文章基本信息

标题：Formal Power Series Approach to Nonlinear Systems with Static Output Feedback ⁎ ⁎
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作者：G.S. Venkatesh ; W. Steven Gray
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2021
卷号：54
期号：9
页码：192-198
DOI：10.1016/j.ifacol.2021.06.076
语种：English
出版社：Elsevier
摘要：AbstractThe goal of this paper is to compute the generating series of a closed-loop system when the plant is described in terms of a Chen-Fliess series and static output feedback is applied. The first step is to reconsider the so called Wiener-Fliess connection consisting of a Chen-Fliess series followed by a memoryless function. Of particular importance will be the contractive nature of this map, which is needed to show that the closed-loop system has a Chen-Fliess series representation. To explicitly compute the generating series, two Hopf algebras are needed, the existing output feedback Hopf algebra used to describe dynamic output feedback, and the Hopf algebra of the shuffle group. These two combinatorial structures are combined to compute what will be called the Wiener-Fliess feedback product. It will be shown that this product has a natural interpretation as a transformation group acting on the plant and preserves the relative degree of the plant.
关键词：KeywordsNonlinear systemsfeedback controlHopf algebras