{
  "id": "2307.13135",
  "version": "v1",
  "published": "2023-07-24T21:28:53.000Z",
  "updated": "2023-07-24T21:28:53.000Z",
  "title": "High-dimensional Optimal Density Control with Wasserstein Metric Matching",
  "authors": [
    "Shaojun Ma",
    "Mengxue Hou",
    "Xiaojing Ye",
    "Haomin Zhou"
  ],
  "comment": "8 pages, 4 figures. Accepted for IEEE Conference on Decision and Control 2023",
  "categories": [
    "math.OC"
  ],
  "abstract": "We present a novel computational framework for density control in high-dimensional state spaces. The considered dynamical system consists of a large number of indistinguishable agents whose behaviors can be collectively modeled as a time-evolving probability distribution. The goal is to steer the agents from an initial distribution to reach (or approximate) a given target distribution within a fixed time horizon at minimum cost. To tackle this problem, we propose to model the drift as a nonlinear reduced-order model, such as a deep network, and enforce the matching to the target distribution at terminal time either strictly or approximately using the Wasserstein metric. The resulting saddle-point problem can be solved by an effective numerical algorithm that leverages the excellent representation power of deep networks and fast automatic differentiation for this challenging high-dimensional control problem. A variety of numerical experiments were conducted to demonstrate the performance of our method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-24T21:28:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93E20",
      "76N25",
      "49L99"
    ],
    "keywords": [
      "high-dimensional optimal density control",
      "wasserstein metric matching",
      "deep network",
      "target distribution",
      "fast automatic differentiation"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}