H. van Ekeren, R.R. Negenborn, P.J. van Overloop, and B. De Schutter, "Time-instant optimization for hybrid model predictive control of the Rhine-Meuse Delta," Journal of Hydroinformatics, vol. 15, no. 2, pp. 271-292, 2013.
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 have been built, while on the other hand large control structures have been installed that can be adjusted dynamically also after they have been constructed. Currently, these control structures are often operated purely locally, without coordination of actions being taken at different structures. Automatically coordinating these actions is hard, since 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. Hereby, the hybrid dynamical nature of the water system is explicitly taken into account. In order to relief 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.