Interpolation-based irrational model control design and stability analysis

TL;DR

This paper explores how Loewner-based interpolation can be used to approximate irrational models with rational ones for control design and stability analysis, demonstrating its effectiveness in data-driven control methods.

Contribution

It introduces an interpolation framework that enables control design and stability analysis directly from data for irrational models, bridging model approximation and control.

Findings

Loewner-based interpolation effectively approximates irrational models with rational ones.

The framework allows for direct data-driven control design with comparable results to model-based methods.

It provides a method to estimate stability of irrational models interconnected with rational controllers.

Abstract

The versatility of data-driven approximation by interpolatory methods, originally settled for model approximation purpose, is illustrated in the context of linear controller design and stability analysis of irrational models. To this aim, following an academic driving example described by a linear partial differential equation, it is shown how the Loewner-based interpolation may be an essential ingredient for control design and stability analysis. More specifically, the interpolatory framework is first used to approximate the irrational model by a rational one that can be used for model-based control, and secondly, it is used for direct data-driven control design, showing equivalent results. Finally, this interpolation framework is employed for estimating the stability of the interconnection of the irrational model with a rational controller.