A. Jamshidnejad, I. Papamichail, H. Hellendoorn, M. Papageorgiou, and B. De Schutter, "Gradient-based model-predictive control for green urban mobility in traffic networks," Proceedings of the 2016 IEEE 19th International Conference on Intelligent Transportation Systems, Rio de Janeiro, Brazil, pp. 1077-1082, Nov. 2016.
To deal with the traffic congestion and emissions, traffic-responsive control approaches can be used. The main aim of the control is then to use the existing capacity of the network efficiently, and to reduce the harmful economical and environmental effects of heavy traffic. In this paper, we design a highly efficient model-predictive control system that uses a gradient-based approach to solve the optimization problem, which has been reformulated as a two-point boundary value problem. A gradient-based approach computes the derivatives to find the optimal value. Therefore, the optimization problem should involve only smooth functions. Hence, for nonsmooth functions that may appear in the internal model of the MPC controller, we propose smoothening approaches. The controller then uses an integrated smooth flow and emission model, where the control objective is to reduce a weighted combination of the total time spent and total emissions of the vehicles. We perform simulations to compare the efficiency and the CPU time of the smooth and nonsmooth optimization approaches. The simulation results show that the smooth approach significantly outperforms the nonsmooth one both in the CPU time and in the optimal objective value.