Dynamics and Control of Mechanical Systems

DMS-0103895 PI：Anthony M.布洛赫动力学和控制的机械systemsAbstract：这是一个建议的延续和延伸的提议者的研究到有限和无限维的非线性机械系统的动力学和控制。具体而言，建议在以下领域开展研究：可积动力系统在有限和无限维包括哈密尔顿和非完整系统，稳定和控制的非线性力学系统通过能量方法和这些方法的扩展系统与非完整（不可积）约束，几何的光滑和离散动力学的刚体，和量子力学系统的控制。一个普遍的兴趣领域，包括几个部分的建议是能量守恒和渐近行为之间的关系，在动力系统和可逆和不可逆的行为。在可积系统领域，提出者感兴趣的是非交换户田格，无限维推广的户田，广义光滑和离散刚体系统。最后，他打算分析各种耦合力学系统的动力学和控制在经典和量子regimes.This建议的目的是研究各种力学系统的行为，在科学和工程中的应用是重要的。这些系统包括轮式或关节式机器人、航空航天系统、潜艇和量子（微观）设备。量子器件中原子和分子的运动规律起着关键作用，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，也就是说，提供在工程应用中以实用、稳定和有效的方式使用这些系统的方法。该提案旨在分析各种关键的例子，这种机械系统的数学结构，这是特别适合详细的定性和定量分析。此外，提议者打算分析系统行为在量子（微观）水平和大尺度（宏观）水平之间的过渡。这种转变对于物理设备在真实的世界中的应用是重要的，从科学的角度来看也是有趣的。

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.