DOAJ Open Access 2023

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

Camilo Garcia-Tenorio Duvan Tellez-Castro Eduardo Mojica-Nava Alain Vande Wouwer

Abstrak

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.

Topik & Kata Kunci

Technology (General)

Penulis (4)

Camilo Garcia-Tenorio

Duvan Tellez-Castro

Eduardo Mojica-Nava

Alain Vande Wouwer

Format Sitasi

APA MLA BibTeX

Garcia-Tenorio, C., Tellez-Castro, D., Mojica-Nava, E., Wouwer, A.V. (2023). Evaluation of the Regions of Attraction of Higher-Dimensional Hyperbolic Systems Using Extended Dynamic Mode Decomposition. https://doi.org/10.3390/automation4010005

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Informasi Jurnal

Tahun Terbit: 2023
Sumber Database: DOAJ
DOI: 10.3390/automation4010005
Akses: Open Access ✓