{
  "id": "1706.05341",
  "version": "v1",
  "published": "2017-06-16T16:39:33.000Z",
  "updated": "2017-06-16T16:39:33.000Z",
  "title": "Taylor Expansions of the Value Function Associated with a Bilinear Optimal Control Problem",
  "authors": [
    "Tobias Breiten",
    "Karl Kunisch",
    "Laurent Pfeiffer"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "A general bilinear optimal control problem subject to an infinite-dimensional state equation is considered. Polynomial approximations of the associated value function are derived around the steady state by repeated formal differentiation of the Hamilton-Jacobi-Bellman equation. The terms of the approximations are described by multilinear forms, which can be obtained as solutions to generalized Lyapunov equations with recursively defined right-hand sides. They form the basis for defining a suboptimal feedback law. The approximation properties of this feedback law are investigated. An application to the optimal control of a Fokker-Planck equation is also provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-16T16:39:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "value function",
      "taylor expansions",
      "general bilinear optimal control problem",
      "bilinear optimal control problem subject",
      "feedback law"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}