A general approach to smoothing nonlinear mixed traffic via control of autonomous vehicles

Shian Wang, Mingfeng Shang, Michael W. Levin, Raphael Stern

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Stop-and-go waves are easily caused by unstable traffic due to the collective behavior of human drivers, resulting in higher vehicle fuel consumption and emissions. In this article, we develop a general approach to synthesizing feedback controllers of autonomous vehicles (AVs) for smoothing unstable nonlinear mixed traffic flow, consisting of AVs and human-driven vehicles (HVs). In the context of traffic smoothing and stabilization, prior studies have mainly focused on analyzing string stability of specific car-following models linearized at flow equilibrium points. By contrast, we are interested to analytically synthesize appropriate feedback controllers of AVs for smoothing nonlinear mixed traffic in its general functional forms, covering a broad class of deterministic car-following models commonly seen in the literature. Specifically, by leveraging feedback control theory AVs are controlled to operate in such a way that they closely track a virtual speed profile, i.e., a subtler version of the disturbance resulting from the immediate preceding vehicle. Thus, traffic waves are reduced when propagating backward across controlled AVs. Based on the general functional form of car-following dynamics, we derive a class of effective additive AV controllers that are proven to be able to ensure convergence in tracking desired speed profiles, leading to smoother traffic. In addition, a set of sufficient conditions is devised for guaranteeing car-following safety. More importantly, head-to-tail string stability of the mixed traffic is likely to be achieved with a sufficient market penetration rate (MPR) of AVs. Notably, unlike many existing studies the feedback controllers synthesized for AVs require only local traffic information without having to rely on high degrees of vehicle connectivity, and the rate of smoothing mixed traffic is readily tunable, which is useful for practical implementations. The proposed approach is further illustrated with a theoretical intelligent driver model (IDM) and commercially available adaptive cruise control (ACC) vehicles represented by a well calibrated IDM. Extensive numerical results are presented to show the effectiveness and robustness of the feedback controllers synthesized for AVs on smoothing nonlinear mixed traffic.

Original languageEnglish (US)
Article number103967
JournalTransportation Research Part C: Emerging Technologies
StatePublished - Jan 2023

Bibliographical note

Funding Information:
This work is supported by the Minnesota Department of Transportation (M.W. Levin), USA as well as by the University of Minnesota Center for Transportation Studies, USA through the Transportation Scholars Program (R. Stern). S. Wang is supported by the University of Minnesota Doctoral Dissertation Fellowship, USA .

Publisher Copyright:
© 2022 Elsevier Ltd


  • Autonomous vehicle
  • Nonlinear feedback control
  • Nonlinear mixed traffic
  • Traffic smoothing


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