{
  "id": "1911.01133",
  "version": "v1",
  "published": "2019-11-04T11:10:42.000Z",
  "updated": "2019-11-04T11:10:42.000Z",
  "title": "Asymptotic behavior and control of a \"guidance by repulsion\" model",
  "authors": [
    "Dongnam Ko",
    "Enrique Zuazua"
  ],
  "comment": "33 pages, 19 figures",
  "categories": [
    "math.OC"
  ],
  "abstract": "We model and analyze a herding problem, where the drivers try to steer the evaders' trajectories while the evaders always move away from the drivers. This problem is motivated by the guidance-by-repulsion model [Escobedo, R., Iba\\~nez, A. and Zuazua, E. COMMUN NONLINEAR SCI 39 (2016) 58-72], where the authors answer how to control the evaders' positions and what is the optimal maneuver of the drivers. First, we obtain the well-posedness and the long-time behavior of the one-driver and one-evader model, assuming of the same friction coefficients. In this case, the exact controllability is proved in a long enough time horizon. We extend the model to the multi-driver and multi-evader case, and develop numerical simulations to systematically explore the nature of controlled dynamics in various scenarios. The optimal strategies turn out to share a common pattern to the one-driver and one-evader case: the drivers rapidly occupy the position behind the target, and want to pursuit evaders in a straight line for most of the time. Inspired by this, we build a feedback strategy which stabilizes the direction of evaders.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-04T11:10:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34D05",
      "93B05",
      "93B52"
    ],
    "keywords": [
      "asymptotic behavior",
      "commun nonlinear sci",
      "optimal strategies turn",
      "authors answer",
      "optimal maneuver"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}