{
  "abstract": "We study adaptive stabilization of known control-affine systems by treating the current parameterized critic itself as a Lyapunov candidate. Its total derivative contains a parameter-velocity term that can compensate unfavorable state evolution. A projection onto the intersection of a bounded admissible velocity set and one decay halfspace enforces parameter invariance and Lyapunov decrease simultaneously. We give an exact pointwise feasibility test, a conditional state-stability theorem, and a counterexample showing why a positive critic family containing a stabilizing member does not imply persistent feasibility. A convex endpoint constraint provides a distinct sampled implementation. A generic periodic polynomial-factor critic with a local Riccati anchor is evaluated on a force-limited cart-pole without mechanical-energy features, replay training, waypoints, or controller switching. The frozen controller passes stabilization and numerical decay checks on 600 sampled initial states across two draw sets; 400 matched continuous trajectories also pass. Independent reintegration audits and a conservative local feasibility certificate are distinguished from a global or machine-arithmetic guarantee. Compared with nonlinear model-predictive control, the measured implementation uses less CPU but has higher cost, settling time, and cart travel. The results support a conditional adaptive stabilization mechanism.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09988",
  "author_total": 1,
  "authors": [
    {
      "name": "Pavel Osinenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bpetkr8j02nhq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09988",
  "fulltext_url": null,
  "id": "bpetkr8j02nhq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09988",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Adaptive Dynamic Programming Control"
    ]
  ],
  "openalex": "W7220952802",
  "pdf_url": "https://arxiv.org/pdf/2610.09988",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bpetkr8j02nhq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09988",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09988"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Continuous-Time Critic as a Lyapunov Function: Projected Adaptation and Cart-Pole Stabilization",
  "title_text": "Continuous-Time Critic as a Lyapunov Function: Projected Adaptation and Cart-Pole Stabilization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/bpetkr8j02nhq",
  "venue": "arXiv",
  "versions": []
}