{
  "id": "1608.00828",
  "version": "v1",
  "published": "2016-07-31T06:58:28.000Z",
  "updated": "2016-07-31T06:58:28.000Z",
  "title": "The continuity and uniqueness of the value function of the hybrid optimal control problem with reach time to a target set",
  "authors": [
    "Myong-Song Ho",
    "Kwang-Nam Oh",
    "Chol-Jun Hwang"
  ],
  "comment": "19 pages",
  "categories": [
    "math.OC",
    "cs.SY"
  ],
  "abstract": "The hybrid optimal control problem with reach time to a target set is addressed and the continuity and uniqueness of the associated value function is proved. Hybrid systems involves interaction of different types of dynamics: continuous and discrete dynamics. The state ofa continuous system is evolved by an ordinary differential equation until the trajectory hits the predefined jump sets: an autonomous jump set and a controlled jump set . At each jump the trajectory is moved discontinuously to another Euclidean space by a discrete system. We study the hybrid optimal control problem with reach time to a target set, prove the continuity of the associated value function with respect to the initial point under the assumption that is lower semicontinuous on the boundary of a target set, and also characterize it as an unique solution of a quasi-variational inequality in a viscosity sense using the dynamic programming principle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-31T06:58:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hybrid optimal control problem",
      "target set",
      "reach time",
      "continuity",
      "jump set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}