Model Predictive Perimeter Control for Urban Areas with Macroscopic Fundamental Diagrams

Recent analysis of empirical data from cities showed that a macroscopic fundamental diagram (MFD) of urban traffic provides for different network regions a unimodal, low-scatter relationship between network vehicle density and network space-mean flow. In this paper, the optimal perimeter control for two-region urban cities is formulated with the tool of MFDs. The controllers operate on the border between the two regions, and manipulate the percentages of flows that transfer between the two regions such that the number of trips reach their destinations is maximized. The perimeter control problem is solved by model predictive control, where the prediction model and the plant (reality) are formulated by macroscopic fundamental diagrams. Examples are presented for different levels of congestion in the regions of the city and the robustness of the controller is tested for different size of error in the MFDs. The direct sequential method is utilized to optimize the nonlinear problem of the open-loop control. Comparison results shows that the performances of the model predictive control are significantly better than a "greedy" feedback control. The results of this paper can be extended to develop efficient hierarchical control strategies for heterogeneously congested cities.