Abstract: A method, computer system, and program product for optimizing a useful objective function with respect to a dynamic parameter vector and a static parameter vector. The method, called the static/dynamic control (MDC) method, either minimizes or maximizes the useful objective function subject to a state equation, initial conditions, terminal conditions, constraints, and dynamic limitations. The SDC method includes an algorithm having two formulations: a period formulation and a fully continuous formulation. With the period formulation, the dynamic optimization variables associated with the dynamic limitations are permitted to be discontinuous, parametric functions of time. With the fully continuous formulation, the dynamic optimization variables are permitted to be continuous, non-parametric functions of time. The SDC method is computer implementable and employs an iterative process including an inner loop and an outer loop.

Abstract: The present invention features a differential dynamic programming (DDP) method for computing optimal, time-varying pumping policies utilized in groundwater remediation. The strategy for treating the groundwater can use a feedback law generated by a constrained differential dynamic programming algorithm with penalty functions. The method has been tested in cases where there is uncertainty in the hydraulic conductivity. Confined transient aquifer flow and transport were modeled, using a two-dimensional Galerkin finite element scheme with implicit time differencing. Optimal policies were calculated using a given or "measured" set of hydraulic conductivities and initial conditions. The optimal policies were applied using the same finite element model with a second, or "true" set of conductivities The "true" sets of conductivities were generated randomly from an autocorrelated lognormal distribution by the spectral method.