Thibault Liard, Raphael Stern, Maria Laura Delle Monache. A PDE-ODE model for traffic control with autonomous vehicles. (2020)
Abstract. We introduce a coupled PDE-ODEs model to describe mixed traffic with humans and autonomous vehicles. The partial differential equation describes the bulk of human traffic while the ordinary differential equations characterize the trajectories of possibly many autonomous vehicles. 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. We propose a control strategy for the speeds of the autonomous vehicles to minimize total fuel consumption. Existence of solutions for the optimal control problem is proved, and show numerically that a greater reduction in total fuel consumption is possible with more AVs acting as moving bottlenecks.