Stabilization of city-scale road traffic networks via macroscopic fundamental diagram-based model predictive perimeter control

Sırmatel, Işık İlber; Geroliminis, Nikolas · 2021 · OpenAlex-citations

DOI: 10.1016/j.conengprac.2021.104750

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Summary

This paper addresses the challenge of stabilizing large-scale urban road traffic networks, which are difficult to manage due to their size, heterogeneity, and complex congestion dynamics. The authors propose nonlinear model predictive control (MPC) schemes based on the Macroscopic Fundamental Diagram (MFD), a model that relates vehicle accumulation to trip completion flow in aggregated urban regions. While MFD-based perimeter control—manipulating traffic flows at region boundaries via traffic light adjustments—is a practical solution, existing literature has largely neglected the closed-loop stability of such MPC formulations. This work fills that gap by designing controllers with stability guaranteed by construction, aiming to efficiently recover networks from high congestion levels. The methodology involves modeling the city-scale network as a set of regions with well-defined MFDs, using vehicle conservation equations to describe dynamics. The authors focus on a "congestion recovery" scenario, where inflow demands drop to low levels but accumulations remain high, requiring the system to stabilize at a new equilibrium. Two primary control strategies are developed: a Control Lyapunov Function-based controller (CLF-C) serving as a computationally efficient benchmark, and a Regulatory MPC formulation designed to steer the system to a desired equilibrium. Both methods incorporate constraints on control inputs and ensure stability through specific optimization structures. The study also considers Economic MPC for optimizing total time spent, though the primary focus is on stabilization. The proposed methods were evaluated using both macroscopic and microscopic simulations. The microscopic simulations utilized a realistic representation of downtown Barcelona, comprising over 600 traffic lights and 1,500 road links, to validate the practical applicability of the control schemes. Results demonstrated that the nonlinear MPC formulations successfully stabilized the traffic network, effectively reducing high accumulations and steering the system toward equilibrium. The simulations confirmed the domain of attraction properties of the controllers, showing their ability to handle various initial congestion states. The CLF-C provided a viable alternative for scenarios where computational resources are limited, while the MPC schemes offered superior performance in managing congestion recovery. The significance of this work lies in providing a theoretically sound and practically viable framework for city-scale traffic control. By ensuring closed-loop stability by construction, the proposed methods offer reliable congestion management where previous approaches lacked rigorous stability guarantees. The successful application to a large-scale urban network like Barcelona highlights the potential for real-world implementation, suggesting that MFD-based perimeter control can significantly improve the efficiency and reliability of urban mobility systems. This research advances the field by bridging the gap between theoretical control stability and practical traffic engineering applications.

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• mental model of traffic