Dynamics and Control of Mechanical Systems

9803181在这个项目中，提出者将继续研究有限维和无限维非线性机械系统的动力学和控制。特别是在以下方面进行了研究：有限维和无限维可积哈密顿系统，非线性力学系统的镇定与控制，带约束的非完整系统的分析与控制，带约束系统的最优控制，无限维系统和具有复杂动力学的系统的动力学与控制。作者将分析两类基本的可积系统--有限维和无限维Toda格子，以及广义刚体方程。作者对这些系统的看法是受应用分析工作--优化和控制问题--启发而来的。提出者还将研究非完整系统的动力学。这类系统是受滚动等不可积约束的机械系统，一般不是哈密顿系统，但仍然守恒。这导致了非常丰富的行为，包括渐近稳定的可能性。与他的合作者一起，这位提出者一直在开发一种控制非线性机械系统的能量方法，这种方法使系统在存在反馈的情况下仍保持经典的拉格朗日形式。这使得通常应用于自治系统的经典稳定性理论能够应用于受控系统的类别。讨论了有限维和无限维系统控制和动力学中的其他几个问题，如关联有限维和无限维系统的结构和稳定性分析。概括地说，这个提倡者将研究在物理学和工程学中很重要的各种机械系统的行为和控制。工程应用包括航空航天系统和机器人技术。他将研究某些可以显式求解的模型系统。这类系统对于揭示只能在计算机上模拟的更复杂系统的行为很重要。他还将考虑各种机械控制系统的行为优化。这种优化不仅对于获得理想的系统行为，而且对于降低成本都很重要。他将研究控制机器人和卫星等系统运动的各种方法。在卫星的建模中，他将考虑天线等柔性附件对卫星运动稳定性的重要性。他还将分析流体中系统的运动--例如水下航行器的运动。总的来说，我们希望能更好地理解一大类工程和物理系统的动力学和控制。

9803181 Bloch In this project the proposer will continue 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 Hamiltonian systems in finite- and infinite-dimensions, the stabilization and control of nonlinear mechanical systems, the analysis and control of nonholonomic systems with constraints, the optimal control of systems with constraints, and the dynamics and control of infinite-dimensional systems and systems with complex dynamics. The proposer will analyze two basic classes of integrable systems -- the Toda lattice in finite- and infinite-dimensions, and the generalized rigid body equations. The proposer's view of these systems is inspired by work in applied analysis -- optimization and control problems. The proposer will also investigate the dynamics of nonholonomic systems. Such systems, which are mechanical systems subject to nonintegrable constraints such as rolling, are not Hamiltonian in general but nonetheless conserve energy. This leads to very rich behavior including the possibility of asymptotic stability. With his collaborators the proposer has been developing an energetic approach to the control of nonlinear mechanical systems which leaves the system in classical Lagrangian form despite the presence of feedback. This enables the classical theory of stability, which is normally applied to autonomous systems, to be applied to classes of controlled systems. Several other problem in the control and dynamics of finite- and infinite-dimensional systems are discussed, such as the analysis of the structure and stability of interconnected systems including linked finite- and infinite-dimensional systems. In broad terms the proposer will study the behavior and control of various mechanical systems that are important in physics and engineering. Engineering applications include aerospace systems and robotics. He will study certain model systems that can be solved explicitly. Such systems are important for the light they shed on the behavior of more complicated systems which can only be simulated on a computer. He will also consider the optimization of the behavior of various mechanical control systems. This optimization is important not only for obtaining desirable system behavior but for reducing cost. He will study various methods for controlling the motion of such systems as robots and satellites. In the modeling of satellites he will consider the importance of flexible appendages such as antennae in the stability of their motion. He will also analyze the motion of systems in fluids -- for example the motion of underwater vehicles. In general the hope is to obtain a better understanding of the dynamics and control of a large class of engineering and physical systems.