Advanced Computational Stochastic Dynamic Programming for Continuous Time Problems

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The objective of this research is to develop fast algorithms for the optimal feedback control of general continuous time stochastic dynamical systems. These stochastic dynamical systems include perturbations by both Gaussian and Poisson white noise. The computational treatment of the optimal feedback control of general, nonlinear, stochastic differential equations with Markov noise in continuous time, including Poisson noise, is a particularly unique feature of this project. The algorithms are being tested on multi-state resource models, but are applicable to a wide variety of applications. The numerical approach directly treats the partial differential equation of stochastic dynamic programming. New data structures and algorithms, such as finite element and multigrid methods, will be developed to alleviate both memory and computation intensive demands from the "curse of dimensionality". Purely parallel methods are being developed for scalable, massively parallel processors and massive memory supercomputers. Results give the optimal feedback control variables and the expected optimal performance index in terms of state variables and time. Large scale scientific computing is essential for managing the computational and memory demands in the optimal control of large applications, such as aerospace dynamics, flexible structures, resources, economics and robotics. The implementation of advanced computational techniques, such as parallelization, vectorization and optimal data structures, make it possible to solve problems of larger dimension.