{
  "abstract": "Power grids are beginning to host AI data centers whose demand can change abruptly and in a correlated way, and operators and planners must decide whether existing controllers can absorb the resulting transients and where new flexibility is worth installing. We cast this as a question in stochastic control: how far from optimal is an implementable controller? For controlled diffusions with affine, state-independent actuation, additive and possibly degenerate noise and quadratic control cost, any Hamilton-Jacobi-Bellman (HJB) subsolution bounds the optimal cost from below and simulation bounds the deployed cost from above, so their gap certifies the permissible suboptimality. We construct subsolutions from path-integral control by completing the control geometry: enlarging the control Gramian until it matches the physical noise makes the problem linearly solvable, and its Feynman-Kac value is an automatic lower bound whose HJB residual is exactly the energy of the fictitious control. A dual noise-deflation construction can be tighter but requires a curvature condition. The geometry yields planning rules: price control authority in proportion to local noise variance, and use shadow values to guide sparse reinforcement. For nonlinear stochastic swing dynamics of the IEEE 118-bus system after a severe load loss, a simple generator controller is certified within 2.8% of optimal under homogeneous forcing; under heterogeneous forcing the gap is 39% with uniform prices and 1.2% once the same total authority is repriced, before any hardware is added.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03275",
  "author_total": 1,
  "authors": [
    {
      "name": "Michael Chertkov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dj6j2wnbgsgkj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03275",
  "fulltext_url": null,
  "id": "dj6j2wnbgsgkj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03275",
  "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",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "physics.soc-ph"
    ],
    [
      "openalex",
      "2208|Electric Power System Optimization"
    ]
  ],
  "openalex": "W7220441039",
  "pdf_url": "https://arxiv.org/pdf/2610.03275",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dj6j2wnbgsgkj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.03275",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03275"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.soc-ph",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "How suboptimal is my stochastic network controller allowed to be? Completion certificates with application to power grids hosting AI data centers",
  "title_text": "How suboptimal is my stochastic network controller allowed to be? Completion certificates with application to power grids hosting AI data centers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/dj6j2wnbgsgkj",
  "venue": "arXiv",
  "versions": []
}