Identification of nonlinear systems with periodic external actions (Part II)

Authors

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2024.4.05

Keywords:

identification, ordinary differential equation, external action, periodic coefficient, constant coefficient

Abstract

The article presents the results of the study, which is a continuation of the author’s previous research. This paper considers more complex problems in identifying nonlinear systems with periodic external actions. The article shows that the previously proposed method is applicable when the periods of external actions in the same differential equation may differ. At the same time, the ratio between the values of the periods can be both integer and fractional. The conditions under which this is possible are formulated. These conditions are based on the theorem proved in the previous work. Part of this study is devoted to the problem of identification of a chaotic system with an external non-sinusoidal action. To create such an external action, a function with three harmonic components was used. A numerical experiment confirmed the effectiveness of the algorithm in this case as well.

Author Biography

Viktor Gorodetskyi, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv

Candidate of Physical and Mathematical Sciences (Ph.D.), an associate professor at the Department of Automation of Electrical and Mechatronic Complexes of Educational and Research Institute of Energy Saving and Energy Management of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine.

References

P.E. Kloeden, M. Rasmussen, “Nonautonomous dynamical systems,” Mathematical Surveys and Monographs, vol. 176. Providence, Rhode Island: American Mathematical Society, 2011. doi: 10.1090/surv/176

P.E. Kloeden, C. Potzsche, “Nonautonomous dynamical systems in the life sciences,” Lecture Notes in Mathematics, vol. 2102, pp. 3–39, 2013. doi: 10.1007/978-3-319-03080-7_1

A. Tarantola, Inverse problem theory and methods for model parameter estimation. Philadelphia: Society for Industrial and Applied Mathematics, 2005. doi: 10.1137/1.9780898717921

B.P. Bezruchko, D.A. Smirnov, “Constructing nonautonomous differential equations from a time series,” Phys. Rev. E., vol. 63, art. no. 016207, 2001. doi: 10.1103/PhysRevE.63.016207

T. Sauer, “Observing periodically forced systems of difference equations,” J. Difference Equ. Appl., vol. 16, no. 2-3, pp. 269–273, 2010. doi: 10.1080/10236190902870439

V.G. Gorodetskyi, “Identification of nonlinear systems with additive external action,” J. Aut. & Inf. Sci., vol. 50, no. 4, pp. 13–24, 2018. doi: 10.1615/JAutomatInfScien.v50.i4.20

V.G. Gorodetskyi, “Identification of nonlinear systems with periodic external actions (Part 1),” System Research and Information Technologies, no. 3, pp. 93–106, 2024. doi: 10.20535/SRIT.2308-8893.2024.3.06

O.E. Rössler, “An equation for continuous chaos,” Phys. Lett. A., vol. 57, no. 5, pp. 397–398, 1976. doi: 10.1016/0375-9601(76)90101-8

Downloads

Published

2024-12-25

Issue

No. 4 (2024)

Section

Mathematical methods, models, problems and technologies for complex systems research

License

This is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. This is in accordance with the BOAI definition of open access.