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 Gardner 该项目由应用数学项目和几何分析项目联合资助。其目标是在时间无关、时间相关和动态反馈下构造和应用控制系统的新不变量、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、外部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大到完全非线性范畴。该程序对精确线性化算法产生了重大改进。 类似的想法将用于研究其他适用范式的算法，例如标准双线性系统。还将研究控制结构的新概念，即非奇异控制系统的更全局的观点。 反馈控制系统理论最初是由工程问题激发的，在应用数学中占据着中心地位，是控制工程应用的基础。该项目将开发高性能自动控制系统动力学的几何基础。它主要关注具有高度非线性动力学并且可能具有许多相互影响的互连组件的系统。对更高性能甚至最优性的工程要求通常需要全新的控制设计，因为用于控制设计的经典线性化技术在这种情况下通常是不够的。通过采用纯数学各个领域的技术（例如微分几何），预计精确线性化算法将得到重大改进，例如应用于非线性自动驾驶仪设计。