56. F. B. Hanson and J. J. Westman, Computational Stochastic Dynamic Programming Problems: Groundwater Quality Remediation, in Proc. 33th IEEE Conf. on Decision and Control, vol. 1, pp. 455-460, December 1994.

Brief Abstract: This paper will be presented at the 33rd CDC in December at Buena Vista, FL. This is an introduction to the stochastic control model for ground water modeling using stochastic dynamic programming with both state and space dependence.

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57. F. B. Hanson and J. J. Westman, " Parallel Stochastic Dynamic Programming Applications: Spatial and State Finite Elements, " Proceedings of International Conference on Control and Information, The Chinese University Press, Chinese University of Hong Kong, Sha Tin, Hong Kong, pp. 145-150, June 1995.

Brief Abstract: This paper covers more of the finite element techniques used in the computational stochastic dynamic programming for groundwater applications.

68. Daniel L. Kern> and Floyd B. Hanson, " Filtering Approximation Using Systematic Perturbations of a Discrete-Time Stochastic Dynamical System," Proceedings of 1999 American Control Conference, Paper no. ACC99-IEEE0116, pp. 445-449, June 1999.

Abstract: The standard problem of groundwater pollutant remediation by well pumping is modeled as a discrete-time LQG stochastic optimal control problem. The control is approximated by using a variation of differential dynamic programming (DDP) that includes systematic perturbations. Kalman filtering is used to estimate the partially observed state variables in a tractable format. This is a filtering application of the DDP method used by the authors in an earlier perturbation paper.

78. Daniel L. Kern, J. J. Westman, and Floyd B. Hanson, " Locally Optimal Pumping and Treatment Rates in Uncertain Environments ," in Fluid Flow and Transport in Porous Media: Mathematical and Numerical Treatment, AMS Contempory Mathematics, vol. 295, Z. Chen and R. E. Ewing (Editors), pp. 305-315, 17 July 2002.

Abstract: Stochastic control theory can be applied to the problem of groundwater remediation in order to determine optimal pumping and treatment rates in an uncertain environment. The approach utilizes stochastic dynamic programming that optimizes a cost functional for treatment subject to the constraints of the contaminant transport equations via a search over the state-control space. However, this approach for even small problems requires huge amounts of memory to solve numerically and is exceptionally prohibitive even using finite elements for the state-control space and time large jumps present. The approach here is to reduce the computational complexity by casting the contaminant flow equations to be linear locally while allowing for jumps and small background fluctuations in the dynamical system. The quasi-LQGP problem can then be used to determine the local optimal rates for pumping and treating, which does not require prohibitive amounts of memory. This linearized model can then be used as the starting iterate to hopefully accelerate the solution to the true nonlinear system for the contaminant transport equations.

This material is based upon work supported by the National Science Foundation under Grants Numbers 880699, 9102343, 9301107, 9626692, 9973231.

Supercomputing research support was provided by San Diego Supercomputing Center NPACI Account UIL203, National Center for Supercomputing Applications Grant Numbers DCR860001N, DMS890009N, DMS900016N, DMS920003N, DMS960002N; Pittsburgh Supercomputing Center Grant Numbers DMS940001P and DMS9400011P; Argonne National Laboratory's Advanced Computing Research Facility; Los Alamos National Laboratory's Advanced Computing Laboratory ACL-Accounts Z803835 and gwqfbh-d.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation or other agency.

September 24, 2001