Mathematical Sciences: Differential Geometric and Real Analytic Methods in NonLinear Control Theory

数学科学：非线性控制理论中的微分几何和实解析方法

• 批准号: 8902994
• 负责人: Hector Sussmann
• 金额: $ 17.53万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902994&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Differential; Geometric; Real

Research will be carried out on nonlinear control theory, continuing the Principal Investigator's previous work in this area on a broad class of problems on local and global controllability, observability, minimal realizations, applications to robotics, optimal control and feedback stabilization. The methods used will be those commonly known as "differential geometric control theory," the theory of real analytic maps and their associated stratifications, and the theory of real analytic desingularization. Specifically, efforts will be made to solve a number of open problems in the areas of optimal control, controllability, and realization theory of both continuous time and sampled continuous time systems, while pursuing the development of the necessary mathematical tools -- especially on the theory of real analytic stratifications.

将对非线性控制理论进行研究， 继续首席研究员以前的工作， 一个关于地方和全球问题的广泛类别的区域 可控性，可观测性，最小实现， 应用于机器人、最优控制和反馈 稳定化 所使用的方法通常称为 “微分几何控制理论”的理论真实的 分析地图及其相关分层，以及 真实的解析去奇异化理论。 具体而言，努力 将解决以下领域的一些悬而未决的问题： 最优控制、可控性和两者的实现理论 连续时间和采样连续时间系统，而 追求必要的数学工具的发展-- 特别是关于真实的分析层次理论。