{
  "id": "2506.17610",
  "version": "v1",
  "published": "2025-06-21T06:23:22.000Z",
  "updated": "2025-06-21T06:23:22.000Z",
  "title": "The Dirac--Bergmann approach to optimal control theory",
  "authors": [
    "Davit Aghamalyan",
    "Aleek Maity",
    "Varun Narasimhachar",
    "V V Sreedhar"
  ],
  "comment": "25+2 pages",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP",
    "physics.class-ph"
  ],
  "abstract": "We present a novel framework for optimal control in both classical and quantum systems. Our approach leverages the Dirac--Bergmann algorithm: a systematic method for formulating and solving constrained dynamical systems. In contrast to the standard Pontryagin principle, which is used in control theory, our approach bypasses the need to perform a variation to obtain the optimal solution. Instead, the Dirac--Bergmann algorithm generates the optimal solution dynamically. The efficacy of our framework is demonstrated through two quintessential examples: the classical and quantum brachistochrone problems, the latter relevant for quantum technological applications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-06-21T06:23:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal control theory",
      "dirac-bergmann approach",
      "optimal solution",
      "quantum brachistochrone problems",
      "dirac-bergmann algorithm generates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 2,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}