A Linear Formulation for Model Predictive Perimeter Traffic Control in Cities

An alternative approach for real-time network-wide traffic control in cities that has recently gained a lot of interest is perimeter flow control. 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 inter-regional 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 the current work is to study three aspects that are not covered in the perimeter control literature, which are: (a) the treatment of some model parameters that are not measurable in real life implementations and can affect the performance of the controller (e.g. advanced online estimation schemes can be developed for this purpose), (b) integration of appropriate external demand information that has been considered system disturbance in the derivation of feedback control laws in previous works, and (c) mathematical formulation of the original nonlinear problem in a linear 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. Preliminary 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. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.