Thomas分解与非线性控制系统
Thomas Decomposition and Nonlinear Control Systems
摘要：
本文将Thomas分解技术应用于非线性控制系统，特别是研究系统行为对参数的依赖性。Thomas算法是一种符号方法，它将给定的非线性偏微分方程系统分裂成有限族所谓的简单系统，这些简单系统形式上是可积的，并定义了原始微分系统解集的一个分区。托马斯分解的不同简单系统一般描述控制系统的不同结构行为。本文介绍了托马斯分解方法，并显示如何的概念，如可逆性，可观测性和平坦的输出可以研究。一个Maple实现托马斯的算法被用来说明显式的例子上的技术。
英文摘要：
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.
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