{
  "abstract": "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.",
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  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28582",
  "author_total": 2,
  "authors": [
    {
      "name": "Karine Beauchard"
    },
    {
      "name": "Frédéric Marbach"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3za1641akrywt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28582",
  "fulltext_url": null,
  "id": "3za1641akrywt",
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  "landing_url": "https://arxiv.org/abs/2608.28582",
  "language": "en",
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
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      "2207|Control and Stability of Dynamical Systems"
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  "openalex": "W7204767318",
  "pdf_url": "https://arxiv.org/pdf/2608.28582",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3za1641akrywt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.28582",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28582"
    },
    {
      "first_seen": "2026-10-30T12:17:43Z",
      "native_id": "hal-05769620",
      "source": "hal",
      "url": "https://hal.science/hal-05769620v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Some quartic control results for scalar-input systems",
  "title_text": "Some quartic control results for scalar-input systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:43Z",
  "url": "https://research.draconitic.com/paper/3za1641akrywt",
  "venue": "arXiv",
  "versions": []
}