Practical challenges in data‐driven interpolation: Dealing with noise, enforcing stability, and computing realizations

Abstract

SummaryIn this contribution, we propose a detailed study of interpolation‐based data‐driven methods that are of relevance in the model reduction and also in the systems and control communities. The data are given by samples of the transfer function of the underlying (unknown) model, that is, we analyze frequency‐response data. We also propose novel approaches that combine some of the main attributes of the established methods, for addressing particular issues. This includes placing poles and hence, enforcing stability of reduced‐order models, robustness to noisy or perturbed data, and switching from different rational function representations. We mention here the classical state‐space format and also various barycentric representations of the fitted rational interpolants. We show that the newly‐developed approaches yield, in some cases, superior numerical results, when comparing to the established methods. The numerical results include a thorough analysis of various aspects related to approximation errors, choice of interpolation points, or placing dominant poles, which are tested on some benchmark models and data‐sets.