Least Squares Model Reduction: A Two-Stage System-Theoretic Interpretation

TL;DR

This paper offers a new two-stage system-theoretic interpretation of least squares model reduction, enhancing understanding of classical methods through surrogate modeling and projection techniques.

Contribution

It introduces a novel two-step framework for least squares model reduction using output regulation and Krylov projections, providing deeper theoretical insights.

Findings

Reinterprets least squares model reduction as a two-stage process

Connects classical methods with system-theoretic tools

Provides new insights into the structure of existing algorithms

Abstract

Model reduction simplifies complex dynamical systems while preserving essential properties. This paper revisits a recently proposed system-theoretic framework for least squares moment matching. It interprets least squares model reduction in terms of two steps process: constructing a surrogate model to satisfy interpolation constraints, then projecting it onto a reduced-order space. Using tools from output regulation theory and Krylov projections, this approach provides a new view on classical methods. For illustration, we reexamine the least-squares model reduction method by Lucas and Smith, offering new insights into its structure.