Boundary Stabilization for Mixed Traffic Flow in the Presence of Autonomous Vehicle Platooning

This paper investigates the boundary stabilization problem for a mixed traffic flow system composed of the traditional human-driven traffic flow and a platoon of autonomous vehicles. Firstly, we employ the first-order LWR model to describe the mixed traffic flow, which is with a bilateral moving spatial domain governed by the platoon. In order to stabilize the mixed traffic flow into the desired density and platoon length, a downstream boundary controller is designed based on the information of upstream density and platoon length. To facilitate the well-posedness and stabilization analysis, we transform the system into a coupled PDE-ODE system with fixed spatial domain. Then we prove the well-posedness of the system, and we further derive sufficient conditions for ensuring the local exponential stability of the system by employing the Lyapunov function method. Finally, numerical simulations are provided to validate the theoretical results.