Algebraic and Differential Topology in Robust Control

鲁棒控制中的代数和微分拓扑

• 批准号: 9300016
• 负责人: Edmond Jonckheere
• 金额: $ 10万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-09-01 至 1995-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9300016&HistoricalAwards=false
• 关键词: Algebraic; Differential; Topology; Robust; Control

9300016 Jonckheere The proposed research is aimed at achieving a deeper understanding of the closed-loop (robust) stability issue in feedback systems under uncertain parameters. Three different directions of attack of the problem, all inspired from algebraic and differential topology, are proposed - the Simplicial Approximation Theorem, The Morse Theory, and Obstruction Theory. From there, new "simplicial" algorithms for computing the stability boundary in the space of uncertainties emerge. The general feature of these algorithms is that they are based on the idea of simplicial decomposition of the space of uncertainty. A byproduct of this approach is the elucidation of the topology of the separating boundary, bounds on the Betti numbers of the stability, and most importantly, its structural stability under perturbation of the parameters that have been declared "certain." ***

9300016 Jonckheere建议的研究是为了实现更深入的了解闭环（鲁棒）的不确定参数下的反馈系统的稳定性问题。 三个不同的攻击方向的问题，所有的启发，从代数和微分拓扑，提出了-单纯形逼近定理，莫尔斯理论和障碍理论。 从那里，新的“单纯”算法计算的不确定性空间中的稳定性边界出现。 这些算法的一般特点是，它们是基于不确定性空间的单纯分解的思想。 这种方法的一个副产品是阐明的拓扑结构的分离边界，边界上的Betti数的稳定性，最重要的是，它的结构稳定性的参数扰动下，已被宣布为“一定的”。" ***