{
  "id": "1612.05704",
  "version": "v1",
  "published": "2016-12-17T03:58:38.000Z",
  "updated": "2016-12-17T03:58:38.000Z",
  "title": "Finite Codimensional Controllability for Evolution Equations",
  "authors": [
    "Xu Liu",
    "Qi Lu",
    "Xu Zhang"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "Motivated by infinite-dimensional optimal control problems with endpoint state constraints, in this Note, we introduce the notion of finite codimensional exact controllability for evolution equations. It is shown that this new controllability is equivalent to the finite codimensionality condition in the literatures to guarantee Pontryagin's maximum principle. As examples, LQ problems with fixed endpoint state constraints for a wave and a heat equation are analyzed, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-17T03:58:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite codimensional controllability",
      "evolution equations",
      "infinite-dimensional optimal control problems",
      "finite codimensional exact controllability",
      "guarantee pontryagins maximum principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}