On Loewner data-driven control for infinite-dimensional systems

TL;DR

This paper extends the Loewner Data-Driven Control methodology for infinite-dimensional systems by integrating AAA and VF approximation methods, and enhances robustness against data noise and uncertainties.

Contribution

It introduces novel extensions to L-DDC by incorporating AAA and VF algorithms, and addresses robustness to noise and uncertainties in data-driven control.

Findings

Enhanced control design flexibility with AAA and VF methods.

Improved robustness to noisy data and model uncertainties.

Demonstrated effectiveness on infinite-dimensional systems.

Abstract

In this paper, we address extensions of the Loewner Data-Driven Control (L-DDC) methodology. First, this approach is extended by incorporating two alternative approximation methods known as Adaptive-Antoulas-Anderson (AAA) and Vector Fitting (VF). These algorithms also include least squares fitting which provides additional flexibility and enables possible adjustments for control tuning. Secondly, the standard model reference data-driven setting is extended to handle noise affecting the data and uncertainty in the closed-loop objective function. These proposed adaptations yield a more robust data-driven control design.