{
  "id": "2308.08202",
  "version": "v1",
  "published": "2023-08-16T08:06:52.000Z",
  "updated": "2023-08-16T08:06:52.000Z",
  "title": "Norm and time optimal control problems of stochastic heat equations",
  "authors": [
    "Yuanhang Liu",
    "Donghui Yang",
    "Jie Zhong"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "This paper investigates the norm and time optimal control problems for stochastic heat equations. We begin by presenting a characterization of the norm optimal control, followed by a discussion of its properties. We then explore the equivalence between the norm optimal control and time optimal control, and subsequently establish the bang-bang property of the time optimal control. These problems, to the best of our knowledge, are among the first to discuss in the stochastic case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-16T08:06:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J21",
      "93B05",
      "93E20"
    ],
    "keywords": [
      "time optimal control problems",
      "stochastic heat equations",
      "norm optimal control",
      "bang-bang property",
      "stochastic case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}