# Teresa Chiri (Queen's University)

Date

Friday September 20, 20249:30 am - 10:30 am

Location

422 JEFFERY HALL## PDEs & Applications Seminar

**Friday, September 20th, 2024**

**Time:** 9:30 a.m. **Place:** Jeffery Hall, Room 422

**Speaker:** Teresa Chiri (Queen's University)

**Title:** Mean-field Limit and Optimal Control for a Hybrid Multi-Population Traffic Flow Model

**Abstract:** Heterogeneous and multi-lane traffic flow modeling is fundamental to understanding the dynamics and control of complex traffic systems. In this talk, we consider three populations of vehicles: two classes of human-driven vehicles (cars and trucks) and autonomous vehicles (AV). We first develop a finite-dimensional hybrid system that relies on continuous Bando-Follow-the-Leader dynamics coupled with discrete events motivated by lane-change maneuvers. Then we rigorously prove that the mean-field limit is given by a system of Vlasov-type PDE with source terms generated by the lane-change maneuvers of the human-driven vehicles. The PDEs are coupled with ODEs for the dynamic of AVs. Using Γ-convergence, we prove the well-posedness of an optimal control problem for the mean-field limit. This is a Joint work with X. Gong (Amherst College) and B. Piccoli (Rutgers)