An Analysis on Stabilizability and Reliability Relationship in Wireless Networked Control Systems

2025-01-08

AI Summary

To address the challenge of jointly modeling communication reliability and closed-loop stability in wireless networked control systems (WNCS), this paper introduces the novel concept of “stability probability,” which for the first time explicitly links channel randomness—such as small-scale fading—to the eigenvalue dynamics of the controlled system. Leveraging a unified framework integrating stochastic processes, ergodic capacity theory, and linear system stability analysis, we derive a closed-form analytical expression for stability probability, thereby transcending conventional deterministic-rate-based stability criteria. Simulation results quantitatively characterize the impact of signal-to-noise ratio, fading distribution, and system pole locations on stability probability. This work establishes a joint probabilistic characterization of communication reliability and control stability, yielding a computationally tractable and optimization-friendly design criterion for robust WNCS synthesis.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Social Networks and Social Media: Social media analysis through the lenses of networks
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Wireless Networked Control Systems
• Stability-Reliability Relationship
• Average Information Rate

Innovation

• Probabilistic Stability
• Wireless Network Control Systems (WNCSs)
• Communication Reliability