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master's thesis
Modeliranje dinamičkih sustava vođeno podacima
Zagreb: University of Zagreb, Faculty of Science, 2024. urn:nbn:hr:217:792428
Mustafić, Ermin
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Mustafić, E. (2024). Modeliranje dinamičkih sustava vođeno podacima (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:792428

Mustafić, Ermin. "Modeliranje dinamičkih sustava vođeno podacima." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:792428

Mustafić, Ermin. "Modeliranje dinamičkih sustava vođeno podacima." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:792428

Mustafić, E. (2024). 'Modeliranje dinamičkih sustava vođeno podacima', Master's thesis, University of Zagreb, Faculty of Science, accessed 17 May 2024, https://urn.nsk.hr/urn:nbn:hr:217:792428

Mustafić E. Modeliranje dinamičkih sustava vođeno podacima [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2024 [cited 2024 May 17] Available at: https://urn.nsk.hr/urn:nbn:hr:217:792428

E. Mustafić, "Modeliranje dinamičkih sustava vođeno podacima", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:217:792428

Metadata
TitleModeliranje dinamičkih sustava vođeno podacima
Title (english)Data-driven modeling of dynamical systems
AuthorErmin Mustafić
MentorZvonimir Bujanović (mentor)
Committee memberZvonimir Bujanović (predsjednik povjerenstva)
Committee memberMarko Erceg (član povjerenstva)
Committee memberSiniša Slijepčević (član povjerenstva)
Committee memberMarko Tadić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2024-03-01, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu su prezentirane dvije metode za modeliranje dinamičkih sustava vođenih podacima. Prva je dekompozicija na dinamičke modove (DMD) koja, za zadane podatke, nastoji pronaći najbolji linearni operator u smislu najmanjih kvadrata. Uspostavlja se veza s Koopmanovim operatorom. Između ostalih, pokazuje se primjena DMD-a u teoriji upravljanja. Druga metoda je bazirana na učenju operatora dinamike koji daju nelinearni polinomni aproksimativni model također metodom najmanjih kvadrata. Metode su uspoređene na dva numerička eksperimenta. Rad zaključujemo uvođenjem metode Lift \& Learn koja daje alternativu DMD-u za rukovođenje nelinearnim dinamičkim sustavima.
Abstract (english)
This thesis presents two methods for modelling data-driven dynamical systems. First is dynamic mode decomposition (DMD) that creates a linear operator which tries to fit data in the least square sense. Connection with Koopman operator has been established. Among others, applications in control theory have been shown. The second method is based on operator inference that produces a nonlinear polynomial approximate model, also in the least square sense. These methods are compared on two numerical experiments. The thesis is concluded by introducing the Lift & Learn method which gives an alternative to the DMD for handling nonlinear dynamical systems.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:792428
Study programmeTitle: Applied Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-03-13 12:46:14