Uncorrelated Packet Loss Model for Networked Control Systems with $\mathcal{H}_{\infty}$ Design Constraint

Networked Controlled Systems (NCS) are control systems that rely on the performance of the communications to ensure a desired Quality-of-Control (QoC). However, the wireless link is imperfect; the packet has an intrinsic latency, and packets can be lost due to its stochastic nature. Although the newest generation of wireless networks (5G and beyond) can provide Ultra-Reliable Low Latency Communications (URLLC) to attempt to remove the problems caused by the wireless network. This methodology is expensive in terms of communications resources, and for NCS, the constant stream of data could be spared since some updates might contain similar information. Although there are multiple methodologies to design a NCS, not many methods attempt to develop the communications system based on reducing the consumption of communications resources. Therefore, this work finds the maximum transmission interval and delay to optimize the maximum peak Age-of-Information (AoI) while getting a model of the Maximum Allowable Packet Loss Probability (MAPLP) for the case that the
$\mathcal{H}_{\infty}$
norm of the control system must be maintained lower than a specified threshold. Finally, the model is validated in the case of platooning using Cooperative Adaptive Cruise Control (CACC), showing a high accuracy compared to the results of the solution of the optimization problem.