| Issue |
ESAIM: COCV
Volume 30, 2024
|
|
|---|---|---|
| Article Number | 88 | |
| Number of page(s) | 35 | |
| DOI | https://doi.org/10.1051/cocv/2024077 | |
| Published online | 19 November 2024 | |
An optimal control problem of traffic flow on a junction
1
Université Paris-Dauphine, PSL Research University, Ceremade, Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France
2
Department of Mathematics, University of Chicago, Chicago, IL 60637, USA
* Corresponding author: cardaliaguet@ceremade.dauphine.fr
Received:
29
December
2023
Accepted:
24
September
2024
We investigate how to control optimally a traffic flow through a junction on the line by acting only on speed reduction or traffic light at the junction. We show the existence of an optimal control and, under structure assumptions, provide optimality conditions. We use this analysis to investigate thoroughly the maximization of the flux on a space-time subset and show the existence of an optimal control which is bang-bang.
Mathematics Subject Classification: 35L65 / 49J20 / 35F21 / 90B20
Key words: Optimal control of partial differential equation / Conservation law on a junction / Hamilton-Jacobi equation on a junction
© The authors. Published by EDP Sciences, SMAI 2024
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