{
  "id": "1602.05416",
  "version": "v1",
  "published": "2016-02-17T13:58:58.000Z",
  "updated": "2016-02-17T13:58:58.000Z",
  "title": "Cluster-based control of nonlinear dynamics",
  "authors": [
    "Eurika Kaiser",
    "Bernd R. Noack",
    "Andreas Spohn",
    "Louis N. Cattafesta",
    "Marek Morzynski"
  ],
  "comment": "journal submission",
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. Here, a cluster-based control framework is proposed to determine optimal control laws with respect to a cost function for unsteady flows. The proposed methodology frames high-dimensional, nonlinear dynamics into low-dimensional, probabilistic, linear dynamics which considerably simplifies the optimal control problem while preserving nonlinear actuation mechanisms. The data-driven approach builds upon a state space discretization using a clustering algorithm which groups kinematically similar flow states into a low number of clusters. The temporal evolution of the probability distribution on this set of clusters is then described by a Markov model. The Markov model can be used as predictor for the ergodic probability distribution for a particular control law. This probability distribution approximates the long-term behavior of the original system on which basis the optimal control law is determined. The approach is applied to a separating flow dominated by the Kelvin-Helmholtz shedding.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-17T13:58:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear dynamics",
      "cluster-based control",
      "determine optimal control laws",
      "markov model",
      "groups kinematically similar flow states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}