Continuous State Dynamic Programming Algorithms for Supercomputers

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Dynamic programming algorithms are widely used for analyzing the control of nonlinear dynamic systems. These algorithms are computationally intensive, especially for stochastic problems. Supercomputers and parallel processing will facilitate the use of dynamic programming algorithms for realistic problems that could not be addressed in the past because of computational limitations. The proposal concentrates on the following issues: a) parallel processing of Stochastic Dynamic Programming (SDP) and Differential Dynamic Programming (DDP), b) coupling DDP to finite elements models, and c)special algorithms for SDP with binary control variables. The research focuses on systems with continuously valued state variables, and hence the analysis will examine the computation of SDP with linear or nonlinear interpolation in the state space. The computational effect on CPU and on parallel processing of using implicit or explicit finite element models in conjunction with DPP will be investigated. Large-scale numerical results will be computed at the Cornell National Supercomputer Facility (CNSF) in co-operation with CNSF staff. The results of the investigation will be applied to several "real" problems arising in environmental management as well as to hypothetical test examples.//