{
  "id": "1401.7798",
  "version": "v1",
  "published": "2014-01-30T11:14:28.000Z",
  "updated": "2014-01-30T11:14:28.000Z",
  "title": "Kinetic description of optimal control problems and applications to opinion consensus",
  "authors": [
    "Giacomo Albi",
    "Michael Herty",
    "Lorenzo Pareschi"
  ],
  "comment": "25 pages, 18 figures",
  "categories": [
    "math.OC",
    "nlin.AO",
    "physics.soc-ph"
  ],
  "abstract": "In this paper an optimal control problem for a large system of interacting agents is considered using a kinetic perspective. As a prototype model we analyze a microscopic model of opinion formation under constraints. For this problem a Boltzmann-type equation based on a model predictive control formulation is introduced and discussed. In particular, the receding horizon strategy permits to embed the minimization of suitable cost functional into binary particle interactions. The corresponding Fokker-Planck asymptotic limit is also derived and explicit expressions of stationary solutions are given. Several numerical results showing the robustness of the present approach are finally reported.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-30T11:14:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal control problem",
      "kinetic description",
      "opinion consensus",
      "applications",
      "corresponding fokker-planck asymptotic limit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.7798A"
    }
  }
}