{
  "id": "math/0604072",
  "version": "v1",
  "published": "2006-04-04T13:43:34.000Z",
  "updated": "2006-04-04T13:43:34.000Z",
  "title": "Symbolic Computation of Variational Symmetries in Optimal Control",
  "authors": [
    "Paulo D. F. Gouveia",
    "Delfim F. M. Torres",
    "Eugenio A. M. Rocha"
  ],
  "comment": "Presented at the 4th Junior European Meeting on \"Control and Optimization\", Bialystok Technical University, Bialystok, Poland, 11-14 September 2005. Accepted (24-Feb-2006) to Control & Cybernetics",
  "journal": "Control Cybernet. 35 (2006), no. 4, 831--849.",
  "categories": [
    "math.OC"
  ],
  "abstract": "We use a computer algebra system to compute, in an efficient way, optimal control variational symmetries up to a gauge term. The symmetries are then used to obtain families of Noether's first integrals, possibly in the presence of nonconservative external forces. As an application, we obtain eight independent first integrals for the sub-Riemannian nilpotent problem (2,3,5,8).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-04T13:43:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49K15",
      "49-04",
      "49S05"
    ],
    "keywords": [
      "symbolic computation",
      "optimal control variational symmetries",
      "sub-riemannian nilpotent problem",
      "noethers first integrals",
      "computer algebra system"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4072G"
    }
  }
}