论文标题
单输入下三角形形式的分类
Classifications of Single-input Lower Triangular Forms
论文作者
论文摘要
本文的目的是对下部三角形形式进行分类，并确定在什么条件下，非线性系统等效于特定类型的下三角形形式。根据最小的多指数和最大的基本多指数集，这些集合作为新概念引入并可以从系统方程中获得，构建了下部三角形形式的两个分类方案。可以验证给定下三角形形式所属于的类型在任何下部三角形坐标转换下都是不变的。因此，尽管相当于下三角形形式的非线性系统也等同于许多其他适当的下三角形形式，但只有一种类型可以将系统转化为。两种分类中的每一个都会诱导所有等同于下三角形形式的系统的分类。如果可能的话，将提供一种将非线性系统转换为较低三角形形式的新方法，以查找该系统所属的类型。另外，通过使用差异几何控制理论，建立了与给定类型的下三角形形式相当的局部反馈在本地反馈。给出了一个示例来说明如何确定给定的非线性系统的哪种类型的下三角形形式等于而无需进行等效转换。
The purposes of this paper are to classify lower triangular forms and to determine under what conditions a nonlinear system is equivalent to a specific type of lower triangular forms. According to the least multi-indices and the greatest essential multi-index sets, which are introduced as new notions and can be obtained from the system equations, two classification schemes of lower triangular forms are constructed. It is verified that the type that a given lower triangular form belongs to is invariant under any lower triangular coordinate transformation. Therefore, although a nonlinear system equivalent to a lower triangular form is also equivalent to many other appropriate lower triangular forms, there is only one type that the system can be transformed into. Each of the two classifications induces a classification of all the systems that are equivalent to lower triangular forms. A new method for transforming a nonlinear system into a lower triangular form, if it is possible, is provided to find what type the system belongs to. Additionally, by using the differential geometric control theory, several necessary and sufficient conditions under which a nonlinear system is locally feedback equivalent to a given type of lower triangular form are established. An example is given to illustrate how to determine which type of lower triangular form a given nonlinear system is equivalent to without performing an equivalent transformation.
