Statistical Learning for Analysis of Networked Control Systems over Unknown Channels

TL;DR

This paper develops data-driven algorithms to assess the stability of networked control systems over unknown channels, quantifying the number of channel samples needed for high-confidence stability verification.

Contribution

It introduces the first analysis linking sample complexity of channel data to the stability verification of networked control systems, using concentration inequalities.

Findings

Sample complexity depends on system stability margin and channel success rate.

High confidence stability verification requires a large number of channel samples.

Verifying stability becomes impractical for systems with low success rates or large dynamics.

Abstract

Recent control trends are increasingly relying on communication networks and wireless channels to close the loop for Internet-of-Things applications. Traditionally these approaches are model-based, i.e., assuming a network or channel model they are focused on stability analysis and appropriate controller designs. However the availability of such wireless channel modeling is fundamentally challenging in practice as channels are typically unknown a priori and only available through data samples. In this work we aim to develop algorithms that rely on channel sample data to determine the stability and performance of networked control tasks. In this regard our work is the first to characterize the amount of channel modeling that is required to answer such a question. Specifically we examine how many channel data samples are required in order to answer with high confidence whether a given networked control system is stable or not. This analysis is based on the notion of sample complexity from the learning literature and is facilitated by concentration inequalities. Moreover we establish a direct relation between the sample complexity and the networked system stability margin, i.e., the underlying packet success rate of the channel and the spectral radius of the dynamics of the control system. This illustrates that it becomes impractical to verify stability under a large range of plant and channel configurations. We validate our theoretical results in numerical simulations.