{
  "id": "1408.6801",
  "version": "v1",
  "published": "2014-08-27T07:19:52.000Z",
  "updated": "2014-08-27T07:19:52.000Z",
  "title": "Optimal control theory with arbitrary superpositions of waveforms",
  "authors": [
    "Selina Meister",
    "Jürgen T. Stockburger",
    "Rebecca Schmidt",
    "Joachim Ankerhold"
  ],
  "comment": "14 pages, 5 figures",
  "categories": [
    "math.OC",
    "cs.SY",
    "quant-ph"
  ],
  "abstract": "Standard optimal control methods perform optimization in the time domain. However, many experimental settings demand the expression of the control signal as a superposition of given waveforms. Since this type of constraint is not time-local, Optimal Control Theory cannot be used without modifications. Simplex methods, used as a substitute in this case, tend to be less efficient and less reliable than Optimal Control Theory. In this paper, we present an extension to Optimal Control Theory which allows gradient-based optimization for superpositions of arbitrary waveforms. Its key is the use of the Moore-Penrose pseudoinverse as an efficient means of transforming from a time-local to a waveform-based description. To illustrate this optimization technique, we study the parametrically driven harmonic oscillator as model system and reduce its energy, considering both Hamiltonian dynamics and open-system dynamics. We demonstrate the viability and efficiency of the method for these test cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-27T07:19:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal control theory",
      "arbitrary superpositions",
      "optimal control methods perform optimization",
      "standard optimal control methods perform",
      "experimental settings demand"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/47/49/495002",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2014,
      "month": "Dec",
      "volume": 47,
      "number": 49,
      "pages": 495002
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014JPhA...47W5002M"
    }
  }
}