论文标题
非线性输入输出系统及其互连的生成序列的熵
Entropy of Generating Series for Nonlinear Input-Output Systems and Their Interconnections
论文作者
论文摘要
本文有两个主要目标。首先是引入一个熵的概念，该概念非常适合具有具有Chen-Fliess系列表示的非线性输入输出系统。后者是根据其在非共同字母上的生成序列来定义的。这个想法是将生成系列的熵分配为渐变向量空间的元素。第二个目的是描述生成序列的熵，该序列源自在控制理论的背景下出现的陈相互连接系统。结果表明，一组互连永远无法像此处定义那样增加熵，而第二组有可能这样做。本文以简要介绍了熵超级空间和一些开放性问题。
This paper has two main objectives. The first is to introduce a notion of entropy that is well suited for the analysis of nonlinear input-output systems that have a Chen-Fliess series representation. The latter is defined in terms of its generating series over a noncommutative alphabet. The idea is to assign an entropy to a generating series as an element of a graded vector space. The second objective is to describe the entropy of generating series originating from interconnected systems of Chen-Fliess series that arise in the context of control theory. It is shown that one set of interconnections can never increase entropy as defined here, while a second set has the potential to do so. The paper concludes with a brief introduction to an entropy ultrametric space and some open questions.
