Intelligent Simulation Methods for Dynamical Systems

该项目研究具有期望的动力学行为的物理系统原型的新的计算方法，并期望在设计和控制工程中应用。它开发了一个计算环境，通过数值计算和符号计算的组合来可视化和操纵物理系统的动力学。更具体地说，这个项目研究(1)通过解析和几何分析对动力系统进行自动表征，以及(2)动力学的交互综合、优化和可视化技术，例如，剪切和粘贴矢量场并塑造所需的动力学特性(例如，稳定区域)的“计算剪刀”，否则难以设计的复杂系统。

This project investigates new computational methods for prototyping physical systems with desired dynamical behaviors, with expected applications in design and control engineering. It develops a computational environment for visualizing and manipulating dynamics of physical systems through a combination of numerical and symbolic computations. More specifically, this project studies (1) automated characterization of dynamical systems through analytic and geometric analysis, and (2) techniques for interactive synthesis, optimization, and visualization of dynamics, for example, ``computational scissors'' that cut-and-paste vector fields and shape the desired dynamical properties (e.g. stability regions) for a complex system that is otherwise difficult to design.