Postojanje rješenja zadaće optimalnog upravljanja

master's thesis

• Title (english): Existence of a solution to the optimal control problem
• Author: Luka Tišlar
• Mentor: Marko Vrdoljak (mentor)
• Committee member: Marko Vrdoljak (predsjednik povjerenstva)
• Committee member: Bojan Basrak (član povjerenstva)
• Committee member: Miljenko Marušić (član povjerenstva)
• Committee member: Snježana Lubura Strunjak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-05-05, 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: diferencijalne jednadžbe; Radonove vjerojatnosne mjere; Youngove mjere
• Keywords (english): differential equations; Radon’s probability measures; Young’s measures
• Language: croatian
• URN:NBN: urn:nbn:hr:217:468961
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2022-06-08 12:23:03