Traffic Congestion Control on Two-lane Aw-Rascle-Zhang Model

Yu, Huan; Krstić, Miroslav · 2018 · Unknown

DOI: 10.1109/cdc.2018.8619095

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Summary

This paper addresses the problem of traffic congestion control on unidirectional freeways with two lanes, specifically a fast lane and a slow lane. The authors aim to stabilize oscillations in traffic density and velocity, which cause unsafe driving conditions and increased fuel consumption. While previous macroscopic models often treated multilane traffic as a single averaged lane, this work utilizes a two-lane Aw-Rascle-Zhang (ARZ) model that explicitly accounts for lane-changing interactions and distinct equilibrium velocities for each lane. The motivation is to develop a control strategy that suppresses instabilities by leveraging the specific dynamics of each lane rather than treating them cumulatively. The methodology involves modeling the traffic dynamics using coupled second-order nonlinear hyperbolic partial differential equations (PDEs). Lane-changing interactions are represented as source terms coupling the two lanes. The authors linearize this nonlinear system around uniform steady states, which are determined by driver preferences for the fast or slow lane. To stabilize the system, they apply variable speed limits (VSLs) at the outlet boundary of the freeway segment, acting as boundary controls for the velocity of each lane. Using the backstepping transformation method, the coupled hetero-directional hyperbolic system is mapped into a cascade target system. This transformation allows for the design of two full-state feedback boundary control laws that dampen traffic oscillations through actuation at the outlet. The main findings demonstrate that the proposed control laws achieve finite-time convergence to the desired steady states for the closed-loop system. The analysis shows that the steady-state velocity and density relations depend on a parameter $\sigma$, which defines driver preference for the fast lane over the slow lane. When drivers prefer the fast lane ($\sigma > 1$), the fast lane becomes more tolerant to high density risks, resulting in higher traffic flux compared to the slow lane. The backstepping design successfully stabilizes the linearized system, ensuring that deviations in density and velocity decay to zero. The paper establishes that coordinated lane-specific boundary control can effectively manage the complex interactions between lanes, including the segregation of risk-tolerant and risk-averse drivers. The significance of this work lies in being the first result, to the authors' knowledge, to address traffic congestion in a two-lane ARZ model from a control perspective. It extends previous backstepping control results, which were limited to single-lane models, to a more realistic multilane scenario. By providing a theoretical framework for PDE boundary control in multilane traffic, the paper paves the way for more sophisticated traffic management systems that can handle the distinct dynamics and interactions of multiple lanes, potentially improving safety and efficiency on freeways.

Key finding

A backstepping-based full-state feedback boundary control strategy using variable speed limits achieves finite-time convergence to equilibrium, stabilizing traffic density and speed oscillations in a two-lane Aw-Rascle-Zhang model.

Methodology

modeling

Provenance

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Topics

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• traffic density