Optimal control of nonlinear groundwater hydraulics using differential dynamic programming

Abstract

Optimal groundwater management models are based on the hydraulic equations of the aquifer system. These equations relate the state variables of the groundwater system, the head, and the decision variables that control the magnitude, location, and timing of pumping, or artificial recharge. For the unconfined aquifer these management models are large‐scale, nonlinear programming problems. A differential dynamic programming (DDP) algorithm is used for unsteady, nonlinear, groundwater management problems. Due to the stagewise decomposition of DDP, the dimensionality problems associated with embedding the hydraulic equations as constraints in the management model are significantly reduced. In addition, DDP shows a linear growth in computing effort with respect to the number of stages or planning periods, and quadratic convergence. Several example problems illustrate the application of DDP to the optimal control of nonlinear groundwater hydraulics.