Suppression of Oscillations in Two-Class Traffic by Full-State Feedback

Burkhardt, Mark; Yu, Huan; Krstić, Miroslav · 2020 · IFAC-PapersOnLine

DOI: 10.1016/j.ifacol.2020.12.1344

archive: archived pipeline: cataloged verified

Get this paper ↗ (DOI — opens at the source; we link to it, we don't host it)

Summary

This paper addresses the problem of stop-and-go traffic oscillations in congested, heterogeneous traffic flows consisting of two distinct vehicle classes. The authors aim to develop a full-state feedback controller capable of damping these oscillations in traffic density and velocity, thereby achieving convergence to a constant equilibrium in finite time. The motivation stems from the negative impacts of such oscillations, including increased fuel consumption and accident risks, particularly in mixed traffic scenarios where vehicles differ in size and driver behavior. The study utilizes the linearized two-class Aw-Rascle (AR) macroscopic traffic model, which is governed by four first-order hyperbolic partial differential equations (PDEs). This model incorporates the concept of area occupancy to couple the dynamics of the two vehicle classes. The authors analyze the characteristic speeds of the linearized system, identifying that in the congested regime, the system exhibits heterodirectional behavior with three positive characteristic speeds (downstream propagation) and one negative characteristic speed (upstream propagation). The control input is implemented via ramp metering at the outlet of the track section. To design the controller, the authors employ the backstepping method, transforming the system into Riemann coordinates to decouple the PDEs and facilitate the derivation of a stabilizing boundary feedback law. The main finding is the successful derivation of a full-state feedback control law that stabilizes the heterodirectional system of $3+1$ transport PDEs. The control design relies on solving well-posed kernel equations to determine the transformation kernels required for the backstepping approach. The resulting controller ensures that the perturbations in density and velocity converge to zero in finite time, effectively suppressing stop-and-go waves. The performance of this controller is verified through simulations, confirming its ability to stabilize the traffic flow under the specified congested conditions. The significance of this work lies in providing the first result on boundary feedback control for a macroscopic second-order multi-class traffic model using the backstepping technique. It bridges theoretical control design methods with realistic traffic modeling by addressing the complexities of heterogeneous traffic. The study contributes to the field of traffic management by offering a rigorous mathematical framework for dampening oscillations in mixed traffic flows, potentially improving traffic efficiency and safety on freeways equipped with ramp metering systems.

Key finding

A full-state feedback controller designed via backstepping successfully suppresses traffic density and velocity oscillations in a two-class congested traffic model within finite time.

Methodology

simulation_modeling

Provenance

The full processing record for this entry. Every stage of this paper's journey through the pipeline is logged — what ran, with which tool and model, how many attempts it took, and when it last completed. Discovered via author_sweep_intake on 2026-05-28.

Summary generated by qwen3.6-27b-prismaquant on 2026-06-10; verification: verified.

Topics

Ranked by relevance to this paper. Hover a topic for its definition.

• traffic density