A scenario-based distributed model predictive control approach for freeway networks

In this paper a scenario-based Distributed Model Predictive Control (DMPC) approach based on a reduced scenario tree is developed for large-scale freeway networks. In the new scenario-based DMPC approach, uncertainties in a large-scale freeway network are distinguished into two categories: global uncertainties for the overall network and local uncertainties applicable to subnetworks only. We propose to use a reduced scenario tree instead of using a complete scenario tree. A complete scenario tree is defined as a scenario tree consisting of global scenarios and all the combinations of the local scenarios for all subnetworks, while a reduced scenario tree is defined as a scenario tree consisting of global scenarios and a reduced local scenario tree in which local scenarios are combined within each subnetwork, not among subnetworks. Moreover, an expected-value setting and a min-max setting are considered for handling uncertainties in scenario-based DMPC. In the expected-value setting, the expected-value of the cost function values for all considered uncertainty scenarios is optimized by scenario-based DMPC. However, in the min-max setting, the worst-case of the cost function values for all considered uncertainty scenarios is optimized by scenario-based DMPC. The results for a numerical experiment show that the new scenario-based DMPC approach is effective in improving the control performance while at the same time satisfying the queue constraints in the presence of uncertainties. Additionally, the proposed approach results in a relatively low computational burden compared to the case with the complete scenario tree.