{
  "id": "1506.08932",
  "version": "v1",
  "published": "2015-06-30T04:23:28.000Z",
  "updated": "2015-06-30T04:23:28.000Z",
  "title": "Optimal Control of Continuity Equations",
  "authors": [
    "Nikolay Pogodaev"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "An optimal control problem for the continuity equation is considered. The aim of a \"controller\" is to maximize the total mass within a target set at a given time moment. The existence of optimal controls is established. For a particular case of the problem, where an initial distribution is absolutely continuous with smooth density and the target set has certain regularity properties, a necessary optimality condition is derived. It is shown that for the general problem one may construct a perturbed problem that satisfies all the assumptions of the necessary optimality condition, and any optimal control for the perturbed problem, is nearly optimal for the original one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-30T04:23:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuity equation",
      "necessary optimality condition",
      "target set",
      "optimal control problem",
      "perturbed problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}