An Adaptation of the AAA-Interpolation Algorithm for Model Reduction of MIMO Systems

TL;DR

This paper adapts the AAA-interpolation algorithm for MIMO system model reduction, addressing its limitations by developing a low-rank adaptive method that maintains efficiency and compares favorably with balanced reduction.

Contribution

The paper introduces a low-rank adaptive interpolation algorithm for MIMO systems that overcomes the state-space dimension growth issue of previous methods.

Findings

The new algorithm reduces state-space dimension growth.

Comparative results show improved efficiency over block-AAA.

Performance is comparable or better than balanced reduction.

Abstract

We consider the Adaptive Antoulas-Anderson (AAA) rational interpolation algorithm recently developed by Trefethen and co-authors, which can be viewed as a type of moment-matching technique for system realization and approximation. We consider variations on this algorithm that are suitable for model reduction of linear time invariant systems while addressing some of the shortcomings of the block-AAA variant of the algorithm for MIMO systems. In particular, we develop state-space formulas and keep track of the state-space dimension at every step of the adaptive block-AAA algorithm, showing an unfavorable increase of the state dimension. We propose a new low-rank adaptive interpolation algorithm that addresses this shortcoming. Comparative computational results are included for the algorithms above, together with comparisons to balanced reduction.