Model Predictive Control for Large Freeway Networks

Abstract

Due to the yearly increase in the number of vehicles and the need for transportation, traffic congestion has become a crucial problem in today's society. There is a need for a sustainable solution to reduce or even eliminate traffic jams. Freeway traffic control has shown to be a sustainable solution to this problem. Especially the implementation of Ramp Metering (RM) installations and Variable Speed Limits (VSLs) as control measures is currently a widely researched area because the proper coordination of those measures can significantly reduce traffic congestion, traffic emissions and the risk of accidents. The Model Predictive Control (MPC) framework has shown outstanding capabilities for coordinated control of RM installations and VSLs. However, the inherent nonlinearity of traffic flow, in combination with the discrete nature of VSLs and the continuous nature of RM rates, yields a Mixed Integer Nonlinear Programming (MINLP) optimisation problem that has to be solved within every controller sampling interval. The computational time that is needed to solve MINLP problems generally increases exponentially with the size of the problem. Therefore, the implementation of MPC to large freeway networks remains challenging. This work proposes two novel MPC algorithms for coordinated control of continuous RM rates and discrete VSLs on large freeway networks. Both algorithms use a distributed control architecture and an alternating optimisation scheme to relax the MINLP problems and, hence, offer a trade-off between computational complexity and system performance. A case study is performed to evaluate the performance of both algorithms. In this case study a 30 km long freeway network is used that contains six VSLs and three RM installations. The first part of the case study shows that relaxing the VSLs to be continuous decision variables instead of discrete decision variables in the optimisation problems results in a major performance loss with a distributed architecture. This result contrasts with many related works, where the MINLP optimisation problems are relaxed by considering the VSLs to be continuous decision variables. The second part of the case study evaluates the proposed distributed algorithms by comparing their performance to the more conventional centralised and decentralised MPC algorithms. Both proposed algorithms have a lower computational complexity than the centralised algorithm, as they manage to solve the optimisation problems within the controller sampling intervals. Moreover, one of the proposed algorithms has a system performance that is remarkably similar to the optimal performance of the centralised algorithm.