Mathematical Sciences: Research Problems in Stochastic Control and Numerical Approximation

数学科学：随机控制和数值逼近的研究问题

• 批准号: 8702236
• 负责人: Pao Liu Chow
• 金额: $ 4.2万
• 依托单位: Wayne State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-09-01 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8702236&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Problems; Stochastic

The following topics will be investigated: (1) Some Singular Stochastic Control Problems: Two problems: One is concerned with the analysis of a class of singular control problems in several dimensions, and the second pertains to a adapted version of singular stochastic control in one dimension. (2) Impulse Control Problems: Two novel applications of impulse control theory to optimal maintenance and sequential scheduling problems will be studied. (3) Ergodic Control Problems with a class of stochastic control of diffusion with jumps with a long- term average criterion. The emphasis is on the study of the associated invariant measure. (4) Numerical Analysis of Stochastic Control Problems: Numerical algorithm for solving a class of singular control problems in several dimensions. Numerical approximation of some Hamilton-Jacobi-Bellman equations. (5) Some Problems in Stochastic Distributed- Parameter Sytems: The investigators plan to study the solution of an infinite-dimensional H.J.B. equation arising from optimal control of a non-linear stochastic distributed system. The stability and asymptotic behavior of such a system with possible degeneracy will be investigated. This research is part of control theory with potential applications in engineering and computer science.

将研究以下主题：（1）一些 奇异随机控制问题：两个问题：一个是 研究了一类奇异控制问题， 问题在几个方面，第二个涉及到一个 适应版本的奇异随机控制在一维。 (2)脉冲控制问题：脉冲的两种新应用 最优维修和顺序调度的控制理论 将研究问题。 (3)带参数的遍历控制问题 一类带长跳扩散的随机控制， 项平均标准。 重点是研究 关联不变测度 (4)的数值分析 随机控制问题：求解随机控制问题的数值算法 一类多维奇异控制问题。 一类Hamilton-Jacobi-Bellman方程的数值逼近 方程 (5)随机分布函数中的若干问题 参数系统：研究者计划研究解决方案 一个无限维的HJB 最优方程 非线性随机分布系统的控制 的 稳定性和渐近行为 将研究简并性。 这项研究是控制理论的一部分，具有潜力 在工程和计算机科学中的应用