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master's thesis
Usporedba numeričkih metoda za rješavanje problema optimalnog upravljanja u programskim alatima MATLAB i CasADi
Zagreb: University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, 2024. urn:nbn:hr:235:262540
Belokleić, Korina
University of Zagreb
Faculty of Mechanical Engineering and Naval Architecture

Institutional repository: Repository of Faculty of Mechanical Engineering and Naval Architecture University of Zagreb

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Belokleić, K. (2024). Usporedba numeričkih metoda za rješavanje problema optimalnog upravljanja u programskim alatima MATLAB i CasADi (Master's thesis). Zagreb: University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture. Retrieved from https://urn.nsk.hr/urn:nbn:hr:235:262540

Belokleić, Korina. "Usporedba numeričkih metoda za rješavanje problema optimalnog upravljanja u programskim alatima MATLAB i CasADi." Master's thesis, University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, 2024. https://urn.nsk.hr/urn:nbn:hr:235:262540

Belokleić, Korina. "Usporedba numeričkih metoda za rješavanje problema optimalnog upravljanja u programskim alatima MATLAB i CasADi." Master's thesis, University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, 2024. https://urn.nsk.hr/urn:nbn:hr:235:262540

Belokleić, K. (2024). 'Usporedba numeričkih metoda za rješavanje problema optimalnog upravljanja u programskim alatima MATLAB i CasADi', Master's thesis, University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, accessed 28 December 2024, https://urn.nsk.hr/urn:nbn:hr:235:262540

Belokleić K. Usporedba numeričkih metoda za rješavanje problema optimalnog upravljanja u programskim alatima MATLAB i CasADi [Master's thesis]. Zagreb: University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture; 2024 [cited 2024 December 28] Available at: https://urn.nsk.hr/urn:nbn:hr:235:262540

K. Belokleić, "Usporedba numeričkih metoda za rješavanje problema optimalnog upravljanja u programskim alatima MATLAB i CasADi", Master's thesis, University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Zagreb, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:235:262540

Metadata
TitleUsporedba numeričkih metoda za rješavanje problema optimalnog upravljanja u programskim alatima MATLAB i CasADi
Title (english)Comparison of numerical methods for solving optimal control problems in MATLAB and CasADi software tools
AuthorKorina Belokleić
MentorVladimir Milić (mentor)
GranterUniversity of Zagreb
Faculty of Mechanical Engineering and Naval Architecture
Zagreb
Defense date and country2024-03-28, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Mechanical Engineering
Abstract
Optimalno upravljanje dinamičkim sustavima ključno je za postizanje visokih performansi i maksimalno iskorištavanje potencijala tehnologije. Ovaj rad pruža prvo teorijski, a onda i eksperimentalni pregled tri numeričke metode diskretizacije - Eulerove, Runge-Kuttove metode 4. reda i Adamsove metode 4. reda. Također i dvije metode za numeričku optimizaciju – sekvencijalno kvadratično programiranje (sqp) i metodu unutarnje točke (interior-point). Ističu se i relevantni alati poput MATLAB-a i CasADi-ja za implementaciju tih metoda te njihova primjena. Analiza učinkovitosti i točnosti ovih metoda kroz numeričke eksperimente pruža uvid u njihove prednosti, nedostatke i primjenjivost u stvarnim situacijama. Dva su primjera, linearni sustav drugog reda i mehanički sustav s dva stupnja slobode gibanja. Napomena je na tome da ne postoji univerzalna metoda koja bi odgovarala svakom problemu te je stoga bitno odabrati metodu sukladno specifičnim zahtjevima sustava. Kroz primjere riješenih problema, demonstrirana je primjena teorijskih koncepata i numeričkih metoda u praksi. Vide se odstupanja od analitičkih rješenja te međusobna usporedba metoda i korištenih algoritama iz programskih alata. Rad ukazuje na važnost optimalnog upravljanja i njegovu primjenu pogotovo kad se radi o složenijim problemima koji se žele što brže i točnije riješiti.
Abstract (english)
Optimal control of dynamic systems is crucial for achieving high performance and maximizing the potential of technology. This study provides a theoretical and experimental overview of three numerical discretization methods - Euler's, Runge-Kutta’s fourth-order method, and Adams' fourth-order method. Additionally, it covers two numerical optimization methods - sequential quadratic programming (SQP) and interior-point method. Relevant tools such as MATLAB and CasADi for implementing these methods and their application are highlighted. An analysis of the efficiency and accuracy of these methods through numerical experiments provides insight into their advantages, limitations, and applicability in real-life situations. Two examples are presented: a second-order linear system and a mechanical system with two degrees of freedom. It is noted that there is no universal method that would suit every problem, thus it is important to choose a method according to the specific requirements of the system. Through solved problem examples, the application of theoretical concepts and numerical methods in practice is demonstrated. Deviations from analytical solutions are observed, as well as a comparison between methods and algorithms used in software tools. This study emphasizes the importance of optimal control and its application, especially when dealing with more complex problems that require fast and accurate solutions.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:235:262540
Study programmeTitle: Mechanical Engineering
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra inženjer/inženjerka strojarstva (magistar/magistra inženjer/inženjerka strojarstva)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-03-22 11:35:39