{
  "abstract": "This paper extends the least-squares and certainty-equivalence minimum-variance framework of classical linear self-tuning regulators to a broad class of nonlinearly parameterized systems with compact parameter spaces, including commonly used deep neural network models. First, historical nonlinear least-squares fitting guarantees are converted into online one-step prediction bounds under a general modulus of continuity, with explicit regret rates under parameter Lipschitz continuity and finite-moment noise. Second, approximate NLS estimation combined with certainty-equivalence control achieves closed-loop stability and asymptotically optimal tracking under mild conditions without requiring excitation or parameter identifiability. Explicit closed-loop regret and tracking error rates are established in the parameter-Lipschitz case, and closed-loop examples show that the regret rates cannot, in general, be improved for this regulator. Finally, robustness to small unmodeled dynamics is established by showing that closed-loop stability is preserved and the tracking error bounds comprise a vanishing term and a residual term determined by the model discrepancy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35182",
  "author_total": 1,
  "authors": [
    {
      "name": "Haizheng Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d7z09e67b4cch.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35182",
  "fulltext_url": null,
  "id": "d7z09e67b4cch",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35182",
  "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.OC"
    ],
    [
      "openalex",
      "2207|Control Systems and Identification"
    ]
  ],
  "openalex": "W7223879114",
  "pdf_url": "https://arxiv.org/pdf/2610.35182",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d7z09e67b4cch.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35182",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35182"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Adaptive Control for General Nonlinear Stochastic Systems",
  "title_text": "Adaptive Control for General Nonlinear Stochastic Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/d7z09e67b4cch",
  "venue": "arXiv",
  "versions": []
}