A modified AAA algorithm for learning stable reduced-order models from data

TL;DR

This paper introduces stabAAA, an enhanced AAA algorithm that guarantees stability in reduced-order models of LTI systems by incorporating convex constraints, improving reliability in data-driven model reduction.

Contribution

The paper develops a novel algebraic stability characterization and integrates it into AAA, ensuring stable ROMs in a data-driven model reduction framework.

Findings

stabAAA guarantees stability of ROMs

Experimental validation shows improved stability and accuracy

Algorithm effectively applies to large-scale LTI systems

Abstract

In recent years, the Adaptive Antoulas-Anderson AAA algorithm has established itself as the method of choice for solving rational approximation problems. Data-driven Model Order Reduction (MOR) of large-scale Linear Time-Invariant (LTI) systems represents one of the many applications in which this algorithm has proven to be successful since it typically generates reduced-order models (ROMs) efficiently and in an automated way. Despite its effectiveness and numerical reliability, the classical AAA algorithm is not guaranteed to return a ROM that retains the same structural features of the underlying dynamical system, such as the stability of the dynamics. In this paper, we propose a novel algebraic characterization for the stability of ROMs with transfer function obeying the AAA barycentric structure. We use this characterization to formulate a set of convex constraints on the free coefficients of the AAA model that, whenever verified, guarantee by construction the asymptotic stability of the resulting ROM. We suggest how to embed such constraints within the AAA optimization routine, and we validate experimentally the effectiveness of the resulting algorithm, named stabAAA, over a set of relevant MOR applications.