Greedy Rational Approximation for Frequency-Domain Model Reduction of Parametric LTI Systems

TL;DR

This paper introduces a greedy reduced basis method for frequency-domain model reduction of parametric LTI systems, enabling efficient low-order rational approximations of high-order systems.

Contribution

It presents a novel greedy algorithm leveraging error estimation for rational approximation, grounded in theoretical insights on rational function approximability.

Findings

Effective low-order rational approximations achieved

Algorithm demonstrates computational efficiency

Framework applicable to high-dimensional parametric systems

Abstract

We investigate model reduction of parametric linear time-invariant (LTI) dynamical systems. When posed in the frequency domain, this problem can be formulated as seeking a low-order rational function approximation of a high-order rational function. We propose to use a standard reduced basis method (RBM) to construct this low-order rational function. Algorithmically, this procedure is an iterative greedy approach, where the greedy objective is evaluated through an error estimator that exploits the linearity of the frequency domain representation. The greedy framework is motivated through theoretical results of rational approximability of functions. This framework provides a principled approach to rational compression of high-order rational functions, and provides a computational pathway for model reduction of parametric LTI systems.