Moment matching by kernel-based learning
File(s)
Published version
Author(s)
Moreschini, Alessio
Scandella, Matteo
Astolfi, Alessandro
Parisini, Thomas
Type
Journal Article
Abstract
In this article, we introduce a kernel-based moment matching theory that relies upon a novel data-driven model reduction method, employing the estimation of moments within a reproducing kernel Hilbert space. We demonstrate that moment estimation can be enhanced by appropriately tuning the regularization term, regardless of the kernel choice. In addition, we present conditions to ensure that the reproducing kernel Hilbert space contains only functions, which are bona fide moments. While exact moment matching with finite data is impractical in this scenario, we introduce the concepts of weak moment matching and moment matching almost everywhere onto the L2-space. In addition, we address scenarios in which the dataset contains noisy measurements of outputs that are not yet in a steady state, which typically biases the estimation due to the effect of the output transients. We further prove that estimating over a reproducing kernel Hilbert space can ensure weak moment matching asymptotically and, with additional assumptions, also moment matching almost everywhere despite these transients. Finally, we provide a probabilistic bound that guarantees weak moment matching for an arbitrarily finite amount of data.
Date Issued
2026-04-01
Date Acceptance
2025-10-01
Citation
IEEE Transactions on Automatic Control, 2026, 71 (4), pp.2123-2138
ISSN
0018-9286
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Start Page
2123
End Page
2138
Journal / Book Title
IEEE Transactions on Automatic Control
Volume
71
Issue
4
Copyright Statement
© 2025 The Authors. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. For more information, see https://creativecommons.org/licenses/by-nc-nd/4.0/
Publication Status
Published
Date Publish Online
2025-10-06