Data-driven analysis and controller design for discrete-time systems under aperiodic sampling

TL;DR

This paper develops data-driven methods to estimate the maximum sampling interval and design controllers for discrete-time systems under aperiodic sampling, ensuring stability from finite noisy data.

Contribution

It introduces novel tools for computing and maximizing the maximum sampling interval directly from finite data, using robust and switched systems approaches.

Findings

Tools effectively estimate the MSI from noisy data

Methods enable controller design with guaranteed stability

Comparison shows advantages of the two approaches

Abstract

This article is concerned with data-driven analysis of discrete-time systems under aperiodic sampling, and in particular with a data-driven estimation of the maximum sampling interval (MSI). The MSI is relevant for analysis of and controller design for cyber-physical, embedded and networked systems, since it gives a limit on the time span between sampling instants such that stability is guaranteed. We propose tools to compute the MSI for a given controller and to design a controller with a preferably large MSI, both directly from a finite-length, noise-corrupted state-input trajectory of the system. We follow two distinct approaches for stability analysis, one taking a robust control perspective and the other a switched systems perspective on the aperiodically sampled system. In a numerical example and a subsequent discussion, we demonstrate the efficacy of our developed tools and compare the two approaches.