Smoothing Nonlinear Mixed Traffic with Autonomous Vehicles: Control Design

Stop-and-go waves are easily caused by unstable traffic due to the collective behavior of human drivers, resulting in higher fuel consumption and emissions. In this article, we aim to smooth unstable mixed traffic flow in the presence of both autonomous vehicles (AVs) and human-driven vehicles (HVs), via feedback control of AVs. Unlike prior studies focused on analyzing head-to-tail string stability of specific car-following models, we synthesize appropriate feedback controllers of AVs for traffic smoothing using a general functional form of car-following dynamics describing mixed traffic. Notably, the general approach proposed is not limited to any specific car-following model. Instead, AVs are controlled in such a way that they closely track a subtler version of the disturbance resulting from the immediate preceding vehicle. Hence, traffic waves can be reduced when propagating backward across these AVs. Based on the general functional form of car-following dynamics, we derive a class of additive AV controllers that are proven to ensure convergence in speed tracking, with a readily tunable convergence rate. More importantly, only local traffic information is needed for AV controller synthesis, without requiring linearization of nonlinear car-following dynamics. The well-known intelligent driver model (IDM) is employed to demonstrate the general approach on smoothing nonlinear mixed traffic flow. A set of numerical results is presented to show the effectiveness of the class of AV feedback controllers on traffic smoothing.