{
  "id": "1310.6179",
  "version": "v1",
  "published": "2013-10-23T11:00:27.000Z",
  "updated": "2013-10-23T11:00:27.000Z",
  "title": "Null controllability of the heat equation using flatness",
  "authors": [
    "Philippe Martin",
    "Lionel Rosier",
    "Pierre Rouchon"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1303.2344, arXiv:1304.5426",
  "categories": [
    "math.OC",
    "math.AP"
  ],
  "abstract": "We derive in a direct and rather straightforward way the null controllability of the N-dimensional heat equation in a bounded cylinder with boundary control at one end of the cylinder. We use the so-called flatness approach, which consists in parameterizing the solution and the control by the derivatives of a \"flat output\". This yields an explicit control law achieving the exact steering to zero. Replacing the involved series by partial sums we obtain a simple numerical scheme for which we give explicit error bounds. Numerical experiments demonstrate the relevance of the approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-23T11:00:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "null controllability",
      "explicit error bounds",
      "n-dimensional heat equation",
      "simple numerical scheme",
      "boundary control"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.6179M"
    }
  }
}