Distributed MPC for Large Freeway Networks Using Alternating Optimization

The Model Predictive Control (MPC) framework has shown great potential for the control of Variable Speed Limits (VSLs) and Ramp Metering (RM) installations. However, the implementation to large freeway networks remains challenging. One major reason is that, by considering the VSLs to be discrete decision variables, an extremely difficult Mixed Integer Nonlinear Programming (MINLP) optimization problem has to be solved within every controller sampling interval. Consequently, many related papers relax the MINLP problems by considering the VSLs to be continuous variables. This paper proposes two novel MPC algorithms for coordinated control of discrete VSLs and continuous RM rates that do not make this relaxation. The proposed algorithms use a distributed control architecture and an alternating optimization scheme to relax the MINLP optimization problems but still consider the VSLs as discrete variables and, hence, offer a trade-off between computational complexity and system performance. The performance of the proposed algorithms is evaluated in a case study. The case study shows that relaxing the VSLs to be continuous variables with a distributed architecture results in a significant performance loss. Furthermore, both proposed algorithms have a lower computational complexity than the more conventional centralized approach and, as a result, they do manage to solve all optimization problems within the sampling intervals. Moreover, one of the proposed algorithms has a system performance that is remarkably similar to the optimal performance of the centralized approach.