Optimal control for groundwater remediation by differential dynamic programming with Quasi‐Newton Approximations

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Abstract
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.