Automated Linearization of a System of Nonlinear Ordinary Differential Equations

• Autorzy: Mazakova Aigerim , Jomartova Sholpan , Wójcik Waldemar , Mazakov Talgat , Ziyatbekova Gulzat

Identyfikatory

DOI

10.24425/ijet.2023.147684

• Języki publikacji: EN

Abstrakty

EN

This paper investigates the possibility of automatically linearizing nonlinear models. Constructing a linearised model for a nonlinear system is quite labor-intensive and practically unrealistic when the dimension is greater than 3. Therefore, it is important to automate the process of linearisation of the original nonlinear model. Based on the application of computer algebra, a constructive algorithm for the linearisation of a system of non-linear ordinary differential equations was developed. A software was developed on MatLab. The effectiveness of the proposed algorithm has been demonstrated on applied problems: an unmanned aerial vehicle dynamics model and a twolink robot model. The obtained linearized models were then used to test the stability of the original models. In order to account for possible inaccuracies in the measurements of the technical parameters of the model, an interval linearized model is adopted. For such a model, the procedure for constructing the corresponding interval characteristic polynomial and the corresponding Hurwitz matrix is automated. On the basis of the analysis of the properties of the main minors of the Hurwitz matrix, the stability of the studied system was analyzed.

Słowa kluczowe

EN

Ordinary differential equation; Computer algebra; stability; controllability; MatLab

• Wydawca: Polish Academy of Sciences, Committee of Electronics and Telecommunication
• Czasopismo: International Journal of Electronics and Telecommunications
• Rocznik: 2023
• Tom: Vol. 69, No. 4
• Strony: 655--600
• Opis fizyczny: Bibliogr. 24 poz., rys.

Twórcy

autor

Mazakova Aigerim

• Al-Farabi Kazakh NationalUniversity, Kazakhstan

autor

Jomartova Sholpan

• Al-Farabi Kazakh NationalUniversity, Kazakhstan

autor

Wójcik Waldemar

• Lublin Technical University, Poland

autor

Mazakov Talgat

• Institute of Information and Computational Technologies CS MES RK, Al-Farabi Kazakh National University, Kazakhstan

autor

Ziyatbekova Gulzat

• Institute of Information and Computational Technologies CS MES RK, Al-Farabi Kazakh National University, Kazakhstan

Bibliografia

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Uwagi

1. Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).

2. The work was performed at the Research Institute of Mathematics and Mechanics of Kazakh National University named after Al-Farabi at the expense of the program-targeted funding of scientific research for 2023-2025 under the project IRN AR19676966 «Development of hardware-software system for psychophysiological selection and rehabilitation of snipers».