IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v126y2005i3d10.1007_s10957-005-5499-z.html
   My bibliography  Save this article

Optimal Control for Traffic Flow Networks

Author

Listed:
  • M. Gugat

    (Institutfür Angewandte Mathematik, FAU Erlangen-Nürnberg)

  • M. Herty

    (TU Darmstadt)

  • A. Klar

    (TU Darmstadt)

  • G. Leugering

    (FAU Erlangen-Nürnberg)

Abstract

We consider traffic flow models for road networks where the flow is controlled at the nodes of the network. For the analytical and numerical optimization of the control, the knowledge of the gradient of the objective functional is useful. The adjoint calculus introduced below determines the gradient in two ways. We derive the adjoint equations for the continuous traffic flow network model and derive also the adjoint equations for a discretized model. Numerical examples for the solution of problems of optimal control for traffic flow networks are presented.

Suggested Citation

  • M. Gugat & M. Herty & A. Klar & G. Leugering, 2005. "Optimal Control for Traffic Flow Networks," Journal of Optimization Theory and Applications, Springer, vol. 126(3), pages 589-616, September.
    • Handle: RePEc:spr:joptap:v:126:y:2005:i:3:d:10.1007_s10957-005-5499-z
    DOI: 10.1007/s10957-005-5499-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-005-5499-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-005-5499-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jack Reilly & Samitha Samaranayake & Maria Laura Delle Monache & Walid Krichene & Paola Goatin & Alexandre M. Bayen, 2015. "Adjoint-Based Optimization on a Network of Discretized Scalar Conservation Laws with Applications to Coordinated Ramp Metering," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 733-760, November.
    2. Jorge A. Laval & Ludovic Leclercq, 2010. "Continuum Approximation for Congestion Dynamics Along Freeway Corridors," Transportation Science, INFORMS, vol. 44(1), pages 87-97, February.
    3. Reilly, Jack & Martin, Sébastien & Payer, Mathias & Bayen, Alexandre M., 2016. "Creating complex congestion patterns via multi-objective optimal freeway traffic control with application to cyber-security," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 366-382.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:126:y:2005:i:3:d:10.1007_s10957-005-5499-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.