A continuation approach to nonlinear model predictive control of open channel systems

The equations governing open channel flow are strongly nonlinear when considering the full range of possible flows. Hence, optimization problems that aim to select optimal flow regimes for hydraulic structures such as weirs and pumps are subject to nonlinear relations between optimization variables. Such optimization problems are nonconvex, and may admit multiple isolated local minima, rendering them problematic for use in operational model predictive control. This paper introduces the notions of zero-convexity and path stability, i.e., the property of a parametric optimization problem that I) is convex at the starting parameter value and II) that when computing a path of solutions as a function of the parameter, such a path exists and no bifurcations arise. Path stability ensures that the parametric optimization problem can be solved in a deterministic and numerically stable fashion. It is shown that a class of numerical optimal control problems subject to simplified 1D shallow water hydraulics is zero-convex and path stable, and hence suitable for deployment in decision support systems based on model predictive control.