Optimal driving strategies for traffic control with autonomous vehicles

This article considers the possibility of using a small number of autonomous vehicles (AV) for traffic control of the predominantly human-piloted traffic. Specifically, we consider the control of the AV to act as a moving bottleneck, which will be used to optimize traffic flow properties such as fuel consumption of the combined human-piloted and autonomous traffic flow. We use a coupled partial differential equation (PDE)-ordinary differential equation (ODE) framework to model the bulk traffic flow using a PDE, and the trajectory of an autonomous vehicle in the flow using an ODE, depending on the downstream traffic density. The autonomous vehicle acts on the traffic flow as a moving bottleneck via a moving flux constraint. Using this modeling framework, we consider an optimal control problem which consists in finding the optimal AV trajectory to minimize fuel consumption of the entire traffic flow. We prove existence of optimal AV trajectories and we present two different optimal driving strategies depending on the initial traffic conditions.