论文标题
托马斯分解和非线性控制系统
Thomas Decomposition and Nonlinear Control Systems
论文作者
论文摘要
本文将托马斯分解技术应用于非线性控制系统，特别是对系统行为对参数的依赖性的研究。托马斯（Thomas）的算法是一种符号方法，它将给定的非线性偏微分方程系统拆分为一个有限的所谓简单系统的家族，该系统正式可正式整合并定义了原始差分系统的解决方案集的分区。托马斯分解的不同简单系统通常描述了控制系统的不同结构行为。本文对托马斯分解方法进行了介绍，并显示了如何研究诸如可逆性，可观察性和平坦输出之类的概念。托马斯算法的枫树实现用于说明明确示例的技术。
This paper applies the Thomas decomposition technique to nonlinear control systems, in particular to the study of the dependence of the system behavior on parameters. Thomas' algorithm is a symbolic method which splits a given system of nonlinear partial differential equations into a finite family of so-called simple systems which are formally integrable and define a partition of the solution set of the original differential system. Different simple systems of a Thomas decomposition describe different structural behavior of the control system in general. The paper gives an introduction to the Thomas decomposition method and shows how notions such as invertibility, observability and flat outputs can be studied. A Maple implementation of Thomas' algorithm is used to illustrate the techniques on explicit examples.
