Extreme Value Theory based Resource Allocation in Ultra-Reliable Wireless Networked Control Systems

The design of wireless networked control systems (WNCSs) demands precise estimation of the wireless channel for ultra-reliable communication (URC). Even slight discrepancies degrade the communication performance by several orders of magnitude, an unacceptable scenario of URC. Previous studies on evaluating fading channels in the ultra-reliable (UR) region have traditionally relied on the classical statistical methods derived from the central limit theorem, extrapolated to the ultra-reliability regime of operation. In this paper, we propose an extreme value theory (EVT) based methodology to derive the outage probability, and then integrate it into the joint optimization of control and communication systems. First, we derive the outage probability of the UR channel by using its tail statistics through the Generalized Pareto Distribution (GPD) from EVT. Then, we propose a framework for the joint optimization problem with the objective of minimizing power consumption while satisfying the schedulability, rate and reliability constraints of the communication system in the finite blocklength regime and stability constraint of the control system. Decision variables include the sampling period in the control system and blocklength in the communication system. Via extensive simulations, the proposed methodology has been demonstrated to capture the occurrence of rare error events and give a more accurate estimation of the performance as compared to the conventional Rayleigh fading channel under finite blocklength constraints.