{
  "abstract": "This paper studies controllability and minimal norm control problems (NP problems) for mean-field stochastic differential equation (MF-SDE) systems. We first establish an equivalent rank criterion for terminal controllability, namely, that the diffusion matrices $D$ and $D+\\bar D$ are both of full row rank. We then derive an explicit Riccati-based representation of the minimal norm control by applying a parameterization technique. A key step is to identify the value $P(0)$ of an associated Riccati solution with the controllability Gramian of a controllable auxiliary system, which yields the parameter required in the construction. The resulting representation provides a basis for the future development and analysis of numerical methods for NP problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17825",
  "author_total": 3,
  "authors": [
    {
      "name": "Manfen An"
    },
    {
      "name": "Rui Gao"
    },
    {
      "name": "Yanqing Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bcxhwzhra98nb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17825",
  "fulltext_url": null,
  "id": "bcxhwzhra98nb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17825",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7221815817",
  "pdf_url": "https://arxiv.org/pdf/2610.17825",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bcxhwzhra98nb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17825",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17825"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Minimal norm control problems for linear mean-field control systems",
  "title_text": "Minimal norm control problems for linear mean-field control systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/bcxhwzhra98nb",
  "venue": "arXiv",
  "versions": []
}