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Some quartic control results for scalar-input systems — arXiv:2608.28582

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.28582
License (as archived): CC0-1.0
Archived: 2026-10-17T11:17:52.902Z
SHA-256 of the archived text: ca932fdbb22adbdfbdb30e8cd56a9b5d4de845d80c6db6fa3d92d049b02f2066
Stable URL of this page: https://metraipolis.com/documento/dc_00a281b8e05b

How to cite

Some quartic control results for scalar-input systems — arXiv:2608.28582 — arXiv (en), https://arxiv.org/abs/2608.28582 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_00a281b8e05b (Metraipolis archive dc_00a281b8e05b, sha256 ca932fdbb22adbdfbdb30e8cd56a9b5d4de845d80c6db6fa3d92d049b02f2066)

BibTeX

@misc{dc00a281b8e05b,
  title = {Some quartic control results for scalar-input systems — arXiv:2608.28582},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.28582},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_00a281b8e05b; sha256 ca932fdbb22adbdfbdb30e8cd56a9b5d4de845d80c6db6fa3d92d049b02f2066},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.28582. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We investigate the role of quartic terms in the small-time local controllability of scalar-input systems. First, we prove a new sufficient condition for controllability, which exploits simultaneously more good quartic Lie brackets than previous results. Second, we identify a family of quartic obstructions to controllability, relying on Lie brackets whose coordinates of the second kind are positive-definite functionals of the control. Third, we show that the complementarity of these results can be seen as an answer to Kawski's 1987 open problem concerning the construction of a Hall basis which somehow separates good and bad quartic brackets. We give examples and remarks illustrating some of the intricacies of these notions.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-31 in math.OC).
Categorie arXiv: Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2608.28582 — 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 2026-10-17T10:58:16.484Z dalla pagina https://arxiv.org/catchup/math.OC/2026-08-31?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).