Hybrid model predictive control using time-instant optimization for the Rhine-Meuse Delta

In order to provide safety against high sea water levels, in many low-lying countries on the one hand dunes are maintained at a certain safety level and dikes are built, while on the other hand large control structures that can be controlled dynamically are constructed. Currently, these structures are often operated purely locally, without coordination on actions between different structures. Automatically coordinating the actions is particularly difficult, since open water systems are complex, hybrid systems, in the sense that continuous dynamics (e.g., the evolution of the water levels) are 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 different actions. Hereby, the hybrid nature is explicitly addressed. In order to reduce the computational effort required to solve the hybrid MPC problem we propose to use TIO-MPC, where TIO stands for time-instant optimization. A simulation study illustrates the potential of the proposed controller in comparison with the current setup in the Rhine-Meuse delta in The Netherlands.