Dynamics and Control of Mechanical Systems

小行星9803181 在这个项目中，提议者将继续研究动力学， 有限维和无限维非线性机械系统的控制。 特别是，建议在以下领域进行研究： 有限维和无限维的哈密顿系统，稳定化 非线性机械系统的分析与控制， 约束非完整系统，系统的最优控制 以及无限维的动力学和控制 系统和具有复杂动力学的系统。提案人将分析 两类基本的可积系统--有限域中的户田格和 无限维和广义刚体方程。的 提议者对这些系统的看法是受到应用分析工作的启发-- 优化和控制问题。提议者还将调查 非完整系统动力学这种机械系统 系统受到不可积的约束，如滚动，不是 哈密顿量，但仍然保持能量。这导致 非常丰富的行为，包括渐近稳定的可能性。与 他的合作者一直在开发一种充满活力的方法， 涉及非线性机械系统的控制， 经典拉格朗日形式，尽管存在反馈。这使得 经典的稳定性理论，通常适用于自治 系统，适用于各类受控系统。其他几 有限维和无限维的控制和动力学问题 系统进行了讨论，如结构和稳定性分析， 包括连接的有限维和无限维的互连系统 系统. 从广义上讲，提议者将研究各种 在物理学和工程学中很重要的机械系统。 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。这样的系统 对于揭示更复杂的生物的行为很重要 只能在计算机上模拟的系统。他也会考虑 优化各种机械控制系统的行为。 这种优化不仅对于获得理想的系统是重要的， 行为，而是为了降低成本。他将研究各种方法， 控制机器人和卫星等系统的运动。在 卫星建模，他将考虑灵活的重要性， 触角等附属物在运动中的稳定性。他还将 分析系统在流体中的运动--例如 水下航行器。总的来说，希望能得到一个更好的 了解一大类工程的动力学和控制 和物理系统。

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.