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Optimal control for groundwater remediation by differential dynamic programming with Quasi‐Newton Approximations
Author(s) -
Culver Teresa B.,
Shoemaker Christine A.
Publication year - 1993
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 - 10.1029/92wr02480
Subject(s) - differential dynamic programming , dynamic programming , optimal control , aquifer , differential (mechanical device) , mathematical optimization , rank (graph theory) , newton's method , computer science , groundwater , control theory (sociology) , mathematics , control (management) , nonlinear system , engineering , geotechnical engineering , physics , combinatorics , aerospace engineering , quantum mechanics , artificial intelligence
Differential dynamic programming with quasi‐Newton approximations (QNDDP) is combined with a finite element groundwater quality simulation model to determine optimal time‐varying pumping policies for reclamation of a contaminated aquifer. The purpose of the QNDDP model is to significantly reduce the large computational effort associated with calculation of optimal time‐varying policies. A Broyden rank‐one quasi‐Newton technique is developed to approximate the second derivatives of the groundwater quality model; these second derivatives are difficult to calculate directly. The performance of the QNDDP algorithm is compared to the successive approximation linear quadratic regulator (SALQR) technique, which sets the complicated second derivatives to 0. QNDDP converged to the optimal pumping policy in approximately half the time that the SALQR technique required. The QNDDP algorithm thus shows great promise for the management of complex, time‐varying systems.