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undergraduate thesis
Primjena Takensovog teorema u identifikaciji sustava
Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing, 2014. urn:nbn:hr:168:765603
Kolobarić, Viktor
University of Zagreb
Faculty of Electrical Engineering and Computing

Institutional repository: FER Repository

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Kolobarić, V. (2014). Primjena Takensovog teorema u identifikaciji sustava (Undergraduate thesis). Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing. Retrieved from https://urn.nsk.hr/urn:nbn:hr:168:765603

Kolobarić, Viktor. "Primjena Takensovog teorema u identifikaciji sustava." Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2014. https://urn.nsk.hr/urn:nbn:hr:168:765603

Kolobarić, Viktor. "Primjena Takensovog teorema u identifikaciji sustava." Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2014. https://urn.nsk.hr/urn:nbn:hr:168:765603

Kolobarić, V. (2014). 'Primjena Takensovog teorema u identifikaciji sustava', Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, accessed 19 December 2024, https://urn.nsk.hr/urn:nbn:hr:168:765603

Kolobarić V. Primjena Takensovog teorema u identifikaciji sustava [Undergraduate thesis]. Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing; 2014 [cited 2024 December 19] Available at: https://urn.nsk.hr/urn:nbn:hr:168:765603

V. Kolobarić, "Primjena Takensovog teorema u identifikaciji sustava", Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb, 2014. Available at: https://urn.nsk.hr/urn:nbn:hr:168:765603

Metadata
TitlePrimjena Takensovog teorema u identifikaciji sustava
Title (english)System identification using Takens theorem
AuthorViktor Kolobarić
MentorZvonko Kostanjčar (mentor)
Committee memberZvonko Kostanjčar (predsjednik povjerenstva)
Committee memberDražen Jurišić (član povjerenstva)
Committee memberAna Sović Kržić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Electrical Engineering and Computing
Zagreb
Defense date and country2014-07-14, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Electrical Engineering
Abstract
U radu su prikazana dva oblika Takensovog teorema te skice njihovih dokaza radi lakšeg razumijevanja teorema. Teoremi govore o rekonstrukciji rješenja dinamičkog sustava iz samo jedne varijable stanja odnosno jedne mjerene veličine sustava te da takvo rekonstruirano rješenje zadržava svojstva orginalnog. Temeljem toga su pokazane primjene i ideje kako iz samo jedne mjerene veličine se može izračunati dimenzionalnost prostora varijabli stanja. Činjenica da orginalno i rekonstruirano rješenje predstavljaju bijekciju se može iskoristiti u provjeri da li dva vremenska niza pripadaju istom dinamičkom sustavu te da li su stoga kauzalno povezani. Korištenjem statističkog oblika teorema na primjerima je pokazana konstrukcija ergodičke particije odnosno faznog portreta sustava.
Abstract (english)
In this work two forms of Takens' theorem and outlines of their proof are shown for the purpose of easier understanding of theorems. Theorem's talk about solution reconstruction of dynamical system from just one observable and that that solution retains the characteristics of original one. On that ground applications and ideas to calculate dimension of variable state space are shown. Fact that original and reconstructed solution represent one to one mapping (bijection) can be used to verify if two time series belong to same dynamical system and are thus causally related. By using statistical form of the theorem on examples, construction of ergodic partition that is phase portrait is shown.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:168:765603
Study programmeTitle: Electrical Engineering and Information Technology
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka elektrotehnike i informacijske tehnologije (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka elektrotehnike i informacijske tehnologije)
Type of resourceText
File originBorn digital
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Created on2018-02-05 17:37:25