A PDE-ODE model for traffic control with autonomous vehicles

Thibault Liard, Raphael Stern, Maria Laura Delle Monache

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We consider a partial differential equation-ordinary differential equation system to describe the dynamics of traffic flow with autonomous vehicles. In the model, the bulk flow of human drivers is represented by a scalar conservation law, while each autonomous vehicle is described by an ordinary differential equation. The coupled PDE-ODE model is introduced, and existence of solutions for this model is shown, along with a proposed algorithm to construct approximate solutions. Next, we propose a control strategy for the speeds of the autonomous vehicles to minimize the average fuel consumption of the entire traffic flow. Existence of solutions for the optimal control problem is proved, and we numerically show that a reduction in average fuel consumption is possible with an AV acting as a moving bottleneck.

Original languageEnglish (US)
Pages (from-to)1190-1206
Number of pages17
JournalNetworks and Heterogeneous Media
Issue number3
StatePublished - 2023

Bibliographical note

Funding Information:
The first author is supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 694126-DYCON)

Publisher Copyright:
© 2023 the Author(s), licensee AIMS Press.


  • autonomous vehicles
  • PDE-ODE systems
  • scalar conservation laws
  • traffic control
  • traffic flow models


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