Data-driven analysis and control of continuous-time systems under aperiodic sampling

TL;DR

This paper presents a data-driven method for analyzing and designing controllers for continuous-time systems with aperiodic sampling, ensuring stability without explicit system models by using noisy data and robust control techniques.

Contribution

It introduces a novel data-dependent parametrization for all systems consistent with noisy measurements, enabling stability analysis and controller design without explicit models.

Findings

Derived bounds on maximum sampling interval for stability

Designed controllers with large maximum sampling intervals

Guarantees robustness for all systems consistent with data

Abstract

We investigate stability analysis and controller design of unknown continuous-time systems under state-feedback with aperiodic sampling, using only noisy data but no model knowledge. We first derive a novel data-dependent parametrization of all linear time-invariant continuous-time systems which are consistent with the measured data and the assumed noise bound. Based on this parametrization and by combining tools from robust control theory and the time-delay approach to sampled-data control, we compute lower bounds on the maximum sampling interval (MSI) for closed-loop stability under a given state-feedback gain, and beyond that, we design controllers which exhibit a possibly large MSI. Our methods guarantee the stability properties robustly for all systems consistent with the measured data. As a technical contribution, the proposed approach embeds existing methods for sampled-data control into a general robust control framework, which can be directly extended to model-based robust controller design for uncertain time-delay systems under general uncertainty descriptions.