Entropy of Generating Series for Nonlinear Input-Output Systems and Their Interconnections
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 ass...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2022 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2022
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211822 |
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| 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 |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862634191654486016 |
|---|---|
| author | Gray, W. Steven |
| author_facet | Gray, W. Steven |
| citation_txt | Entropy of Generating Series for Nonlinear Input-Output Systems and Their Interconnections. W. Steven Gray. SIGMA 18 (2022), 082, 15 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2026-03-14T21:56:24Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211822 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T21:56:24Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Gray, W. Steven 2026-01-12T10:20:04Z 2022 Entropy of Generating Series for Nonlinear Input-Output Systems and Their Interconnections. W. Steven Gray. SIGMA 18 (2022), 082, 15 pages 1815-0659 2020 Mathematics Subject Classification: 68R15; 94A17; 93C10; 16T30 arXiv:2202.10170 https://nasplib.isofts.kiev.ua/handle/123456789/211822 https://doi.org/10.3842/SIGMA.2022.082 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. The author would like to thank the referees for suggesting some significant clarifications and improvements to this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Entropy of Generating Series for Nonlinear Input-Output Systems and Their Interconnections Article published earlier |
| spellingShingle | Entropy of Generating Series for Nonlinear Input-Output Systems and Their Interconnections Gray, W. Steven |
| title | Entropy of Generating Series for Nonlinear Input-Output Systems and Their Interconnections |
| title_full | Entropy of Generating Series for Nonlinear Input-Output Systems and Their Interconnections |
| title_fullStr | Entropy of Generating Series for Nonlinear Input-Output Systems and Their Interconnections |
| title_full_unstemmed | Entropy of Generating Series for Nonlinear Input-Output Systems and Their Interconnections |
| title_short | Entropy of Generating Series for Nonlinear Input-Output Systems and Their Interconnections |
| title_sort | entropy of generating series for nonlinear input-output systems and their interconnections |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211822 |
| work_keys_str_mv | AT graywsteven entropyofgeneratingseriesfornonlinearinputoutputsystemsandtheirinterconnections |