Entropy of Generating Series for Nonlinear Input-Output Systems and Their Interconnections

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2022
• 1. Verfasser: Gray, W. Steven
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2022
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/211822
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Entropy of Generating Series for Nonlinear Input-Output Systems and Their Interconnections. W. Steven Gray. SIGMA 18 (2022), 082, 15 pages

This paper has two main objectives. The first step is to introduce a notion of entropy that is well-suited for analyzing nonlinear input-output systems with 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.