Mathematical Sciences: Advanced Computational Stochastic Dynamic Programming for Continuous Time Problems

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9301107 Hanson High performance computing is essential for managing massive computational and memory demands in optimal control of large scale applications, such as aerospace, structures, resources, economics and robotics. Implementation of advanced computational techniques, such as parellelization, matrization (including vectorization), graphical visualization and problem mapping make possible the solution of larger dimensional problems. Our research objective is to develop fast algorithms for the optimal feedback control of general continuous time nonlinear stochastic dynamical systems. These systems include perturbations by both Gaussian and distributed Poisson white noise. Advanced computational treatment of these systems, especially with Poisson noise, is a particularly unique feature of this proposal. The algorithms are being testing 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 programming. New algorithms, such as finite element, will be developed to alleviate both memory and computationally intensive demands from the "curse of dimensionality". Purely parallel methods are being developed for scalable, massively parallel and massive memory supercomputers, including new generation "ultracomputers". The development of graphical visualization tools is also essential for analyzing massive amounts of output in many dimensions. There are also several related problems as well. ***