Nonlinear Model Predictive Control for heterogeneous process models in water resources

Abstract

This paper introduces a novel Non-linear Model Predictive Control (NMPC) algorithm for the real-time control of heterogeneous, large-scale water resources systems. The algorithm is based on the idea of defining a Lagrangian function in which the system state transition equations are defined as separate equality constraints of the optimization problem. This enables the derivation of an adjoint of the state transition equations and provides the objective function gradient. The optimization problem can then be solved by any numerical solver, under the consideration of the constraints and the gradient. The main advantage of the proposed approach is the possibility of easily dealing with the process-based models commonly adopted in the environmental literature, under the assumption of both explicit and implicit time-stepping schemes. The proposed procedure computes the gradient of a cost function by computational costs comparable to a model simulation itself, thus enabling the management of large-scale systems. The capabilities of the NMPC algorithm are first evaluated on a test case study, and then demonstrated for the control of six hydraulic structures and two major ood detention basins along the bifurcation points of the Rhine River in The Netherlands. © 2011 IFAC.