Dynamics and Control of Mechanical Systems

机械系统动力学与控制

• 批准号: 0103895
• 负责人: Anthony Bloch
• 金额: $ 20万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-08-01 至 2005-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0103895&HistoricalAwards=false
• 关键词: Dynamics; Control; Mechanical; Systems

DMS-0103895 PI: Anthony M. BlochDynamics and Control of Mechanical SystemsAbstract:This is a proposal for the continuation and extension of the proposer's research into the dynamics and control of nonlinear mechanical systems in finite- and infinite-dimensions. In particular, research is proposed in the following areas: integrable dynamical systems in finite- and infinite- dimensions including both Hamiltonian and nonholonomic systems, the stabilization and control of nonlinear mechanical systems via energy methods and the extension of these methods to systems with nonholonomic (nonintegrable) constraints, the geometry of the smooth and discrete dynamics of rigid bodies, and the control of quantum mechanical systems. A general area of interest that encompasses several parts of this proposal is the relationship between energy preservation and asymptotic behavior in dynamical systems and between reversible and irreversible behavior. In the integrable systems area the proposer is interested in the nonabelian Toda lattice, infinite-dimensional generalizations of Toda, and generalized smooth and discrete rigid body systems. Finally he intends to analyze the dynamics and control of various coupled mechanical systems in both the classical and quantum regimes.This proposal is aimed at studying the behavior of various mechanical systems that are important for applications in science and engineering. These include systems such as wheeled or articulated robots, aerospace systems, submarine vehicles, and quantum (microscopic) devices. Quantum devices, where the laws of motion of atoms and molecules play a key role, have become increasingly important in such areas as communication and coding theory. In addition to studying the behavior of these systems the proposer intends to analyze their control and optimal control -- that is, to provide methods for using such systems in engineering applications in a practical, stable, and efficient manner. The proposerintends to analyze various key examples of such mechanical systems with mathematical structure which is particularly amenable to detailedqualitative and quantitative analysis. Further, the proposer intends toanalyze the transition between the behavior of systems at the quantum(microscopic) level and the large scale (macroscopic) level. This transition is important for the application of physical devices in the real world as well as interesting from the scientific point of view.

DMS-0103895 PI：Anthony M. Bloch 机械系统动力学与控制摘要：这是提案者对有限和无限维非线性机械系统动力学和控制研究的延续和扩展的提案。特别是，在以下领域提出了研究：有限维和无限维的可积动力系统，包括哈密顿系统和非完整系统，通过能量方法稳定和控制非线性机械系统，并将这些方法扩展到具有非完整（不可积）约束的系统，刚体的光滑和离散动力学的几何结构，以及量子力学系统的控制。包含该提案几个部分的一个普遍关注领域是动力系统中能量守恒和渐近行为之间以及可逆和不可逆行为之间的关系。在可积系统领域，提议者对非阿贝尔 Toda 晶格、Toda 的无限维推广以及广义光滑和离散刚体系统感兴趣。最后，他打算分析经典和量子体系中各种耦合机械系统的动力学和控制。该提案旨在研究对于科学和工程应用非常重要的各种机械系统的行为。其中包括轮式或铰接式机器人、航空航天系统、潜艇和量子（微观）设备等系统。原子和分子运动定律在量子器件中发挥着关键作用，在通信和编码理论等领域变得越来越重要。除了研究这些系统的行为之外，提议者还打算分析它们的控制和最优控制，即提供在工程应用中以实用、稳定和高效的方式使用此类系统的方法。该提案旨在分析具有数学结构的此类机械系统的各种关键示例，该数学结构特别适合详细的定性和定量分析。此外，提出者打算分析量子（微观）水平和大规模（宏观）水平的系统行为之间的转变。这种转变对于物理设备在现实世界中的应用非常重要，并且从科学的角度来看也很有趣。