A Linear-Parameter-Varying Formulation for Model Predictive Perimeter Control in Multi-Region MFD Urban Networks

Abstract

An alternative approach for real-time network-wide traffic control in cities that has recently gained attention is perimeter flow control. Many studies have shown that this method is more efficient than state-of-the-art adaptive signal control strategies for heterogeneously congested urban networks. The basic concept of such an approach is to partition heterogeneous cities into a small number of homogeneous regions (zones) and apply perimeter control to the interregional flows along the boundaries between regions. The transferring flows are controlled at the traffic intersections located at the borders between regions so as to distribute the congestion in an optimal way and minimize the total delay of the system. The focus of current work is the mathematical formulation of the original nonlinear problem in a linear parameter-varying (LPV) form so that optimal control can be applied in a (rolling horizon) model predictive concept. This work presents the mathematical analysis of the optimal control problem as well as the approximations and simplifications that are assumed in order to derive the formulation of a linear optimization problem. Numerical simulation results for the case of a macroscopic environment (plant) are presented in order to demonstrate the efficiency of the proposed approach. Results for the closed-loop model predictive control scheme are presented for the nonlinear case, which is used as “benchmark,” as well as the linear case. Furthermore, the developed scheme is applied to a large-scale microsimulation of a European city with more than 500 signalized intersections in order to better investigate its applicability to real-life conditions. The simulation experiments demonstrate the effectiveness of the scheme compared with fixed-time control because all of the performance indicators are significantly improved. Funding: This work was supported by Dit4Tram “Distributed Intelligence & Technology for Traffic & Mobility Management” project from the European Union’s Horizon 2020 research and innovation programme under [Grant agreement 953783].