{
  "abstract": "In this paper, we consider the classical time-optimal elevator problem in the presence of higher-order state constraints. The main contribution is a constructive indirect solution framework based on a Pontryagin Maximum Principle specifically formulated for higher-order constrained systems. First, we derive specialized optimality conditions and analyze the resulting structure of extremal trajectories. Second, we show that the infinite-dimensional optimal control problem can be transformed into a finite-dimensional system of nonlinear algebraic equations involving switching times, boundary-contact times, and multiplier parameters. This provides a computationally efficient procedure for calculating candidate optimal trajectories using standard nonlinear equation solvers. Third, we characterize the geometry of boundary contacts and explain the emergence of contact-chattering phenomena in higher-order constrained systems. In particular, we show that normal extremals cannot evolve along the constraint boundary for a positive amount of time, although sequences of boundary contacts may accumulate indefinitely. The proposed approach is demonstrated on a fourth-order elevator model, and the computed solutions are independently verified using a direct IPOPT-based optimization method.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11348",
  "author_total": 4,
  "authors": [
    {
      "name": "Dmitry Karamzin"
    },
    {
      "name": "Aleksandra Zhukova"
    },
    {
      "name": "Roman Chertovskih"
    },
    {
      "name": "Pedro A. Aguiar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1eqmdavtem151.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11348",
  "fulltext_url": null,
  "id": "1eqmdavtem151",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11348",
  "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.NA"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.OC"
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      "openalex",
      "1703|Optimization and Variational Analysis"
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  "openalex": "W7212320012",
  "pdf_url": "https://arxiv.org/pdf/2609.11348",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1eqmdavtem151.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11348",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11348"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Time-optimal elevator control with higher-order state constraints: analysis and computation of boundary contacts",
  "title_text": "Time-optimal elevator control with higher-order state constraints: analysis and computation of boundary contacts",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/1eqmdavtem151",
  "venue": "arXiv",
  "versions": []
}