{
  "id": "0912.2033",
  "version": "v1",
  "published": "2009-12-10T16:09:05.000Z",
  "updated": "2009-12-10T16:09:05.000Z",
  "title": "Optimal Control of Underactuated Mechanical Systems: A Geometric Approach",
  "authors": [
    "L. Colombo",
    "D. Martin de Diego",
    "M. Zuccalli"
  ],
  "comment": "20 pages, 2 figures",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, we consider a geometric formalism for optimal control of underactuated mechanical systems. Our techniques are an adaptation of the classical Skinner and Rusk approach for the case of Lagrangian dynamics with higher-order constraints. We study a regular case where it is possible to establish a symplectic framework and, as a consequence, to obtain a unique vector field determining the dynamics of the optimal control problem. These developments will allow us to develop a new class of geometric integrators based on discrete variational calculus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-12-10T16:09:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70H45",
      "70H50",
      "70Q05",
      "49K15",
      "45.20.Jj",
      "02.40.Yy",
      "45.10.Na",
      "02.30.Xx",
      "45.10.Db"
    ],
    "keywords": [
      "underactuated mechanical systems",
      "geometric approach",
      "optimal control problem",
      "discrete variational calculus",
      "higher-order constraints"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1063/1.3456158",
      "journal": "Journal of Mathematical Physics",
      "year": 2010,
      "month": "Aug",
      "volume": 51,
      "number": 8,
      "pages": 3519
    },
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010JMP....51h3519C"
    }
  }
}