A tangential interpolation framework for the AAA algorithm

Abstract

AbstractInterpolation‐based data‐driven methods, such as the Loewner framework or the Adaptive Antoulas‐Anderson (AAA) algorithm, are established and effective approaches to find a realization of a dynamical system from frequency response data (measurements of the system's transfer function). If a system‐theoretic representation of the original model is not available or unfeasible to evaluate efficiently, such reduced realizations enable effective analysis and simulation. This is especially relevant for models of interconnected dynamical systems, which typically have a high number of inputs and outputs to model their coupling conditions correctly.Tangential interpolation is an established strategy to construct accurate reduced‐order models while ensuring a reasonably small size even if many inputs and/or outputs have to be considered. In this contribution, we evaluate the applicability and effectiveness of data‐driven interpolation methods to compute reduced‐order models of dynamical systems with many inputs and outputs. Additionally, we extend AAA to a tangential interpolation setting and thus enable the use of AAA‐like methods in the context of transfer function interpolation for systems with many inputs and outputs.