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master's thesis
Newtonova metoda u Banachovim prostorima i optimalno upravljanje
Zagreb: University of Zagreb, Faculty of Science, 2014. urn:nbn:hr:217:234144
Malkoč, Barbara
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Malkoč, B. (2014). Newtonova metoda u Banachovim prostorima i optimalno upravljanje (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:234144

Malkoč, Barbara. "Newtonova metoda u Banachovim prostorima i optimalno upravljanje." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:234144

Malkoč, Barbara. "Newtonova metoda u Banachovim prostorima i optimalno upravljanje." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:234144

Malkoč, B. (2014). 'Newtonova metoda u Banachovim prostorima i optimalno upravljanje', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:234144

Malkoč B. Newtonova metoda u Banachovim prostorima i optimalno upravljanje [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2014 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:234144

B. Malkoč, "Newtonova metoda u Banachovim prostorima i optimalno upravljanje", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2014. Available at: https://urn.nsk.hr/urn:nbn:hr:217:234144

Metadata
TitleNewtonova metoda u Banachovim prostorima i optimalno upravljanje
AuthorBarbara Malkoč
MentorMarko Vrdoljak (mentor)
Committee memberMarko Vrdoljak (predsjednik povjerenstva)
Committee memberLavoslav Čaklović (član povjerenstva)
Committee memberBoris Guljaš (član povjerenstva)
Committee memberZvonko Čerin (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2014-07-11, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Ovaj rad se sastoji od dva dijela koje povezuje jaki rezultat, . U prvom dijelu je osigurana teorijska podloga tako da bi se moglo doći do nekih važnih rezultata. Dotaknuli smo se Newtonove metode pomoću koje smo dokazali važne teoreme poput teorema o inverznom preslikavanju i teorema o implicitnoj funkciji. Također smo dokazali egzistenciju i jedinstvenost rješenja za nekoliko postavljenih Cauchyjevih problema za obične diferencijalne jednadžbe. Time je pokazana sva snaga na prvi pogled prilično jednostavne Newtonove metode. Na kraju prvog poglavlja je obrađen Lagrangeov problem varijacijskog računa s ograničenjem i Lagrangeov problem optimalnog upravljanja. Prvi dio rada završava Pontrjaginovim principom maksimuma koji daje nužne uvjete za optimalno upravljanje. On nam omogućuje da u drugom dijelu rada u primjerima problema upravljanja odredimo optimalno upravljanje te optimalnu trajektoriju. Cilj ovog rada je bio pokazati kako nas upravljanje prati u svakodnevnom životu te nam omogućuje da što bolje iskoristimo ponuđeno. Zato je drugi dio temeljen na primjerima na kojima je pokušano što jednostavnije demonstrirati važnost teorije upravljanja.
Abstract (english)
This thesis consists of two parts connected by a strong result, Pontryagin Maximum Principle. In the first part a theoretical basis is presented so that we could reach some important conclusions. We have studied Newton’s method, which enables us to prove some important theorems like the Inverse mapping theorem and the Implicit function theorem. Also, we proved the existence and uniqueness of solution to several Cauchy problems for ordinary differential equations. This way we have shown all the strength of, at first glance, quite simple Newton’s method. We elaborated the Lagrange problem of calculus of variation and the Lagrange problem of optimal control. The first part ends with the Pontryagin Maximum Principle that will allow us to determine the necessary conditions for optimal control and the optimal trajectory of some examples presented in the second part of this thesis. The goal of this work was to demonstrate how control is present in everyday life and it allows us to take more advantage of what is given. That is why the second part was based on examples in which we tried to explain, as simply as we could, the importance of control theory.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:234144
Study programmeTitle: Applied Mathematics
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 on2019-01-21 11:34:32