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

数学科学：连续时间问题的高级计算随机动态规划

• 批准号: 9626692
• 负责人: Floyd Hanson
• 金额: $ 10.2万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-15 至 2000-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9626692&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Advanced; Computational; Stochastic

Hanson 9626692 The investigator and associates develop advanced computational methods to solve large scale dynamic programming problems in uncertain environments. These methods include parallel computation, graphical visualization, problem mapping, memory management and data restructuring on massively parallel and massive memory processors to solve large dimensional problems that could not be solved by ordinary methods. The objective is develop fast algorithms for the optimal feedback control of large, general, continuous time, nonlinear, stochastic dynamical systems, perturbed by both Gaussian and distributed Poisson white noise. The treatment of the random jumps of Poisson processes for modeling rare, disastrous events is a special and challenging feature of this research. The main application of this research is to optimal remediation for groundwater quality in an uncertain environment. Other applications are to parameter uncertainty in partially observed control systems, i.e., the dual control problem, and to just-in-time manufacturing systems. The numerical approach of the investigators directly treats the partial differential equation of stochastic dynamic programming. New algorithms, such as spatial and state finite elements, are used to alleviate both memory and computational demands. Purely parallel algorithms based on intelligent state space search are also being developed. The development of graphical visualization and data management tools are essential for analyzing massive amounts of output in many dimensions. The investigator and associates are developing optimal solutions to environmental and manufacturing problems when there is some uncertainty involved. Examples of the cause of uncertainty in the problem are the unexpected introduction of pollution and unknown parameters in the case of the environment, while in the case of manufacturing an example would be the random failure of machines. The reason for seeking optimal solutio ns is to minimize costs or wasting precious materials or resources. A large and important application that the investigator studies is the cleanup of groundwater resources where the source of the pollution or the underground state is uncertain. Since polluted groundwater sites can costs from millions to billions and more (there are some sites for which cleanup procedures are unknown), optimal solutions could save millions over existing sub-optimal procedures. Similar savings can be obtained for just-in-time manufacturing systems that are optimally managed, enhancing our globally competitive capabilities. The investigator and associates develop advanced computing techniques to compute the optimal solutions using high performance computing, which is essential when uncertain environments or parameters make the amount of computation for the solution very large. The high performance computing involves using massive computers for fast optimal solutions and graphical visualization to make the immense amount of output understandable, for instance to the environmental resource or manufacturing plant manager who would be the prime user.

汉森9626692 研究人员和同事开发先进的计算方法来解决不确定环境中的大规模动态规划问题。 这些方法包括在大规模并行和大内存处理器上进行并行计算、图形可视化、问题映射、内存管理和数据重组等，以解决常规方法无法解决的高维问题。 本文的目标是研究受高斯和分布泊松白色噪声干扰的大型、一般、连续时间、非线性、随机动态系统的最优反馈控制的快速算法。 处理泊松过程的随机跳跃建模罕见的，灾难性的事件是本研究的一个特殊的和具有挑战性的功能。 该研究的主要应用是在不确定环境中对地下水水质进行优化修复。 其他应用是部分观测控制系统中的参数不确定性，即，双重控制问题，以及准时制制造系统。 研究者的数值方法直接处理随机动态规划的偏微分方程。 新的算法，如空间和状态有限元，用于减轻内存和计算的需求。 基于智能状态空间搜索的并行算法也正在开发中。 图形可视化和数据管理工具的开发对于在多个维度上分析大量输出至关重要。 当存在一些不确定性时，研究人员和同事正在开发环境和制造问题的最佳解决方案。 问题中不确定性原因的例子是在环境的情况下意外引入污染和未知参数，而在制造的情况下，一个例子是机器的随机故障。 寻求最佳解决方案的原因是最大限度地减少成本或浪费宝贵的材料或资源。 研究人员研究的一个重要应用是地下水资源的净化，其中污染源或地下状态不确定。 由于受污染的地下水场地可能需要数百万到数十亿甚至更多的费用（有些场地的清理程序是未知的），最佳解决方案可以比现有的次优程序节省数百万美元。 通过优化管理的即时生产系统也可以实现类似的节约，从而增强我们的全球竞争力。 研究人员和同事开发先进的计算技术，使用高性能计算来计算最优解，这在不确定的环境或参数使解的计算量非常大时是必不可少的。 高性能计算涉及使用大规模计算机快速优化解决方案和图形可视化，以使大量的输出可以理解，例如环境资源或制造厂经理，他们将是主要用户。