systems (WNCSs), to ensure information freshness in the sensor-controller-actuator loop with two-way delay. Also, the impact of fading channel and finite block length due to limited transmission bits are considered. A closed-form expression for Peak AoL(PAoL) is derived with respect to block length and the number of allowable transmissions in the presence of block error probability. It is shown that the average PAoL is less than the sum of the average peak Age of information (PAoI) in uplink (PAoU) and the PAoI in downlink (PAoD), due to the coupling of uplink and downlink. In addition, the average PAoL is proved to be convex with respect to block length and mono-decreasing with respect to the allowable transmission time. We then propose a low-complexity PAoL-aware block length adaptation scheme with retransmission policy and optimal control. Simulation results verify the correctness of our analytical results and demonstrate the effectiveness of the proposed PAoL-aware block length adaptation scheme in terms of information freshness and control performance.