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master's thesis
Hamilton-Jacobi-Bellmanova jednadžba
Zagreb: University of Zagreb, Faculty of Science, 2023. urn:nbn:hr:217:807376
Miškić, Tomislav
University of Zagreb
Faculty of Science
Department of Physics

Institutional repository: Repository of the Faculty of Science

Cite this document

Miškić, T. (2023). Hamilton-Jacobi-Bellmanova jednadžba (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:807376

Miškić, Tomislav. "Hamilton-Jacobi-Bellmanova jednadžba." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:807376

Miškić, Tomislav. "Hamilton-Jacobi-Bellmanova jednadžba." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:807376

Miškić, T. (2023). 'Hamilton-Jacobi-Bellmanova jednadžba', Master's thesis, University of Zagreb, Faculty of Science, accessed 19 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:807376

Miškić T. Hamilton-Jacobi-Bellmanova jednadžba [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2023 [cited 2024 December 19] Available at: https://urn.nsk.hr/urn:nbn:hr:217:807376

T. Miškić, "Hamilton-Jacobi-Bellmanova jednadžba", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:217:807376

Metadata
TitleHamilton-Jacobi-Bellmanova jednadžba
Title (english)Hamilton-Jacobi-Bellman equation
AuthorTomislav Miškić
MentorPetra Posedel Šimović (mentor)
MentorDavor Horvatić (komentor)
Committee memberDavor Horvatić (predsjednik povjerenstva)
Committee memberPetra Posedel Šimović (član povjerenstva)
Committee memberNikola Poljak (član povjerenstva)
Committee memberMatko Glunčić (član povjerenstva)
Committee memberIvan Kupčić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Physics)
Zagreb
Defense date and country2023-01-02, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Physics
Abstract
Hamilton-Jacobi-Bellmanova jednadžba je temeljna parcijalna diferencijalna jednadžba u teoriji optimalnog upravljanja. Teoriju dinamičkog programiranja uveli su Richard Bellman i suradnici sredinom prošlog stoljeća. U slučaju procesa koje promatramo u diskretnim vremenski trenutcima jednadžbu obično nazivamo Bellmanova jednadžba. U neprekidnom vremenu, ona se može promatrati kao produžetak ranijih radova u klasičnoj fizici baziranih na Hamilton-Jacobijevoj jednadžbi. Rješenje Hamilton-Jacobi-Bellmanove jednadžbe daje optimalni trošak za dani dinamički sustav s pridruženom funkcijom troška. Varijacijski problemi u klasičnoj mehanici, na primjer, problem brahistokrone krivulje mogu se riješiti ovom metodom, no značajno je da se navedena metoda može primijeniti i na stohastičke sustave. Rad bi pored teorijskog pregleda imao i primjenu u interdisciplinarnom području ekonofizike.
Abstract (english)
Hamilton-Jacobi-Bellman equation is a fundamental partial differential equation in the theory of optimal control. The theory of dynamic programming was introduced by Richard Bellman and his associates at the midpoint of the last century. Regarding the temporally discretized problem we are considering, the equation is usually called Bellman’s equation. On a continual time domain, said equation can be observed from a perspective of earlier works in physics, hereby mentioning the famous Hamilton- Jacobi equation and principle. The solution of the Hamilton-Jacobi-Bellman equation allows us to find optimal cost trajectory for a given dynamical system with an adjoined cost function. Variational problems in classical mechanics, for example the brachistochrone curve problem can be solved using this method, but what’s meaningful is that said method can be applied to stochastic systems as well. The thesis would besides the theoretical overview of the topic, also cover an application in the interdisciplinary field of econophysics.
Keywords
Languagecroatian
URN:NBNurn:nbn:hr:217:807376
Study programmeTitle: Physics; specializations in: Research
Course: Research
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra fizike (magistar/magistra fizike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2023-01-17 10:24:17