Output feedback control of two-lane traffic congestion

Yu, Huan; Krstić, Miroslav · 2020 · Automatica

DOI: 10.1016/j.automatica.2020.109379

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Summary

This paper addresses the problem of mitigating traffic congestion on unidirectional two-lane freeways by developing an output feedback boundary control strategy. The research is motivated by the limitations of single-lane macroscopic models, which fail to capture distinct lane dynamics and lane-changing interactions that contribute to congestion. The authors utilize the Aw-Rascle-Zhang (ARZ) model to describe the macroscopic traffic dynamics, resulting in a system of coupled $4 \times 4$ nonlinear hyperbolic partial differential equations (PDEs) that govern traffic density and velocity for both fast and slow lanes. Lane-changing interactions are modeled as exchanging source terms between the lanes. The methodology involves linearizing the nonlinear ARZ model around lane-specific uniform steady states, which are determined by drivers' preferences for each lane. The linearized system is transformed into Riemann coordinates to yield a coupled first-order heterodirectional hyperbolic system. The authors employ the backstepping transformation to map this system into a stable target system where traffic oscillations are damped. Control is achieved through two distinct variable speed limits (VSLs) applied at the outlet boundary to actuate the velocity of each lane. A key contribution is the design of a collocated boundary observer that estimates the full state using only density sensing at the outlet, which is combined with full-state feedback controllers to form the output feedback control law. This approach is noted as more practically applicable than previous methods requiring anti-collocated observers. The study establishes theoretical results demonstrating finite-time convergence to equilibrium for both the controller and observer designs. The control laws stabilize traffic densities and velocities to the desired steady states, effectively suppressing stop-and-go oscillations. Numerical simulations validate the design across two different traffic scenarios, confirming the effectiveness of the proposed output feedback boundary control in managing two-lane traffic congestion. The significance of this work lies in being the first application of PDE backstepping control techniques to a multi-lane traffic model. It bridges the gap between theoretical control results for heterodirectional hyperbolic PDEs and practical traffic management applications. By accounting for lane-specific dynamics and driver preferences, the paper provides a rigorous framework for using VSLs to stabilize multi-lane traffic flows, offering a foundation for future research in advanced traffic control systems.

Key finding

Output feedback boundary control laws, combining a collocated observer with full-state feedback, successfully stabilize two-lane traffic densities and velocities to uniform steady states in finite time.

Methodology

simulation_modeling

Provenance

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Topics

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• traffic density