Mathematical Sciences: Geometric Methods in the Control of Nonlinear Systems

数学科学：非线性系统控制中的几何方法

• 批准号: 9100043
• 负责人: Heinz Schaettler
• 金额: $ 5.72万
• 依托单位: Washington University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1993-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9100043&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Methods; Control

This project will study optimal control and symmetry principles of nonlinear systems. In optimal control the principal investigator will attempt to develop a formal procedure to calculate the cut-loci between surfaces consisting of endpoints of trajectories with different switching structures. These cut-loci are the dominant geometric feature for local optimality of trajectories near a reference point. In symmetry principles the principal investigator will try to extend to singular systems recent results on the calculation of feedback functions. These studies will lead to further understanding of the optimal design of mechanical systems where symmetries (e.g. rotational) are present.

本项目将研究非线性系统的最优控制和对称原理。在最优控制中，首席研究员将尝试开发一个正式的程序来计算由不同开关结构的轨迹端点组成的表面之间的切割轨迹。这些切割轨迹是参考点附近轨迹局部最优性的主要几何特征。在对称原理中，首席研究员将尝试将反馈函数计算的最新结果推广到奇异系统。这些研究将导致对存在对称性（例如旋转）的机械系统的最佳设计的进一步理解。