Advanced Computational Stochastic Dynamic Programming for Continuous Time Problems

研究者及其同事开发了用于最优随机控制问题的大规模计算程序。大规模并行处理器和并行算法的进步对于管理大规模计算和存储需求是必不可少的，特别强调地下水污染修复和制造系统中的大规模应用。先进计算技术的实现，如并行化，图形可视化，有效的数据结构使得解决更大维度的问题成为可能。 这里的重点是形式上合理的和有用的计算方法，而不是有限的高度严格的结果。 本文的目标是为一般连续时间非线性随机动态系统的最优反馈控制发展与大规模并行处理相结合的快速算法。 这些随机系统中既有高斯噪声又有分布泊松白色噪声，因而是混合随机模型，对这些系统进行先进的计算处理，特别是将泊松噪声用于灾害性事件的建模，是本研究的一个独特之处。 计算方法在地下水污染模型和多级制造系统上进行了测试，但适用于广泛的应用，从而为计算方法提供了更高水平的鲁棒性。 数值方法直接处理随机动态规划的偏微分方程。 新的算法，包括有限元和随机模拟，开发，以减轻内存和计算密集型需求的“灾难的维度。" 研究人员和同事开发地下水污染和制造问题的最佳计算解决方案的不确定性。 地下水和制造业问题分别是重大和国家挑战问题的例子。 在地下水的情况下，不确定性的原因是意外引入的污染和变化的环境参数，而在制造系统的情况下，它是故障和维修的机器与波动的制造参数。 寻求最佳解决方案的原因是使成本最小化。 大规模的计算是必要的，由于governingphysical方程的复杂性和必要的数值近似。 由于清理受污染的地下水可能花费数十亿美元，在可行的情况下，最佳解决方案可以比非最佳方法节省数百万美元。 同样的节约也可以从及时生产系统中获得，这些系统能够最大限度地降低成本，增强我们的全球竞争力。 先进的计算技术是利用大规模并行计算机的高性能计算来获得最优解的，图形可视化对于使环境资源或制造厂管理者的巨大输出可用是重要的，他们将是主要用户。

The investigator and associates develop large scalecomputational procedures for optimal stochastic control problems.Massively parallel processor and parallel algorithm advances areessential for managing massive computational and memory demands,with particular emphasis on large scale applications in groundwater pollution remediation and manufacturing systems.Implementation of advanced computational techniques, such asparallelization, graphical visualization, and efficient datastructures make possible the solution of larger dimensionalproblems. The emphasis here is on formally justified and usefulcomputational methods rather than limited highly rigorousresults. The objective is to develop fast algorithms coupledwith massively parallel processing for the optimal feedbackcontrol of general continuous-time nonlinear stochastic dynamicalsystems. These stochastic systems include both Gaussian anddistributed Poisson white noise, thus hybrid stochastic models.Advanced computational treatment of these systems, especiallywith Poisson noise for modeling disastrous events, is aparticularly unique feature of this research. The computationalmethods are tested on ground water pollution models andmultistage manufacturing systems, but are applicable to a widevariety of applications, yielding a higher level of robustnessfor the computational methods. The numerical approach directlytreats the partial differential equation of stochastic dynamicprogramming. New algorithms, including finite element and randomsimulations, are developed to alleviate both memory andcomputationally intensive demands from the "curse ofdimensionality." The investigator and associates develop optimalcomputational solutions to ground water pollution andmanufacturing problems perturbed by uncertainty. Ground waterand manufacturing problems are examples of grand and nationalchallenge problems, respectively. In the case of ground waterthe cause of uncertainty is the unexpected introduction ofpollution and varying environmental parameters, while in the caseof the manufacturing systems it is the failure and repair ofmachines with fluctuating manufacturing parameters. The reasonfor seeking optimal solutions is to minimize costs. Large scalecomputations are necessary due to the complexity of the governingphysical equations and essential numerical approximations. Sincethe cleanup of polluted ground water sites can cost billionswhere feasible, optimal solutions could save millions overnonoptimal methods. Similar savings can be obtained forjust-in-time manufacturing systems that are managed to minimizecosts, enhancing our globally competitive capabilities. Advancedcomputing techniques are developed to get optimal solutions usinghigh performance computation with massively parallel computers.Graphical visualization is important to make the immense outputusable to the environmental resource or manufacturing plantmanager who would be the prime user.