Optimal Control of Autonomous Vehicles for Traffic Smoothing

Uniform traffic flow has been shown to be unstable in certain flow regimes due to collective behaviors of human drivers, resulting in the well-observed stop-and-go waves. These traffic waves can arise even in the absence of merges, bottlenecks, or lane changing, and may lead to higher vehicle fuel consumption and emissions. In this article, we aim to smooth unstable traffic flow via optimal control of autonomous vehicles (AVs) in a predominantly human-driven traffic flow. These controlled AVs act as mobile actuators in the traffic without changing the way human-driven vehicles (HVs) normally operate. We develop a dynamic model to describe mixed traffic flow in the presence of both HVs and AVs, whose dynamics follow general nonlinear car-following principles. Based on this general framework, we formulate an optimal control problem with the objective of minimizing vehicle speed perturbation, and prove the existence of optimal AV control policy. Following the necessary conditions of optimality prescribed by the well-known Pontryagin's minimum principle, we present a computational algorithm to determine the optimal AV control strategy and prove its convergence. The mathematical model is further illustrated using the intelligent driver model (IDM) and optimal velocity with relative velocity (OVRV) model for HVs and AVs, respectively. Numerical results are presented to show the effectiveness of the proposed approach on traffic smoothing, as well as the improvement on vehicle fuel economy.