Robust perimeter control design for an urban region

Recent works have introduced perimeter feedback-control strategies for a homogenous urban region and multiple urban regions with the help of the Macroscopic Fundamental Diagram (MFD) representation, that relates average flow and density (or accumulation) across the network. The perimeter controller is located on the region border, and manipulates the transfer flows across the border, while aiming at regulating around (nearby) the critical densities or accumulations, whereby the system throughput is maximized. While the desired state in the one urban region system is known in advance (given the MFD shape), for the system with multiple urban regions the desired accumulation points are not well known. Moreover, in some traffic scenarios the controller cannot regulate around the critical accumulations for both systems, e.g. because of high demand. In this paper, a robust perimeter controller for an urban region is designed. The controller aims at satisfying the control specifications and having a good performance for the whole accumulation set, uncongested and congested accumulations, and not necessary for a value range nearby the critical accumulation set-point. Moreover, unlike previous works, the robust controller is also designed to handle uncertainty in the MFD and the control constraints within the design level in a systematic way, where the constraints are explicitly integrated utilizing the so-called describing function. Comparison results show that the performances of the robust controller are significantly better than a "standard" feedback controller, for different traffic scenarios.