Usporedba numeričkih metoda za rješavanje problema optimalnog upravljanja u programskim alatima MATLAB i CasADi

master's thesis

• Title (english): Comparison of numerical methods for solving optimal control problems in MATLAB and CasADi software tools
• Author: Korina Belokleić
• Mentor: Vladimir Milić (mentor)
• Granter: University of Zagreb; Faculty of Mechanical Engineering and Naval Architecture; Zagreb
• Defense date and country: 2024-03-28, 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: optimalno upravljanje; metode diskretizacije; metode numeričke optimizacije; MATLAB; CasADi
• Keywords (english): optimal control; discretization methods; numerical optimization methods; MATLAB; CasADi
• Language: croatian
• URN:NBN: urn:nbn:hr:235:262540
• Study programme: Title: Mechanical Engineering; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra inženjer/inženjerka strojarstva (magistar/magistra inženjer/inženjerka strojarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-03-22 11:35:39