{
  "id": "1304.7699",
  "version": "v2",
  "published": "2013-04-29T16:20:29.000Z",
  "updated": "2014-05-19T09:44:35.000Z",
  "title": "Unified formalism for higher-order variational problems and its applications in optimal control",
  "authors": [
    "Leonardo Colombo",
    "Pedro D. Prieto-Martínez"
  ],
  "comment": "28 pp. Revised version: Minor corrections done",
  "journal": "Int. J. Geom. Methods Mod. Phys. 11(4) (2014) 1450034",
  "doi": "10.1142/S0219887814500340",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper we consider an intrinsic point of view to describe the equations of motion for higher-order variational problems with constraints on higher-order trivial principal bundles. Our techniques are an adaptation of the classical Skinner-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. As an interesting application we deduce the equations of motion for optimal control of underactuated mechanical systems defined on principal bundles.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-19T09:44:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70H50",
      "22E70",
      "49J15",
      "53C80"
    ],
    "keywords": [
      "higher-order variational problems",
      "optimal control",
      "unified formalism",
      "application",
      "higher-order trivial principal bundles"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.7699C"
    }
  }
}