Evaluation of the Regions of Attraction of Higher-Dimensional Hyperbolic Systems Using Extended Dynamic Mode Decomposition

This paper provides the theoretical foundation for the approximation of the regions of attraction in hyperbolic and polynomial systems based on the eigenfunctions deduced from the data-driven approximation of the Koopman operator. In addition, it shows that the same method is suitable for analyzing...
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Autor*in:	Camilo Garcia-Tenorio [verfasserIn] Duvan Tellez-Castro [verfasserIn] Eduardo Mojica-Nava [verfasserIn] Alain Vande Wouwer [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	regions of attraction extended dynamic mode decomposition Koopman operator nonlinear systems

Übergeordnetes Werk:	In: Automation - MDPI AG, 2021, 4(2023), 1, Seite 57-77
Übergeordnetes Werk:	volume:4 ; year:2023 ; number:1 ; pages:57-77

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/automation4010005

Katalog-ID:	DOAJ087437147

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520			\|a This paper provides the theoretical foundation for the approximation of the regions of attraction in hyperbolic and polynomial systems based on the eigenfunctions deduced from the data-driven approximation of the Koopman operator. In addition, it shows that the same method is suitable for analyzing higher-dimensional systems in which the state space dimension is greater than three. The approximation of the Koopman operator is based on extended dynamic mode decomposition, and the method relies solely on this approximation to find and analyze the system’s fixed points. In other words, knowledge of the model differential equations or their linearization is not necessary for this analysis. The reliability of this approach is demonstrated through two examples of dynamical systems, e.g., a population model in which the theoretical boundary is known, and a higher-dimensional chemical reaction system constituting an original result.
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spelling	10.3390/automation4010005 doi (DE-627)DOAJ087437147 (DE-599)DOAJ01a1b3f8c8f94a0cba29dfe7a9e8d08b DE-627 ger DE-627 rakwb eng T1-995 Camilo Garcia-Tenorio verfasserin aut Evaluation of the Regions of Attraction of Higher-Dimensional Hyperbolic Systems Using Extended Dynamic Mode Decomposition 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper provides the theoretical foundation for the approximation of the regions of attraction in hyperbolic and polynomial systems based on the eigenfunctions deduced from the data-driven approximation of the Koopman operator. In addition, it shows that the same method is suitable for analyzing higher-dimensional systems in which the state space dimension is greater than three. The approximation of the Koopman operator is based on extended dynamic mode decomposition, and the method relies solely on this approximation to find and analyze the system’s fixed points. In other words, knowledge of the model differential equations or their linearization is not necessary for this analysis. The reliability of this approach is demonstrated through two examples of dynamical systems, e.g., a population model in which the theoretical boundary is known, and a higher-dimensional chemical reaction system constituting an original result. regions of attraction extended dynamic mode decomposition Koopman operator nonlinear systems Technology (General) Duvan Tellez-Castro verfasserin aut Eduardo Mojica-Nava verfasserin aut Alain Vande Wouwer verfasserin aut In Automation MDPI AG, 2021 4(2023), 1, Seite 57-77 (DE-627)1729200109 26734052 nnns volume:4 year:2023 number:1 pages:57-77 https://doi.org/10.3390/automation4010005 kostenfrei https://doaj.org/article/01a1b3f8c8f94a0cba29dfe7a9e8d08b kostenfrei https://www.mdpi.com/2673-4052/4/1/5 kostenfrei https://doaj.org/toc/2673-4052 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 4 2023 1 57-77
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allfieldsSound	10.3390/automation4010005 doi (DE-627)DOAJ087437147 (DE-599)DOAJ01a1b3f8c8f94a0cba29dfe7a9e8d08b DE-627 ger DE-627 rakwb eng T1-995 Camilo Garcia-Tenorio verfasserin aut Evaluation of the Regions of Attraction of Higher-Dimensional Hyperbolic Systems Using Extended Dynamic Mode Decomposition 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper provides the theoretical foundation for the approximation of the regions of attraction in hyperbolic and polynomial systems based on the eigenfunctions deduced from the data-driven approximation of the Koopman operator. In addition, it shows that the same method is suitable for analyzing higher-dimensional systems in which the state space dimension is greater than three. The approximation of the Koopman operator is based on extended dynamic mode decomposition, and the method relies solely on this approximation to find and analyze the system’s fixed points. In other words, knowledge of the model differential equations or their linearization is not necessary for this analysis. The reliability of this approach is demonstrated through two examples of dynamical systems, e.g., a population model in which the theoretical boundary is known, and a higher-dimensional chemical reaction system constituting an original result. regions of attraction extended dynamic mode decomposition Koopman operator nonlinear systems Technology (General) Duvan Tellez-Castro verfasserin aut Eduardo Mojica-Nava verfasserin aut Alain Vande Wouwer verfasserin aut In Automation MDPI AG, 2021 4(2023), 1, Seite 57-77 (DE-627)1729200109 26734052 nnns volume:4 year:2023 number:1 pages:57-77 https://doi.org/10.3390/automation4010005 kostenfrei https://doaj.org/article/01a1b3f8c8f94a0cba29dfe7a9e8d08b kostenfrei https://www.mdpi.com/2673-4052/4/1/5 kostenfrei https://doaj.org/toc/2673-4052 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 4 2023 1 57-77
language	English
source	In Automation 4(2023), 1, Seite 57-77 volume:4 year:2023 number:1 pages:57-77
sourceStr	In Automation 4(2023), 1, Seite 57-77 volume:4 year:2023 number:1 pages:57-77
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	regions of attraction extended dynamic mode decomposition Koopman operator nonlinear systems Technology (General)
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container_title	Automation
authorswithroles_txt_mv	Camilo Garcia-Tenorio @@aut@@ Duvan Tellez-Castro @@aut@@ Eduardo Mojica-Nava @@aut@@ Alain Vande Wouwer @@aut@@
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callnumber-first	T - Technology
author	Camilo Garcia-Tenorio
spellingShingle	Camilo Garcia-Tenorio misc T1-995 misc regions of attraction misc extended dynamic mode decomposition misc Koopman operator misc nonlinear systems misc Technology (General) Evaluation of the Regions of Attraction of Higher-Dimensional Hyperbolic Systems Using Extended Dynamic Mode Decomposition
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topic_title	T1-995 Evaluation of the Regions of Attraction of Higher-Dimensional Hyperbolic Systems Using Extended Dynamic Mode Decomposition regions of attraction extended dynamic mode decomposition Koopman operator nonlinear systems
topic	misc T1-995 misc regions of attraction misc extended dynamic mode decomposition misc Koopman operator misc nonlinear systems misc Technology (General)
topic_unstemmed	misc T1-995 misc regions of attraction misc extended dynamic mode decomposition misc Koopman operator misc nonlinear systems misc Technology (General)
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title	Evaluation of the Regions of Attraction of Higher-Dimensional Hyperbolic Systems Using Extended Dynamic Mode Decomposition
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title_sort	evaluation of the regions of attraction of higher-dimensional hyperbolic systems using extended dynamic mode decomposition
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title_auth	Evaluation of the Regions of Attraction of Higher-Dimensional Hyperbolic Systems Using Extended Dynamic Mode Decomposition
abstract	This paper provides the theoretical foundation for the approximation of the regions of attraction in hyperbolic and polynomial systems based on the eigenfunctions deduced from the data-driven approximation of the Koopman operator. In addition, it shows that the same method is suitable for analyzing higher-dimensional systems in which the state space dimension is greater than three. The approximation of the Koopman operator is based on extended dynamic mode decomposition, and the method relies solely on this approximation to find and analyze the system’s fixed points. In other words, knowledge of the model differential equations or their linearization is not necessary for this analysis. The reliability of this approach is demonstrated through two examples of dynamical systems, e.g., a population model in which the theoretical boundary is known, and a higher-dimensional chemical reaction system constituting an original result.
abstractGer	This paper provides the theoretical foundation for the approximation of the regions of attraction in hyperbolic and polynomial systems based on the eigenfunctions deduced from the data-driven approximation of the Koopman operator. In addition, it shows that the same method is suitable for analyzing higher-dimensional systems in which the state space dimension is greater than three. The approximation of the Koopman operator is based on extended dynamic mode decomposition, and the method relies solely on this approximation to find and analyze the system’s fixed points. In other words, knowledge of the model differential equations or their linearization is not necessary for this analysis. The reliability of this approach is demonstrated through two examples of dynamical systems, e.g., a population model in which the theoretical boundary is known, and a higher-dimensional chemical reaction system constituting an original result.
abstract_unstemmed	This paper provides the theoretical foundation for the approximation of the regions of attraction in hyperbolic and polynomial systems based on the eigenfunctions deduced from the data-driven approximation of the Koopman operator. In addition, it shows that the same method is suitable for analyzing higher-dimensional systems in which the state space dimension is greater than three. The approximation of the Koopman operator is based on extended dynamic mode decomposition, and the method relies solely on this approximation to find and analyze the system’s fixed points. In other words, knowledge of the model differential equations or their linearization is not necessary for this analysis. The reliability of this approach is demonstrated through two examples of dynamical systems, e.g., a population model in which the theoretical boundary is known, and a higher-dimensional chemical reaction system constituting an original result.
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title_short	Evaluation of the Regions of Attraction of Higher-Dimensional Hyperbolic Systems Using Extended Dynamic Mode Decomposition
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Evaluation of the Regions of Attraction of Higher-Dimensional Hyperbolic Systems Using Extended Dynamic Mode Decomposition

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