{
  "id": "2302.05416",
  "version": "v1",
  "published": "2023-02-10T18:32:40.000Z",
  "updated": "2023-02-10T18:32:40.000Z",
  "title": "Approximate Dynamic Programming for a Mean-field Game of Traffic Flow: Existence and Uniqueness",
  "authors": [
    "Amoolya Tirumalai",
    "John S. Baras"
  ],
  "comment": "41 pages, 5 figures",
  "categories": [
    "math.OC",
    "cs.SY",
    "eess.SY"
  ],
  "abstract": "Highway vehicular traffic is an inherently multi-agent problem. Traffic jams can appear and disappear mysteriously. We develop a method for traffic flow control that is applied at the vehicular level via mean-field games. We begin this work with a microscopic model of vehicles subject to control input, disturbances, noise, and a speed limit. We formulate a discounted-cost infinite-horizon robust mean-field game on the vehicles, and obtain the associated dynamic programming (DP) PDE system. We then perform approximate dynamic programming (ADP) using these equations to obtain a sub-optimal control for the traffic density adaptively. The sub-optimal controls are subject to an ODE-PDE system. We show that the ADP ODE-PDE system has a unique weak solution in a suitable Hilbert space using semigroup and successive approximation methods. We additionally give a numerical simulation, and interpret the results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-10T18:32:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "approximate dynamic programming",
      "traffic flow",
      "discounted-cost infinite-horizon robust mean-field game",
      "ode-pde system",
      "sub-optimal control"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}