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.

首席研究员将研究几个问题， 最优确定性或随机控制和概率， 利用非线性偏微分方程理论。 该项目包括三个部分。 的最优控制 奇异控制布朗运动将研究使用 自由边界问题。 这一做法产生了 当维数等于2且 产生构造的第一个多维结果 最佳的过程。 现在看来， 推广到更高的维度。 第二部分 项目致力于无穷大的扰动理论 维Hamilton Jacobi方程 作为案例研究， 首席研究员将研究一个渐近问题， 到简单的排除过程。 最后，给出了 产生式问题的有限维扰动理论 规划描述。 要研究的模型容易失败 机器，目标是构建近似最优的 通过利用模型的层次结构来制定策略。