Stop-and-go suppression in two-class congested traffic

Burkhardt, Mark; Yu, Huan; Krstić, Miroslav · 2020 · Automatica

DOI: 10.1016/j.automatica.2020.109381

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Summary

This paper addresses the problem of suppressing stop-and-go traffic oscillations in congested regimes involving heterogeneous vehicle populations. The authors focus on a macroscopic two-class Aw-Rascle (AR) traffic model, which accounts for differences in vehicle size and driver behavior between two distinct classes. Stop-and-go waves, characterized by density and velocity perturbations, increase fuel consumption and accident risks. While previous control efforts often assumed homogeneous traffic, this work specifically targets the challenge of regulating mixed traffic flows using boundary control, specifically ramp metering at the outlet of a highway section. The study employs a control-theoretic approach based on the linearized two-class AR model, which consists of four coupled hyperbolic partial differential equations (PDEs). The model utilizes the concept of area occupancy to couple the dynamics of the two vehicle classes. The authors analyze the characteristic speeds of the linearized system to distinguish between free-flow and congested regimes, identifying that the congested regime is characterized by one negative characteristic speed, leading to heterodirectional information propagation. To stabilize the system, the authors apply the backstepping control design method. They first derive a full-state feedback controller that ensures finite-time convergence of density and velocity perturbations to zero. Since full state measurement is impractical, they then design an anti-collocated observer to estimate the internal states using only measurements of velocities and densities at the inlet of the track section. This observer is combined with the feedback law to create an output feedback controller. The main findings demonstrate that the proposed output feedback control law effectively damps out stop-and-go waves in finite time. The control input, realized as a ramp metering signal at the outlet, successfully stabilizes the 4x4 heterodirectional hyperbolic PDEs. The theoretical results are verified through simulations, confirming that the controller can suppress oscillations and return the traffic flow to its equilibrium state despite the presence of two different vehicle classes with distinct parameters. The work establishes a rigorous connection between backstepping control theory and multi-class traffic modeling. The significance of this research lies in providing the first boundary control design results for traffic congestion consisting of two different vehicle classes. It advances the field by extending control strategies from single-class or homogeneous models to more realistic heterogeneous traffic scenarios. The methodology serves as a foundational step for controlling systems with more than two vehicle classes or multiple lanes. By demonstrating that ramp metering can be used to stabilize mixed traffic flows in the congested regime, the paper offers a theoretical basis for improving traffic management systems to reduce inefficiencies and safety risks associated with stop-and-go traffic.

Key finding

Boundary feedback control laws based on backstepping design can suppress stop-and-go waves in two-class congested traffic in finite time by regulating outlet flow through ramp metering.

Methodology

simulation_modeling

Provenance

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Topics

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• traffic density