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.

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In Model Predictive Control (MPC) for traffic networks, traffic models are crucial since they are used as prediction models for determining the optimal control actions. In order to reduce the computational complexity of MPC for traffic networks, macroscopic traffic models are often used instead of microscopic traffic models. These macroscopic traffic models can be divided into homogeneous, single-class models and heterogeneous, multi-class models. In general, multi-class models are more accurate than single-class models, without increasing the computational complexity significantly. In MPC a more accurate model in general implies a better prediction of the controlled system, providing the controller more accurate information for determining the control actions. Therefore, developing and using multi-class traffic models is one way to improve the effectiveness of MPC. Apart from the above characteristics of traffic models, other factors such as uncertainties in external inputs and model parameters can also affect the accuracy of predictions. Thus another way for improving the effectiveness of MPC is to take into account the effects of these uncertainties and to develop robust MPC approaches for handling these uncertainties. Apart from improving the effectiveness of MPC, making MPC feasible for large-scale traffic networks is also important, due to the rapid increase of the computational complexity of the MPC optimization problem with the size of the controlled system. For large-scale systems, Distributed Model Predictive Control (DMPC) is often considered for making the control approach computationally feasible. Moreover, robust DMPC can be developed for ensuring both feasibility and robustness.@en

In this paper we develop a scenario-based Distributed Model Predictive Control (DMPC) approach for large-scale freeway networks. The uncertainties in a large-scale freeway network are categorized into global uncertainties for the overall network and local uncertainties for subnetworks. A reduced scenario tree is proposed, consisting of global scenarios and a reduced local scenario tree. For handling uncertainties in the scenario-based DMPC problem, a min-max setting is considered. A case study is implemented for investigating the scenario-based DMPC approach, and the results show that in the presence of uncertainties it is effective in improving the control performance with the queue length constraint being satisfied.

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