{
  "id": "1210.4281",
  "version": "v2",
  "published": "2012-10-16T07:37:25.000Z",
  "updated": "2012-12-11T10:18:12.000Z",
  "title": "Asymptotic controllability and optimal control",
  "authors": [
    "Monica Motta",
    "Franco Rampazzo"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "We consider a control problem where the state must reach asymptotically a target while paying an integral payoff with a non-negative Lagrangian. The dynamics is just continuous, and no assumptions are made on the zero level set of the Lagrangian. Through an inequality involving a positive number $\\bar p_0$ and a Minimum Restraint Function $U=U(x)$ --a special type of Control Lyapunov Function-- we provide a condition implying that (i) the control system is asymptotically controllable, and (ii) the value function is bounded above by $U/\\bar p_0$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-12-11T10:18:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal control",
      "asymptotic controllability",
      "minimum restraint function",
      "zero level set",
      "control lyapunov"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.jde.2013.01.006",
      "journal": "Journal of Differential Equations",
      "year": 2013,
      "volume": 254,
      "number": 7,
      "pages": 2744
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013JDE...254.2744M"
    }
  }
}