{
  "abstract": "We consider minimum-time control for the linear system $$ \\dot{z}(t)=Az(t)+Bu(t),\\qquad \\|u\\|_{L^\\infty(0,\\infty;\\mathbb{R}^m)}\\leq 1, $$ with $A\\in\\mathbb R^{n\\times n}$ and $B\\in\\mathbb R^{n\\times m}$. While the individual point-target and ball-target problems are classical, we study a different question: when are their optimal controls exactly compatible, in the sense that, for every nonzero initial state $x$ and all sufficiently small $\\varepsilon>0$, the optimal control for the tolerance ball $\\overline{B}_\\varepsilon(0)$ is precisely the restriction of the point-target optimal control? We prove that this {\\it{exact truncation}} property is equivalent to the rigidity conditions $$ B B^\\top=βI_n,\\qquad A+A^\\top=2aI_n, \\qquad β>0,\\; a\\leq 0, $$ and also to Euclidean radiality of the point-target minimum-time function. Thus exact truncation holds precisely when the sublevel sets of the point-target minimum-time function are Euclidean balls centered at the origin, matching the geometry of the tolerance targets. Moreover, the local property automatically extends to every $0<\\varepsilon<|x|$, and the resulting optimal times and point-target optimal feedback are both explicit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22802",
  "author_total": 4,
  "authors": [
    {
      "name": "Changqin Quan"
    },
    {
      "name": "Gengsheng Wang"
    },
    {
      "name": "Lijuan Wang"
    },
    {
      "name": "Qishu Yan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ds80wtgw79ssp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22802",
  "fulltext_url": null,
  "id": "ds80wtgw79ssp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22802",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Advanced Control Systems Optimization"
    ]
  ],
  "openalex": "W7214045571",
  "pdf_url": "https://arxiv.org/pdf/2609.22802",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ds80wtgw79ssp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22802",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22802"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Exact Truncation and Radial Rigidity in Time-Optimal Control",
  "title_text": "Exact Truncation and Radial Rigidity in Time-Optimal Control",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/ds80wtgw79ssp",
  "venue": "arXiv",
  "versions": []
}