Mathematical Sciences: Discrete Time Control

数学科学：离散时间控制

• 批准号: 8803396
• 负责人: Eduardo Sontag
• 金额: $ 3.54万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1991-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8803396&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Discrete; Time; Control

This project concerns the theory of discrete deterministic nonlinear control systems and their relationship to continuous time models. The interest is both discrete time results as such and on sampling and other discretization techniques, with an emphasis on certain subclasses such as invertible, polynomial and piecewise linear systems. The theory builds on past research by the PI and others in these areas. For invertible systems, it is now possible to obtain Lie-algebraic accessibility conditions very analogous to those known for continuous time systems. In polynomial case, elementary techniques from algebraic geometry become useful. Regarding sampling, the main objective is the understanding of how properties of continuous time physical systems are preserved under digital control.

本项目涉及离散确定性非线性控制系统的理论及其与连续时间模型的关系。它的兴趣既包括离散时间结果本身，也包括采样和其他离散化技术，重点是某些子类，如可逆线性系统、多项式系统和分段线性系统。这一理论建立在PI和其他人过去在这些领域的研究基础上。对于可逆系统，现在可以获得非常类似于连续时间系统的李代数可达性条件。在多项式的情况下，代数几何中的基本技巧变得有用。关于采样，主要目标是了解如何在数字控制下保留连续时间物理系统的性质。