Premium
Optimal control of nonlinear groundwater hydraulics using differential dynamic programming
Author(s) -
Jones LaDon,
Willis Robert,
Yeh William W.G.
Publication year - 1987
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr023i011p02097
Subject(s) - differential dynamic programming , nonlinear system , aquifer , sequential quadratic programming , optimal control , hydraulics , curse of dimensionality , dynamic programming , mathematical optimization , groundwater model , groundwater , groundwater recharge , computer science , quadratic programming , control theory (sociology) , mathematics , geology , engineering , geotechnical engineering , control (management) , physics , quantum mechanics , aerospace engineering , machine learning , artificial intelligence
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.