Mathematical Sciences: Nonlinear Partial Differential Equations in Optimal Control and Probability

数学科学：最优控制和概率中的非线性偏微分方程

• 批准号: 9002249
• 负责人: Halil Soner
• 金额: $ 4.31万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002249&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Partial; Differential

The principal investigator will study several problems in optimal deterministic or stochastic control and probability, using the theory of nonlinear partial differential equations. The project consists of three parts. The optimal control of a singularly controlled Brownian motion will be studied using the results for free boundary problems. This approach has yielded regularity results when the dimension is equal to two and it is the first multi-dimensional result which yields the construction of the optimal process. It now appears that it can be generalized to higher dimensions. The second part of this project is devoted to the perturbation theory of infinite dimensional Hamilton-Jacobi equations. As a case study, the principal investigator will study an asymptotic problem related to simple exclusion processes. Finally, an application of the finite dimensional perturbation theory to a problem of production planning is described. The model to be studied has failure-prone machines, and the goal is to construct approximate optimal policies by exploiting the hierarchical structure of the model.

首席研究员将利用非线性偏微分方程理论研究最优确定性或随机控制和概率中的几个问题。 该项目由三部分组成。 将使用自由边界问题的结果来研究奇异控制布朗运动的最优控制。 当维数等于 2 时，这种方法产生了规律性结果，并且它是第一个产生最优过程构造的多维结果。 现在看来它可以推广到更高的维度。 该项目的第二部分致力于无限维 Hamilton-Jacobi 方程的微扰理论。 作为案例研究，主要研究者将研究与简单排除过程相关的渐近问题。 最后，描述了有限维摄动理论在生产计划问题中的应用。 要研究的模型具有容易发生故障的机器，目标是通过利用模型的层次结构构建近似最优策略。