Advanced Computational Stochastic Dynamic Programming for Continuous Time Problems

本研究的目的是发展一般连续时间随机动力系统最优反馈控制的快速算法。这些随机动力系统包括高斯白噪声和泊松白噪声的扰动。计算处理一般的，非线性的，随机的，连续时间的马尔可夫噪声，包括泊松噪声的最优反馈控制，是这个项目的一个特别的特点。这些算法在多态资源模型上进行了测试，但适用于广泛的应用。数值方法直接处理随机动态规划的偏微分方程。新的数据结构和算法，如有限元和多重网格法，将被开发出来，以缓解“维度灾难”对存储和计算的密集需求。人们正在为可伸缩的大规模并行处理器和海量存储的超级计算机开发纯并行方法。结果给出了关于状态变量和时间的最优反馈控制变量和期望的最优性能指标。大规模科学计算对于管理大型应用程序的计算和内存需求至关重要，这些应用程序包括航天动力学、柔性结构、资源、经济和机器人等。并行、向量化和优化数据结构等先进计算技术的应用，使得解决更大规模的问题成为可能。

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.