Hamilton-Jacobi-Bellmanova jednadžba

master's thesis

• Title (english): Hamilton-Jacobi-Bellman equation
• Author: Tomislav Miškić
• Mentor: Petra Posedel Šimović (mentor)
• Mentor: Davor Horvatić (komentor)
• Committee member: Davor Horvatić (predsjednik povjerenstva)
• Committee member: Petra Posedel Šimović (član povjerenstva)
• Committee member: Nikola Poljak (član povjerenstva)
• Committee member: Matko Glunčić (član povjerenstva)
• Committee member: Ivan Kupčić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2023-01-02, 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: Hamilton-Jacobi-Bellmanova jednadžba; teorija dinamičkog programiranja
• Language: croatian
• URN:NBN: urn:nbn:hr:217:807376
• Study programme: Title: 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 resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2023-01-17 10:24:17