Modeliranje dinamičkih sustava vođeno podacima

master's thesis

• Title (english): Data-driven modeling of dynamical systems
• Author: Ermin Mustafić
• Mentor: Zvonimir Bujanović (mentor)
• Committee member: Zvonimir Bujanović (predsjednik povjerenstva)
• Committee member: Marko Erceg (član povjerenstva)
• Committee member: Siniša Slijepčević (član povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2024-03-01, 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: dekompozicija na dinamičke modove (DMD); Koopmanov operator; Lift \& Learn
• Keywords (english): dynamic mode decomposition (DMD); Koopman operator; Lift & Learn method
• Language: croatian
• URN:NBN: urn:nbn:hr:217:792428
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-03-13 12:46:14