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.
Bibliographical noteFunding Information:
M. L. Delle Monache was supported by the IDEX-IRS 2018 project “MAVIT”. T. Liard was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement NO. 694126-DyCon), by the ELKA-RTEK project KK-2018/00083 ROAD2DC of the Basque Government, by the Grant MTM2017-92996-C2-1-R/2-R COSNET of MINECO (Spain), by the Air Force Office of Scientific Research (AFOSR) under Award NO. FA9550-18-1-0242 and by the grant ICON-ANR-16-ACHN-0014 of the French ANR.
Copyright © 2020 The Authors. This is an open access article under the CC BY-NC-ND license
- Autonomous vehicles
- Control of partial differential equations
- Intelligent transportation systems
- Modeling for control optimization
- Traffic control systems