Metraipolis › archive › dc_4bc56fe5b402

Demystifying Linear Operator Learning for Control Systems — arXiv:2609.19428

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.19428
License (as archived): CC0-1.0
Archived: 2026-10-10T04:09:12.725Z
SHA-256 of the archived text: 058ae355511e9a53307be57b38119ede63837c88db7656145872c2313f411c9d
Stable URL of this page: https://metraipolis.com/documento/dc_4bc56fe5b402

How to cite

Demystifying Linear Operator Learning for Control Systems — arXiv:2609.19428 — arXiv (en), https://arxiv.org/abs/2609.19428 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_4bc56fe5b402 (Metraipolis archive dc_4bc56fe5b402, sha256 058ae355511e9a53307be57b38119ede63837c88db7656145872c2313f411c9d)

BibTeX

@misc{dc4bc56fe5b402,
  title = {Demystifying Linear Operator Learning for Control Systems — arXiv:2609.19428},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.19428},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_4bc56fe5b402; sha256 058ae355511e9a53307be57b38119ede63837c88db7656145872c2313f411c9d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.19428. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

This paper proposes a structured approach to learning linear operators for control systems from data. We address both structural and learning-theoretic aspects of the problem. To derive structural assumptions, we propose using the well-established framework of (semi)groups for evolution equations, as operators in control systems are of the same type. Further, we propose analyzing learning algorithms through the lens of the inverse problems framework. This reveals how a learned model depends on the data via error decompositions, convergence guarantees, and optimal regularization -- enabling us to compare existing methods and derive provably advantageous algorithms. In order to obtain these results, we restrict our scope to bounded operators on Hilbert spaces. Although this may appear restrictive, existing approaches often make this assumption implicitly to obtain matrix-like representations. We demonstrate the power of using these frameworks by deriving a convergent estimator for time-varying systems.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-18 in cs.LG).
Categorie arXiv: Systems and Control (eess.SY) ; Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2609.19428 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-10T03:48:18.394Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-09-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).