Dynamics and Control of Mechanical Systems

在这个项目中，申请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。主要研究方向包括：有限维和无限维可积哈密顿系统、非线性机械系统的镇定与控制、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、无限维系统和复杂动力学系统的动力学与控制。本文将分析两类基本的可积系统——有限维和无限维的Toda格，以及广义刚体方程。作者对这些系统的看法受到应用分析工作的启发——优化和控制问题。申请者也将研究非完整系统的动力学。这样的系统是受不可积约束（如滚动）约束的机械系统，一般来说不是哈密顿的，但仍然守恒能量。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，提出了一种充满活力的方法来控制非线性机械系统，使系统保持经典拉格朗日形式，尽管存在反馈。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。本文还讨论了有限维和无限维系统的控制和动力学中的其他几个问题，例如包括连接的有限维和无限维系统在内的互联系统的结构和稳定性分析。从广义上讲，申请者将研究物理和工程中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。他将研究某些可以明确求解的模型系统。这些系统很重要，因为它们揭示了只能在计算机上模拟的更复杂系统的行为。他还将考虑各种机械控制系统行为的优化。这种优化不仅对获得理想的系统行为很重要，而且对降低成本也很重要。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属物对卫星运动稳定性的重要性。他还将分析系统在流体中的运动，例如水下航行器的运动。总的来说，希望是更好地理解大量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.