{
  "abstract": "We prove a new sufficient condition for small-time global exact controllability of finite-dimensional control-affine systems. It points out that, under a natural Lie algebra rank condition, quadratic Lie brackets are the only possible obstacles to controllability. This result extends to infinite-dimensional settings such as the global approximate controllability of diffeomorphisms. It also allows us to interpret recent results in PDE control theory.",
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  "article_type": null,
  "arxiv": "2611.02293",
  "author_total": 2,
  "authors": [
    {
      "name": "Karine Beauchard"
    },
    {
      "name": "Eugenio Pozzoli"
    }
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  "bibtex": "https://research.draconitic.com/paper/51kg386z9zpk2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02293",
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  "pdf_url": "https://hal.science/hal-05847509/document",
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  "published": "2026-11-01",
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  "ris": "https://research.draconitic.com/paper/51kg386z9zpk2.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:20:44Z",
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  "subjects": [
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      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
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  "title": "Small-time controllability of affine systems and quadratic Lie brackets",
  "title_text": "Small-time controllability of affine systems and quadratic Lie brackets",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/51kg386z9zpk2",
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}