The general objective is the development of supercomputing algorithms for the optimal feedback control of larger scale, continuous time, nonlinear, Markov stochastic dynamical systems. The numerical procedures are based on PDE methods such as the finite element or difference methods for stochastic dynamic programming, as well as other advanced numerical methods. The algorithms have been implemented on the Cray vector multiprocessors and massively parallel Connection Machines. These implementations have utilized advanced supercomputing techniques such as parallelization, vectorization and data structures and decompositions. Problems in 5 state space dimensions have been solved. Large dimensions are required by some applications, such as groundwater remediation and resource management. The principal application focus here is the remediation for groundwater quality through the control of pumping policies when the groundwater is subject to uncertain introduction of contaminants.
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