Mathematical Sciences: Abnormality in Optimization and Optimal Control Problems

数学科学：最优化和最优控制问题中的异常

• 批准号: 9109324
• 负责人: Urszula Ledzewicz
• 金额: $ 1.8万
• 依托单位: Southern Illinois University at Edwardsville
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9109324&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Abnormality; Optimization; Optimal

In this project the principal investigator will explore the use of new techniques to study what are called "abnormal" cases in optimization and optimal control problems that involve nonregular operators. These techniques come from functional analysis, and they have been applied successfully to treat abnormal cases involving the Euler-Lagrange equations and the Pontryagin Maximum Principle. The principal investigator is concerned specifically with determining the limits of these techniques and with obtaining sharper results than those obtained previously for the derivation of nontrivial optimality conditions for general extremal problems. The derivation and exploitation of optimality conditions for problems in optimization and optimal control have been one of the major success stories of the decades since World War II. These results have paved the way for the development of a host of control systems that have improved the quality of life. More recent advances involving robotic systems can be traced to this work as well. In this project the principal investigator will examine optimality conditions in atypical cases where the traditional theory is inadequate. To do so requires the use of powerful methods of abstract functional analysis combined with a thorough knowledge of classical control theory.

在这个项目中，首席研究员将探索 使用新技术来研究所谓的"异常"病例， 最优化和最优控制问题，涉及非正则 运营商 这些技术来自功能分析， 它们已成功地应用于治疗异常病例 包括欧拉-拉格朗日方程和庞特里亚金最大值 原则 首席研究员特别关注 通过确定这些技术的极限并通过获得 比以前推导得到的结果更清晰 一般极值问题的非平凡最优性条件。 最优性条件的推导和利用 最优化和最优控制中的问题一直是 二战以来几十年的主要成功故事。 这些 结果为开发一系列控制系统铺平了道路。 改善生活质量的系统。最近 涉及机器人系统的进步可以追溯到这项工作， 好. 在这个项目中，首席研究员将研究 非典型情况下的最优性条件，其中传统的 理论是不够的。 要做到这一点，需要使用强大的 方法的抽象功能分析结合了一个彻底的 经典控制理论知识。