{
  "id": "2107.11941",
  "version": "v1",
  "published": "2021-07-26T03:30:08.000Z",
  "updated": "2021-07-26T03:30:08.000Z",
  "title": "Computation of Reachable Sets Based on Hamilton-Jacobi-Bellman Equation with Running Cost Function",
  "authors": [
    "Wei Liao",
    "Taotao Liang",
    "Xiaohui Wei",
    "Jizhou Lai"
  ],
  "categories": [
    "eess.SY",
    "cs.SY",
    "math.OC"
  ],
  "abstract": "A novel method for computing reachable sets is proposed in this paper. In the proposed method, a Hamilton-Jacobi-Bellman equation with running cost functionis numerically solved and the reachable sets of different time horizons are characterized by a family of non-zero level sets of the solution of the Hamilton-Jacobi-Bellman equation. In addition to the classical reachable set, by setting different running cost functions and terminal conditionsof the Hamilton-Jacobi-Bellman equation, the proposed method allows to compute more generalized reachable sets, which are referred to as cost-limited reachable sets. In order to overcome the difficulty of solving the Hamilton-Jacobi-Bellman equation caused by the discontinuity of the solution, a method based on recursion and grid interpolation is employed. At the end of this paper, some examples are taken to illustrate the validity and generality of the proposed method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-26T03:30:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reachable set",
      "hamilton-jacobi-bellman equation",
      "computation",
      "non-zero level sets",
      "time horizons"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}