NONLINEAR WEIGHTED FEEDBACK-CONTROL OF GROUNDWATER REMEDIATION UNDER UNCERTAINTY

Differential dynamic programming is used to compute optimal time-varyi ng pumping policies for a pump and treat strategy for groundwater reme diation. The feedback law generated by a constrained differential dyna mic programming algorithm with penalty functions is used as the basis of feedback laws tested in cases where there is uncertainty in the hyd raulic conductivity. Confined transient aquifer flow and transport are modeled using a two-dimensional Galerkin finite element scheme with i mplicit time differencing. Optimal policies are calculated using a giv en or ''measured'' set of hydraulic conductivities and initial conditi ons. The optimal policies (with and without feedback) are applied usin g the same finite element model with a second or ''true'' set of condu ctivities. The ''true'' sets of conductivities are generated randomly from an autocorrelated lognormal distribution by the spectral method. The approach used here has an advantage over other uncertainty approac hes because it is not necessary to specify precisely which parameters are considered uncertain and which are certain. Also no single probabi lity distribution need be assumed for each uncertain parameter. By adj usting the relative weight assigned each penalty function, robust feed back laws were obtained that perform equally well under nine different assumed error distributions. In our examples, well-designed feedback policies cost between 4% and 51% less than the cost of applying the ca lculated optimal policies without using a feedback law.