Model predictive control of urban drainage systems: A review and perspective towards smart real-time water management

Model predictive control (MPC) can be used to manage combined urban drainage systems more efficiently for protection of human health and the environment, but examples of operational implementations are rare. This paper reviews more than 30years of partly heterogeneous research on the topic. We propose a terminology for MPC of urban drainage systems and a hierarchical categorization where we emphasize four overall components: the receding horizon principle, the optimization model, the optimization solver, and the internal MPC model. Most of the reported optimization models share the trait of a multiobjective optimization based on a conceptual internal MPC model. However, there is a large variety of both convex and non-linear optimization models and optimization solvers as well as constructions of the internal MPC model. Furthermore, literature disagrees about the optimal length of the components in the receding horizon principle. The large number of MPC formulations and evaluation approaches makes it problematic to compare different MPC methods. This review highlights methods, challenges, and research gaps in order to make MPC of urban drainage systems accessible for researchers and practitioners from different disciplines. This will pave the way for shared understanding and further development within the field, and eventually lead to more operational implementations.