Malkoč, Barbara (2014) Newtonova metoda u Banachovim prostorima i optimalno upravljanje. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract
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.
Item Type:  Thesis (Diploma thesis) 

Supervisor:  Vrdoljak, Marko 
Date:  2014 
Number of Pages:  40 
Subjects:  NATURAL SCIENCES > Mathematics 
Divisions:  Faculty of Science > Department of Mathematics 
Depositing User:  Iva Prah 
Date Deposited:  03 Jun 2015 12:26 
Last Modified:  03 Jun 2015 12:26 
URI:  http://digre.pmf.unizg.hr/id/eprint/3999 
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