Inserted: 12 oct 2021
Last Updated: 12 oct 2021
Heterogeneous and multi-lane traffic flow modeling is fundamental to understand the dynamics and control of complex traffic systems. In this article, we consider three populations of vehicles: two classes of human-driven vehicles (cars and trucks) and autonomous vehicles. The latter is distinguished by the presence of control in the acceleration. We model the multi-lane traffic by hybrid systems because of its hybrid nature: the continuous dynamics on each lane and the discrete events due to lane-changing maneuvers and study the optimal control problem associated with the hybrid systems. In particular, we investigate controlled hybrid systems from both a microscopic and macroscopic point of view. Furthermore, using $\Gamma$-convergence, we prove the well-posedness of an optimal control problem for a mean-field limit of a finite-dimensional hybrid system modeling heterogeneous multi-lane traffic with controlled autonomous vehicles.