Sinteza optimalnog regulatora stanja linearnih sustava primjenom algoritma povratnog prostiranja kroz vrijeme

master's thesis

• Title (english): Optimal state controller synthesis for linear systems using the back-propagation through time algorithm
• Author: Klara Trbara
• Mentor: Vladimir Milić (mentor)
• Granter: University of Zagreb; Faculty of Mechanical Engineering and Naval Architecture; Zagreb
• Defense date and country: 2023-12-07, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Mechanical Engineering

Abstract

Diplomski rad istražuje optimalno upravljanje linearnim dinamičkim sustavima kroz primjenu numeričkih metoda, s posebnim naglaskom na sintezu optimalnog regulatora stanja. Zbog kompleksnosti analitičkih metoda, koriste se numeričke metode kako bi se omogućila praktična implementacija optimalnog regulatora. Fokus rada je na upotrebi jednoslojne neuronske mreže sa saturacijskom aktivacijskom funkcijom kao zakonom upravljanja, osiguravajući pritom zadovoljavanje ograničenja varijabli upravljanja. Rad uključuje algoritam podešavanja težina neuronske mreže, temeljen na algoritmu povratnog prostiranja kroz vrijeme (eng. BackPropagation Through Time – BPTT), uz integraciju Eulerove metode za vremensku diskretizaciju, metode konjugiranog gradijenta, te kompleksne koračne metode za računanje Jacobijana funkcije dinamike sustava. Navedene metode su integrirane u jedan numerički algoritam za sintezu regulatora prema kvadratnom kriteriju optimalnosti. Izvedeni algoritam je provjeren na sintezi regulatora mehaničkog sustava masa-prigušnica-opruga.

Abstract (english)

The master's thesis explores optimal control of linear dynamic systems through the application of numerical methods, with a particular focus on the synthesis of an optimal state regulator. Due to the complexity of analytical methods, numerical methods are used to enable the practical implementation of the optimal regulator. The focus of the thesis is on the use of a single-layer neural network with a saturation activation function as the control law, ensuring the satisfaction of control variable constraints. The work includes a weight adjustment algorithm for the neural network based on the Backpropagation Through Time (BPTT) algorithm, integrating Euler's method for time discretization, conjugate gradient method, and complex step method for computing the system's Jacobian function. These methods are integrated into a single numerical algorithm for synthesizing the regulator according to the quadratic optimality criterion. The derived algorithm is validated in the synthesis of a regulator for a mechanical system consisting of mass-damper-spring components.

• Keywords: linearni vremenski invarijantni sustavi; linearni kvadratni regulator; neuronske mreže; algoritam povratnog prostiranja kroz vrijeme; konjugirani gradijent; SuperSAB algoritam
• Keywords (english): linear time-invariant systems; linear quadratic regulator; neural networks; backpropagation through time algorithm; conjugate gradient; SuperSAB algorithm
• Language: croatian
• URN:NBN: urn:nbn:hr:235:075066
• 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: 2023-12-04 14:17:42