Chronological Calculus and Nonlinear Control
时间演算和非线性控制
基本信息
- 批准号:0509030
- 负责人:
- 金额:$ 18万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2005
- 资助国家:美国
- 起止时间:2005-08-01 至 2009-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The chronological calculus (CC) is a tool for computation and analysis of time-varying nonlinear vector fields and noncommuting flows. It is based on the classical technique of lifting dynamical systems to the space of linear operators on an algebra of smooth functions. This project will use the CC to investigate the geometric and algebraic foundations of fully nonlinear control systems as they commonly appear, in particular, in models in the bio-medical sciences. Typical items are the curvature of optimal control, and ideal structures in Zinbiel algebras. One challenge is to merge the formal work in combinatorics and nonassociative algebra with rigorous justifications how these formal objects map onto analytic and geometric structures. A key objective is to understand how the underlying geometry affects and limits the structural behavior of dynamical systems that model diverse applications. Moreover, the algebraic and combinatorial tools developed in this project also yield compact algorithmic tools that lend themselves to high performance computation.This project will have diverse broader impacts, both horizontally and vertically: The tools and methodologies to be developed are immediately applicable in a diverse set of disciplines, basically everywhere where it matters in which order actions are taken. The classes of systems considered in this project have uses that include quantum systems, high performance numerical computation, operations research, and many areas in the biomedical sciences, from population dynamics to pharmacokinetics and molecular biology. Motivated by applied problems, this project develops new mathematical tools, and makes them available to the applied sciences, thereby strengthening interdisciplinary ties. Complementing the horizontal impacts, this project will also enhance the vertical integration and the local infrastructure by developing an attractive control curriculum that acts as a pipeline to funnel new talents from all backgrounds into becoming active participants in the discovery process. Principal means for this are exciting problems that connect control theory and the biosciences, and the highly experimental nature of using interactive visualization tools in this project. Both of these allow undergraduates to start meaningful participation with only minimal formal prerequisites while seamlessly leading to advanced theoretical work.
时间演算(CC)是计算和分析时变非线性向量场和非交换流的工具。它是基于经典的技术提升动力系统的线性算子空间上的代数光滑函数。这个项目将使用CC来研究完全非线性控制系统的几何和代数基础,因为它们通常出现在生物医学科学的模型中。典型的项目是最优控制的曲率和Zinbiel代数中的理想结构。一个挑战是合并的正式工作,在组合和非结合代数与严格的理由如何这些正式对象映射到分析和几何结构。一个关键目标是了解底层几何结构如何影响和限制对不同应用进行建模的动力系统的结构行为。此外,本项目开发的代数和组合工具也产生了紧凑的算法工具,这些工具适用于高性能计算。本项目将在横向和纵向上产生广泛的影响:所开发的工具和方法立即适用于各种学科,基本上适用于所有重要的领域。在这个项目中考虑的系统类的用途,包括量子系统,高性能数值计算,运筹学,和许多领域的生物医学科学,从人口动力学的药代动力学和分子生物学。 受应用问题的推动,该项目开发新的数学工具,并使其可用于应用科学,从而加强跨学科的联系。作为对横向影响的补充,该项目还将通过开发一个有吸引力的控制课程来加强纵向一体化和当地基础设施,该课程将作为一个渠道,汇集来自各种背景的新人才,使其成为发现过程的积极参与者。主要手段是连接控制理论和生物科学的令人兴奋的问题,以及在这个项目中使用交互式可视化工具的高度实验性。这两个允许本科生开始有意义的参与,只有最小的正式先决条件,同时无缝地导致先进的理论工作。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Matthias Kawski其他文献
Matthias Kawski的其他文献
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{{ truncateString('Matthias Kawski', 18)}}的其他基金
Trimester in Combinatorics and Control COCO 2010
组合学和控制三个学期 COCO 2010
- 批准号:
0960589 - 财政年份:2010
- 资助金额:
$ 18万 - 项目类别:
Standard Grant
Geometry of Nonlinear Control with Applications
非线性控制几何及其应用
- 批准号:
0908204 - 财政年份:2009
- 资助金额:
$ 18万 - 项目类别:
Standard Grant
IGMS: Optimizing Supply Networks and Re-Entrant Manufacturing Systems in the Semiconductor Industry
IGMS:优化半导体行业的供应网络和可重入制造系统
- 批准号:
0107666 - 财政年份:2002
- 资助金额:
$ 18万 - 项目类别:
Standard Grant
Geometry and Algebra of Nonlinear Control Systems
非线性控制系统的几何和代数
- 批准号:
0072369 - 财政年份:2000
- 资助金额:
$ 18万 - 项目类别:
Continuing Grant
Vector Calculus via Linearization: Visualization and ModernApplications
通过线性化进行向量微积分:可视化和现代应用
- 批准号:
9752453 - 财政年份:1998
- 资助金额:
$ 18万 - 项目类别:
Standard Grant
Mathematical Sciences: Geometry of highly nonlinear multi-input systems
数学科学:高度非线性多输入系统的几何
- 批准号:
9308289 - 财政年份:1993
- 资助金额:
$ 18万 - 项目类别:
Continuing Grant
Mathematical Sciences: The Geometry of Highly Nonlinear Control Systems
数学科学:高度非线性控制系统的几何
- 批准号:
9007547 - 财政年份:1990
- 资助金额:
$ 18万 - 项目类别:
Continuing Grant
Mathematical Sciences: The Geometry of Highly Nonlinear Control Systems
数学科学:高度非线性控制系统的几何
- 批准号:
8805815 - 财政年份:1988
- 资助金额:
$ 18万 - 项目类别:
Standard Grant
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