Mathematical Sciences: Optimal Control Problems and Nonsmooth Analysis

数学科学：最优控制问题和非光滑分析

• 批准号: 9200303
• 负责人: R. Tyrrell Rockafellar
• 金额: $ 15.64万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-04-15 至 1995-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9200303&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Optimal; Control; Problems

The principal investigator will conduct research on problems of optimal control, both in continuous and discrete time. Optimality conditions recently obtained for the control of differential inclusions will be applied to Bolza problems, and results are to be derived for Hamilton-Jacobi theory and feedback rules. In addition, a new theory of generalized second- derivatives will be applied to sensitivity analysis and parametric methods of optimization. Optimal control problems are useful as mathematical models in many areas of engineering and operations management. By better understanding their structure and properties, the gained insight will lead to improved numerical optimization algorithms.

首席研究员将对连续和离散时间的最优控制问题进行研究。将最近得到的微分夹杂控制的最优性条件应用于Bolza问题，并推导出Hamilton-Jacobi理论和反馈规则的结果。此外，一个新的广义二阶导数理论将应用于灵敏度分析和参数优化方法。最优控制问题作为数学模型在工程和运营管理的许多领域都很有用。通过更好地了解它们的结构和性质，获得的洞察力将导致改进的数值优化算法。