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A Weak Notion of Symmetry for Control Systems — arXiv:2609.34173

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.34173
License (as archived): CC0-1.0
Archived: 2026-10-08T00:17:41.840Z
SHA-256 of the archived text: b53e0e03b6f186f7163ff116fe3337044e07f86284cb1b08b34f5c8708d54ecb
Stable URL of this page: https://metraipolis.com/documento/dc_dfd51f4cd658

How to cite

A Weak Notion of Symmetry for Control Systems — arXiv:2609.34173 — arXiv (en), https://arxiv.org/abs/2609.34173 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_dfd51f4cd658 (Metraipolis archive dc_dfd51f4cd658, sha256 b53e0e03b6f186f7163ff116fe3337044e07f86284cb1b08b34f5c8708d54ecb)

BibTeX

@misc{dcdfd51f4cd658,
  title = {A Weak Notion of Symmetry for Control Systems — arXiv:2609.34173},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.34173},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_dfd51f4cd658; sha256 b53e0e03b6f186f7163ff116fe3337044e07f86284cb1b08b34f5c8708d54ecb},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.34173. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Symmetry (or invariance) is a powerful structural property that enables efficient, effective solutions for estimation and control. However, the constraints imposed on a system's dynamics by classical invariance make symmetry a very rigid property, which may be broken by external forces or confined to only a portion of the overall system. Seeking greater flexibility, this work introduces a novel relaxed notion of symmetry, termed ``weak invariance'', in which the non-symmetric part of the dynamics (the ``residual'') can be captured entirely by another control system evolving on the symmetry group. Weakly invariant systems are strictly more general than classical invariant systems, but they nonetheless enjoy many similar favorable properties. In particular, we prove that any weakly invariant system admits a cascade decomposition in which the driven subsystem is group affine, showing that weak symmetry generalizes not only classical symmetry, but also the (thus far distinct) class of group affine systems. We also show that a weak symmetry with autonomous residual can be factored out of the system's error dynamics, enabling yet a greater reduction of dimensionality as compared to classical symmetries. Finally, we study the example of an aerial vehicle under the influence of gravity, for which we propose a nine-dimensional weak symmetry (strictly containing the system's familiar four-dimensional classical symmetry). Weak invariance thus generalizes classical symmetry while also preserving key structural properties, thereby laying a foundation for more flexible methods of symmetry-informed control.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-09-29 in cs.RO).
Categorie arXiv: Systems and Control (eess.SY) ; Robotics (cs.RO).
Pagina del lavoro: https://arxiv.org/abs/2609.34173 — 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 2026-10-07T23:52:16.649Z dalla pagina https://arxiv.org/catchup/cs.RO/2026-09-29?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).