Time-instant optimization for hybrid model predictive control of the Rhine–Meuse delta

In order to ensure safety against high sea water levels, in many low-lying countries, water levels are maintained at certain safety levels, and dikes have been built, while large control structures have been installed that can also be adjusted dynamically after they have been constructed. Currently, these control structures are often operated purely locally, without coordination of actions being taken at different locations. Automatically coordinating these actions is difficult, as open water systems are complex, hybrid dynamical systems, in the sense that continuous dynamics (e.g. the evolution of the water levels) appear mixed with discrete events (e.g. the opening or closing of barriers). In low lands, this complexity is increased further due to bi-directional water flows resulting from backwater effects and interconnectivity of flows in different parts of river deltas. In this paper, we propose a model predictive control (MPC) approach that is aimed at automatically coordinating the actions of control structures. The hybrid dynamical nature of the water system is explicitly taken into account. In order to relieve the computational complexity involved in solving the MPC problem, we propose TIO-MPC, where TIO stands for time-instant optimization. Using this approach, the original MPC optimization problem that uses both continuous and integer variables is transformed into a problem involving only continuous variables. Simulation studies of current and future situations are used to illustrate the behavior of the proposed scheme.