The p-AAA algorithm for data driven modeling of parametric dynamical systems
Abstract
The AAA algorithm has become a popular tool for data-driven rational approximation of single variable functions, such as transfer functions of a linear dynamical system. In the setting of parametric dynamical systems appearing in many prominent applications, the underlying (transfer) function to be modeled is a multivariate function. With this in mind, we develop the AAA framework for approximating multivariate functions where the approximant is constructed in the multivariate barycentric form. The method is data-driven, in the sense that it does not require access to full state-space model and requires only function evaluations. We discuss an extension to the case of matrix-valued functions, i.e., multi-input/multi-output dynamical systems, and provide a connection to the tangential interpolation theory. Several numerical examples illustrate the effectiveness of the proposed approach.
Cite
@article{arxiv.2003.06536,
title = {The p-AAA algorithm for data driven modeling of parametric dynamical systems},
author = {Andrea Carracedo Rodriguez and Linus Balicki and Serkan Gugercin},
journal= {arXiv preprint arXiv:2003.06536},
year = {2022}
}