{
  "id": "2203.03070",
  "version": "v1",
  "published": "2022-03-06T23:21:43.000Z",
  "updated": "2022-03-06T23:21:43.000Z",
  "title": "Goh conditions for minima of nonsmooth problems with unbounded controls",
  "authors": [
    "Francesca Angrisani",
    "Franco Rampazzo"
  ],
  "categories": [
    "math.OC",
    "math.DS"
  ],
  "abstract": "Higher order necessary conditions for a minimizer of an optimal control problem are generally obtained for systems whose dynamics is continuously differentiable in the state variable. Here, by making use of the notion of set-valued Lie bracket we obtain a Goh-type condition for a control affine system with Lipschitz continuous dynamics and unbounded controls. In order to manage the simultaneous lack of smoothness of the adjoint equation and of the Lie bracket-like variations we make use of the notion of Quasi Differential Quotient. We conclude the paper with a worked out example where the established higher order condition is capable to rule out the optimality of a control verifying the standard maximum principle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-06T23:21:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unbounded controls",
      "goh conditions",
      "nonsmooth problems",
      "higher order necessary conditions",
      "optimal control problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}