{
  "id": "0905.2767",
  "version": "v2",
  "published": "2009-05-17T20:16:21.000Z",
  "updated": "2011-12-01T22:34:08.000Z",
  "title": "Pontryagin Maximum Principle - a generalization",
  "authors": [
    "Janusz Grabowski",
    "Michal Jozwikowski"
  ],
  "comment": "64 pages, a revised and extended version of an article from SIAM Journal on Control and Optimization, 49(3) pp. 1306-1357",
  "journal": "SIAM J. Control Optim. 49 (2011), 1306-1357",
  "categories": [
    "math.OC",
    "math.DG"
  ],
  "abstract": "The fundamental theorem of the theory of optimal control, the Pontryagin maximum principle (PMP), is extended to the setting of almost Lie (AL) algebroids, geometrical objects generalizing Lie algebroids. This formulation of the PMP yields, in particular, a scheme comprising reductions of optimal control problems similar to the reduction for the rigid body in analytical mechanics. On the other hand, in the presented approach the reduced and unreduced PMPs are parts of the same universal formalism. The framework is based on a very general concept of homotopy of measurable paths and the geometry of AL algebroids.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-12-01T22:34:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49K15",
      "49K99",
      "93C25",
      "17B66",
      "22A22"
    ],
    "keywords": [
      "pontryagin maximum principle",
      "generalization",
      "optimal control problems similar",
      "geometrical objects generalizing lie algebroids",
      "fundamental theorem"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 64,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.2767G"
    }
  }
}