An Analysis on Stabilizability and Reliability Relationship in Wireless Networked Control Systems
Zeinab Askari Donbeh, Mehdi Rasti, Shiva Kazemi Taskooh, Mehdi Monemi
TL;DR
This paper analyzes how wireless channel variability affects the probability of achieving asymptotic stabilizability in wireless networked control systems (WNCS). It defines the probability of stabilizability $\beta$ and the sensor–controller link reliability $\alpha$, and derives a closed-form connection between the product of unstable eigenvalues $\prod_{|\lambda(A)|>1}|\lambda(A)|$ and $\alpha$ under Rayleigh fading: $\alpha = \exp(-\frac{\mathcal{N}_0 \mathcal{L}_0 d^{\eta}}{2\mathcal{P}_t}(\prod_{|\lambda(A)|>1}|\lambda(A)| - 1))$, which yields $\prod_{|\lambda(A)|>1}|\lambda(A)| = -\frac{2\mathcal{P}_t}{\mathcal{N}_0 \mathcal{L}_0 d^{\eta}} \ln \alpha + 1$. The maximum feasible stabilizability probability equals $\alpha$ for given channel parameters. The work also analyzes single- and multi-interference scenarios to produce explicit reliability expressions per link, and numerical results illustrate the exponential sensitivity of stabilizability to system instability, underscoring the need for ultra-reliable, low-latency communications and advanced propagation-control technologies in WNCS applications.
Abstract
The stabilizability of wireless networked control systems (WNCSs) is a deterministic binary valued parameter proven to hold if the communication data rate is higher than the sum of the logarithm of unstable eigenvalues of the open-loop control system. In this analysis, it is assumed that the communication system provides a fixed deterministic transmission rate between the sensors and controllers. Due to the stochastic parameters of communication channels, such as small-scale fading, the instantaneous rate is an intrinsically stochastic parameter. In this sense, it is a common practice in the literature to use the deterministic ergodic rate in analyzing the asymptotic stabilizability. Theoretically, there exists no work in the literature investigating how the ergodic rate can be incorporated into the analysis of asymptotic stabilizability. Considering the stochastic nature of channel parameters, we introduce the concept of probability of stabilizability by interconnecting communication link reliability with the system's unstable eigenvalues and derive a closed-form expression that quantifies this metric. Numerical results are provided to visualize how communication and control systems' parameters affect the probability of stabilizability of the overall system.