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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
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Jorge A. Laval & Ludovic Leclercq, 2010. "Continuum Approximation for Congestion Dynamics Along Freeway Corridors," Transportation Science, INFORMS, vol. 44(1), pages 87-97, February.

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