On a weaker notion of ring stability for mixed traffic with human-driven and autonomous vehicles

Abstract

This article considers criteria to determine when stop-and-go waves form in platoons of human-driven vehicles, and when they can be dissipated by the presence of an autonomous vehicle. Our analysis takes the start from the observation that the standard notion of string/ring stability definition, which requires uniformity with respect to the number of vehicles in the platoon, is too demanding for a mixed traffic scenario. The setting under consideration is the following: the vehicles run along a ring road and the human-driven vehicles obey a combined follow-the-leader and optimal velocity model, while the autonomous vehicle obeys an appropriately designed model. The criteria are tested on a linearized version of the resulting platoon dynamics and simulation tests using nonlinear model are carried out.

Traffic Flow on a Ring With a Single Autonomous Vehicle: An Interconnected Stability Perspective

“…Since in practice it happens that ||Γ|| ∞ > 1 for the HVs, we can conclude that, according to the linear criteria proposed in this work, the stabilizing AV in the experiments of [6] does meet weak ring stability criteria (we will further elaborate on our interpretation of the these experiments in Section V). In order to overcome this apparent lack of string stability, clearly it is preferable for the AV to have ||Γ AV || ∞ ≤ 1, so as to damp the frequency peak of the HVs according to (13). Note from (32) that the AV is merely a second-order system with little degrees of freedom with respect to frequency shaping.…”

“…P. Frasca was partly supported by ANR via project HANDY, number ANR-18-CE40-0010. The authors are grateful to mr. Maolong Lv for some preliminary HVs simulations that were included in an early and incomplete account of this research [13].…”

Output Feedback Controller Design for a Mixed Traffic Flow System Moving in a Loop

“…where H i (•) is the acceleration of vehicle i, that is a nonlinear function of its velocity v i , the spacing s i , and the relative velocityṡ i . Note that unlike most of the works in literature (e.g., [1], [8], [18]), in this paper, HDVs are assumed to be heterogeneous, and thus, the dynamics of each vehicle i is described by a distinct nonlinear function H i (•).…”

“…In recent decades, the transition phase from using humandriven vehicles (HDVs) to fully connected and automated vehicles (CAVs) results in new challenges and creates a strong motivation to study the mixed traffic systems, that include both HDVs and CAVs [1]. More traditional methodologies for controlling traffic flow employ controllers and actuators at fixed locations, among which variable speed limits (VSLs) and ramp metering (RMs) can be mentioned [2].…”

Impact of Disturbances on Mixed Traffic Control with Autonomous Vehicles

“…The powerful implications of the experiment in [4] has motivated recent research, including [8], [9], [10], into analysing its results from a control theoretic perspective. Doing so provides insight into the formation of the "stopand-go" waves and answers how there could exist a control law that could optimally dissipate them.…”