Single-region robust perimeter traffic flow control

Kulcsár, Balázs; Ampountolas, Konstantinos; Dabiri, Azita · 2015 · Crossref

DOI: 10.1109/ecc.2015.7330934

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Summary

This paper addresses the challenge of preventing congestion in single-region urban transport networks by proposing a robust perimeter traffic flow control policy. The motivation stems from the limitations of existing control strategies, which often rely on nominal Macroscopic Fundamental Diagrams (MFDs) that fail to account for significant parametric uncertainties caused by spatial congestion distribution, traffic composition, and signal control variations. The authors aim to develop a control scheme that remains effective despite these uncertainties, ensuring stable vehicle accumulation and maximized throughput. The methodology employs a two-stage robust control framework based on Linear Parameter Varying (LPV) systems. First, the nonlinear MFD dynamics are reformulated into an uncertain LPV model where the scheduling parameter is the real-time vehicle accumulation. This transformation captures parametric, input, and reference uncertainties. In the first design stage, a two-degree-of-freedom LPV controller is synthesized to minimize the induced L2 norm between disturbances and performance outputs, ensuring robust tracking of a critical accumulation setpoint. In the second stage, an optimal quadratic control allocation algorithm distributes the controller’s commanded input flow to green time stages at perimeter junctions, respecting physical constraints such as minimum and maximum green times. The proposed scheme is validated through macroscopic simulations of a 2.5-square-mile area in Downtown San Francisco, comprising 100 junctions and 400 links. The simulation incorporates a second-order polynomial MFD and introduces parametric uncertainties ranging from 10% to 40%, which increase as the network enters congested regimes. The results demonstrate that the LPV controller effectively tracks the critical accumulation despite significant model mismatches and disturbances. When compared to a reference bang-bang controller, the proposed LPV approach exhibits superior robustness, providing rapid and accurate tracking behavior. The control allocation successfully translates the robust controller’s output into feasible green times for 15 perimeter junctions, maintaining system stability even when the MFD parameters vary significantly. The significance of this work lies in its ability to handle the inherent uncertainties of urban traffic dynamics without requiring precise, static MFD calibrations. By decoupling the robust control design from the physical implementation constraints via control allocation, the method offers a practical, real-time applicable solution for perimeter flow control. The findings suggest that LPV-based robust control can improve mobility and throughput in single-region networks by maintaining vehicle accumulation at optimal levels, even under highly uncertain and varying traffic conditions. This approach provides a more reliable alternative to nominal linearized controllers, particularly in heterogeneous urban environments where MFD shapes are not fixed.

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