The model reduction problem for (single-input, single-output) linear and nonlinear systems
is addressed using the notion of moment. A re-visitation of the linear theory allows to obtain …

Abstract Theory and methods to obtain reduced order models by moment matching from
input/output data are presented. Algorithms for the estimation of the moments of linear and …

Mathematical models are at the core of modern science and technology. An accurate
description of behaviors, systems and processes often requires the use of complex models …

This paper discusses balanced realization and model order reduction for both continuous-
time and discrete-time general nonlinear systems based on singular value analysis of the …

In this survey we present in an organic, complete, and accessible style the interconnection
framework for model order reduction. While this framework originally started as a revisitation …

Data-driven reduced-order models often fail to make accurate forecasts of high-dimensional
nonlinear dynamical systems that are sensitive along coordinates with low-variance …

We introduce a data-driven model approximation method for nonlinear control systems,
drawing on recent progress in machine learning and statistical-dimensionality reduction …

Nonlinear balanced truncation is a model order reduction technique that reduces the
dimension of nonlinear systems in a manner that accounts for either open-or closed-loop …

We introduce a data-based approach to estimating key quantities which arise in the study of
nonlinear control systems and random nonlinear dynamical systems. Our approach hinges …

Reduced-order models of the nonlinear complex Ginzburg–Landau (CGL) equation are
computed using a nonlinear generalization of balanced truncation. The method involves …