Simultaneous downstream and upstream output-feedback stabilization of cascaded freeway traffic

Yu, Huan; Auriol, Jean; Krstić, Miroslav · 2021 · Automatica

DOI: 10.1016/j.automatica.2021.110044

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 challenge of stabilizing traffic flow on a network of two cascaded freeway segments connected by a junction, specifically aiming to suppress stop-and-go oscillations. The authors focus on an under-actuated system where control is applied at only one boundary—either the middle junction or the downstream outlet—while the system dynamics are governed by the second-order Aw-Rascle-Zhang (ARZ) macroscopic model. This model describes traffic density and velocity via nonlinear hyperbolic partial differential equations (PDEs). The motivation stems from the limitations of existing control strategies, which often assume homogeneous road conditions or require actuation at all boundaries, failing to address the distinct equilibria and coupled dynamics inherent in cascaded networks with varying lane configurations. The study employs a PDE backstepping methodology to design boundary output-feedback controllers. The authors first linearize the ARZ model around congested steady states and transform it into Riemann coordinates to simplify the control design. They develop two distinct full-state feedback laws: one for actuation at the junction ($x=0$) and another for actuation at the outlet ($x=L$). To implement these as output-feedback controllers, the authors design collocated boundary observers that estimate the full state using only local measurements of flow rate and velocity at the actuator location. The control laws are derived using Volterra integral transformations that map the original under-actuated system to a target system with desired stability properties. The design ensures exponential stability of the closed-loop system in the $L^2$ norm and incorporates robustness margins for input delays. Numerical simulations validate the proposed control designs, demonstrating that both the junction-based and outlet-based controllers successfully stabilize the traffic on both upstream and downstream segments simultaneously. The results show that the backstepping-based controllers achieve exponential convergence to the desired steady state, effectively damping out traffic oscillations. The study also investigates the robustness of the controllers to input delays, confirming their stability under such conditions. Furthermore, the authors compare the performance of their proposed backstepping controllers against traditional Proportional Integral (PI) boundary feedback controllers. The simulations indicate that the backstepping approach offers superior stabilization performance, particularly in handling the complex coupling dynamics of the cascaded network. The significance of this work lies in its theoretical contribution to the control of under-actuated hyperbolic PDE networks, a problem previously unaddressed in this specific context. By providing the first output-feedback control laws for cascaded freeway traffic modeled by the ARZ network, the paper bridges a gap between advanced control theory and practical traffic management. The findings imply that sophisticated boundary control strategies can effectively manage traffic congestion in complex network structures using limited sensing and actuation resources. This advances the field by offering a rigorous mathematical framework for designing robust traffic control systems that can handle the non-homogeneous and coupled nature of real-world freeway networks.

Key finding

The proposed PDE backstepping-based output-feedback controllers successfully stabilize traffic on cascaded freeway segments using single-point actuation and measurement, ensuring exponential stability and robustness to delays.

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