Data-Driven Model Reduction by Two-Sided Moment Matching

TL;DR

This paper introduces a data-driven approach for model order reduction of linear systems using two-sided moment matching, leveraging time-domain samples to approximate key matrices and construct reduced models.

Contribution

It presents a novel algorithm that asymptotically approximates the matrix product from time-domain data to achieve two-sided moment matching for model reduction.

Findings

Algorithm effectively approximates the matrix product from samples.

Reduced models match moments at specified interpolation points.

Method's robustness analyzed under disturbances and data distortions.

Abstract

In this brief paper, we propose a time-domain data-driven method for model order reduction by two-sided moment matching for linear systems. An algorithm that asymptotically approximates the matrix product $\Upsilon \Pi$ from time-domain samples of the so-called two-sided interconnection is provided. Exploiting this estimated matrix, we determine the unique reduced-order model of order $\nu$, which asymptotically matches the moments at $2 \nu$ distinct interpolation points. Furthermore, we discuss the impact that certain disturbances and data distortions may have on the algorithm. Finally, we illustrate the use of the proposed methodology by means of a benchmark model.