Mathematical Sciences: Control Structures

数学科学：控制结构

• 批准号: 9409037
• 负责人: Robert Gardner
• 金额: $ 10.03万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-15 至 1997-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9409037&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Control; Structures

9409037 Gardner This project is funded jointly by the Applied Mathematics Program and the Geometric Analysis Program. Its goal is to construct and apply new invariants, structure theorems and normal forms of control systems under time-independent, time-dependent, and dynamic feedback. The tools involve the method of equivalence as refined by the principal investigator, exterior differential systems, and the theory of infinite pseudogroups. An important principle is the enlargement of the notion of feedback equivalence to the fully nonlinear category. This program has resulted in major improvements in exact linearization algorithms. Similar ideas will be used to investigate algorithms for other applicable normal forms such as standard bilinear systems. A new concept of control structure, a more global viewpoint of nonsingular control systems, will also be investigated. The theory of feedback control systems, originally motivated by problems in engineering, occupies a central place in applied mathematics and is fundamental to control engineering applications. This project will develop the geometric foundations that underlie the dynamics of high-performance automatic control systems. It focuses primarily on systems that have highly nonlinear dynamics and which may have many interconnected components influencing each other. The engineering demands for ever higher performance, or even optimality, often require completely new control designs since classical linearization techniques for control design is often inadequate in such situations. By employing techniques from various areas of pure mathematics, such as differential geometry, major improvements in exact linearization algorithms, with applications to nonlinear autopilot design, for example, are expected.

9409037加德纳这个项目由应用数学项目和几何分析项目共同资助。它的目的是构造和应用时间无关、时间相关和动态反馈下的控制系统的新的不变量、结构定理和范式。这些工具包括由主要研究者改进的等价方法、外微分系统和无限伪群理论。一个重要的原则是将反馈等价的概念扩展到完全非线性范畴。该程序在精确线性化算法方面取得了重大改进。类似的想法将被用来研究其他适用的范式的算法，如标准双线性系统。还将研究一种新的控制结构概念，即非奇异控制系统的更全面的观点。反馈控制系统理论最初是由工程问题引起的，在应用数学中占有中心地位，是控制工程应用的基础。该项目将发展构成高性能自动控制系统动力学基础的几何基础。它主要关注具有高度非线性动力学的系统，这些系统可能有许多相互关联的组件相互影响。工程上对更高性能甚至最优性的要求往往需要全新的控制设计，因为在这种情况下，传统的线性化控制设计技术往往是不够的。通过使用纯数学的各个领域的技术，例如微分几何，可以预期精确线性化算法的重大改进，并应用于例如非线性自动驾驶仪设计。