{
  "abstract": "This paper develops a constrained linear-quadratic (LQ) optimal control framework within the behavioral approach. Unlike classical formulations that rely on state-input representations, our method treats both the system dynamics and the constraints as trajectory-level objects. The system is modeled through a kernel representation, while inequality constraints are captured using behavioral inequalities defined over infinite-dimensional convex cones. Using quadratic differential forms (QDFs) to encode performance indices, we formulate the constrained LQ problem as a convex variational optimization over trajectories. By employing Gateaux differentials, we derive the stationarity and complementarity conditions and show that they admit a representation as an augmented behavioral system whose unique decomposition into autonomous and controllable sub-behaviors yields a complete parameterization of all optimal constrained trajectories. The resulting conditions constitute a behavioral analogue of the Karush-Kuhn-Tucker (KKT) framework. A numerical example illustrates the effect of inequality constraints on the optimal behavior. The framework provides a general, trajectory-level representation for constrained optimal control and opens avenues for closed-loop and data-driven extensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40542",
  "author_total": 3,
  "authors": [
    {
      "name": "Soutrik Bandyopadhyay"
    },
    {
      "name": "Debasattam Pal"
    },
    {
      "name": "Shubhendu Bhasin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3er30p89b0185.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40542",
  "fulltext_url": null,
  "id": "3er30p89b0185",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40542",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40542",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3er30p89b0185.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:35Z",
      "native_id": "2610.40542",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40542"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A Behavioral approach to Constrained Linear Quadratic Control: Feasibility and Optimality",
  "title_text": "A Behavioral approach to Constrained Linear Quadratic Control: Feasibility and Optimality",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:53Z",
  "url": "https://research.draconitic.com/paper/3er30p89b0185",
  "venue": "arXiv",
  "versions": []
}