Dynamics, Integrability, and Control of Mechanical and Nonholonomic Systems

机械和非完整系统的动力学、可积性和控制

• 批准号: 1613819
• 负责人: Anthony Bloch
• 金额: $ 24.63万
• 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: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2021-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1613819&HistoricalAwards=false
• 关键词: Dynamics; Integrability; Control; Mechanical; Nonholonomic

The project focuses on problems in mechanics, dynamics, and control. The theory of nonholonomic dynamics is the study of mechanical systems subject to constraints on velocities, such as rolling without slipping. Examples where we use this theory in practical systems include wheeled vehicles, such as cars (in particular self-steering cars) and robots. The mathematics behind the control of nonholonomic systems plays a key role in control of mechanical systems in general, such as the control of aircraft. Also important is how dissipation, or friction, affects the behavior and stability of such systems. This research project explores how to explicitly solve for the dynamics to predict the behavior of such mechanical systems. The methods under development are expected also to be useful in studying quantum control problems, with applications to quantum computing among others. The project involves graduate and undergraduate students in the research. This research project aims to broaden and deepen understanding of the geometry, dynamics, and control of mechanical systems including Hamiltonian and Lagrangian systems, integrable systems, nonholonomic systems, and gradient flows. The investigator will study the dynamics of various mechanical systems including integrable Hamiltonian systems in finite and infinite dimensions, coupled Hamiltonian and gradient systems, systems with nonholonomic constraints, optimal control equations on manifolds, and quantum control systems. The research will consider the geometry of integrable systems in several new contexts, including extensions of the Toda lattice flow and rigid body flows, as well as applications to optimal control of certain systems on Lie groups. It is expected that similar methods can be used to study the control and dynamics of open quantum systems that involve coupled Hamiltonian and dissipative dynamics.

该项目重点关注力学、动力学和控制方面的问题。非完整动力学理论是研究受速度约束的力学系统，如无滑动的滚动。我们在实际系统中使用这一理论的例子包括轮式车辆，如汽车（特别是自转向汽车）和机器人。非完整系统控制背后的数学在一般机械系统的控制中起着关键作用，例如飞机的控制。同样重要的是耗散或摩擦如何影响这种系统的行为和稳定性。本研究项目探讨如何明确解决动态预测这样的机械系统的行为。正在开发的方法预计也将有助于研究量子控制问题，并应用于量子计算等。该项目涉及研究生和本科生的研究。该研究项目旨在拓宽和加深对力学系统的几何，动力学和控制的理解，包括哈密顿和拉格朗日系统，可积系统，非完整系统和梯度流。研究人员将研究各种力学系统的动力学，包括有限维和无限维的可积哈密顿系统，耦合哈密顿和梯度系统，非完整约束系统，流形上的最优控制方程和量子控制系统。该研究将考虑几何可积系统在几个新的背景下，包括扩展的户田格流和刚体流，以及应用程序的李群某些系统的最优控制。人们期望类似的方法可以用于研究涉及耦合哈密顿和耗散动力学的开放量子系统的控制和动力学。