prikaz prve stranice dokumenta Postojanje rješenja zadaće optimalnog upravljanja
  Download
PDF 226.05 KB
master's thesis
Postojanje rješenja zadaće optimalnog upravljanja
Zagreb: University of Zagreb, Faculty of Science, 2022. urn:nbn:hr:217:468961
Tišlar, Luka
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Tišlar, L. (2022). Postojanje rješenja zadaće optimalnog upravljanja (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:468961

Tišlar, Luka. "Postojanje rješenja zadaće optimalnog upravljanja." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:468961

Tišlar, Luka. "Postojanje rješenja zadaće optimalnog upravljanja." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:468961

Tišlar, L. (2022). 'Postojanje rješenja zadaće optimalnog upravljanja', Master's thesis, University of Zagreb, Faculty of Science, accessed 02 June 2024, https://urn.nsk.hr/urn:nbn:hr:217:468961

Tišlar L. Postojanje rješenja zadaće optimalnog upravljanja [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2024 June 02] Available at: https://urn.nsk.hr/urn:nbn:hr:217:468961

L. Tišlar, "Postojanje rješenja zadaće optimalnog upravljanja", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:217:468961

Metadata
TitlePostojanje rješenja zadaće optimalnog upravljanja
Title (english)Existence of a solution to the optimal control problem
AuthorLuka Tišlar
MentorMarko Vrdoljak (mentor)
Committee memberMarko Vrdoljak (predsjednik povjerenstva)
Committee memberBojan Basrak (član povjerenstva)
Committee memberMiljenko Marušić (član povjerenstva)
Committee memberSnježana Lubura Strunjak (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2022-05-05, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U radu se proučavaju zadaće optimalnog upravljanja opisane sustavima običnih diferencijalnih jednadžbi. Funkcija cilja koju želimo optimizirati može ovisiti o rubnim vrijednostima funkcije upravljanja i stanja i/ili, u vidu integrala, o njihovim vrijednostima duž promatranog integrala. Na funkcije upravljanja i stanja se dodatno postavljaju ograničenja. Proučava se pitanje egzistencije rješenja te se u tu svrhu uvode relaksirana upravljanja koja poprimaju vrijednosti u Radonovim vjerojatnosnim mjerama (poput Youngovih mjera u varijacijskom računu). Dokazuje se egzistencija optimalnog relaksiranog upravljanja te, uz dodatne pretpostavke konveksnosti, da je dobiveno relaksirano optimalno upravljanje zapravo klasično.
Abstract (english)
The thesis studies the optimal control problems described by systems of ordinary differential equations. The goal function we want to optimize may depend on the boundary values of the control and state function and/or, in the form of an integral, on their values along the observed integral. Restrictions are additionally placed on control and state functions. The question of the existence of a solution is studied, and for this purpose relaxed controls are introduced that take on values in Radon’s probability measures (such as Young’s measures in the calculus of variations). The existence of optimal relaxed control is proved and, with additional assumptions of convexity, that the obtained relaxed optimal control is in fact classical.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:468961
Study programmeTitle: Mathematical Statistics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-06-08 12:23:03