{
  "id": "1910.13885",
  "version": "v1",
  "published": "2019-10-30T14:28:20.000Z",
  "updated": "2019-10-30T14:28:20.000Z",
  "title": "Simultaneous Stabilization of Traffic Flow on Two Connected Roads",
  "authors": [
    "Huan Yu",
    "Jean Auriol",
    "Miroslav Krstic"
  ],
  "categories": [
    "math.OC",
    "math.AP"
  ],
  "abstract": "In this paper we develop a boundary state feedback control law for a traffic flow network system in its most fundamental form: one incoming and one outgoing road connected by a junction. The macroscopic traffic dynamics on each road segment are governed by Aw-Rascle-Zhang (ARZ) model, consisting of second-order nonlinear partial differential equations (PDEs) for traffic density and velocity. Different equilibrium road conditions are considered for the connected segments. For stabilization of the stop-and-go traffic congestion on the two roads, we consider a ramp metering located at the connecting junction. The traffic flow rate entering from the on-ramp to the mainline junction is actuated. The objective is to simultaneously stabilize the upstream and downstream traffic to a given spatially-uniform constant steady-state. We design a full state feedback control law for this under-actuated network of two systems of two hetero-directional linear first-order hyperbolic PDEs interconnected through the boundary condition (junction). The exponential stability is validated by numerical simulation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-30T14:28:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "traffic flow",
      "simultaneous stabilization",
      "connected roads",
      "full state feedback control law",
      "boundary state feedback control law"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}