Primjena Hopfieldovih neuronskih mreža u rješavanju optimizacijskih problema

undergraduate thesis

• Title (english): Application of Hopfield neural networks to solution of optimization problems
• Author: Boris Kosanović
• Mentor: Josip Kasać (mentor)
• Granter: University of Zagreb; Faculty of Mechanical Engineering and Naval Architecture; Zagreb
• Defense date and country: 2017-03-03, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Mechanical Engineering

Abstract

Hopfieldove neuronske mreže predstavljaju klasu dinamičkih neuronskih mreža sa širokim poljem primjena u rješavanju raznih optimizacijskih problema. Također mnogi algebarski

problemi, mogu se formulirati kao optimizacijski problemi i riješiti primjenom Hopfieldove neuronske mreže. U ovom radu riješeni su problemi kvadratičnog programiranja, invertiranja matrica i rješavanja linearnih matričnih jednadžbi, te su primijenjeni kod sinteze linearnog

regulatora inverznog njihala. Prilikom učenja Hopfieldove neuronske mreže korišten je gradijentni algoritam. Upravljački sustav inverznog njihala testiran je nizom simulacija s različitim kutevima otklona od inverznog položaja. Rezultati simulacija pokazuju da Hopfieldova neuronska mreža daje zadovoljavajuća rješenja u području gdje je sustav moguće upravljati linearnim regulatorom.

Za implementaciju Hopfieldovih neuronskih mreža i usporedbu dobivenih rezultata s egzaktnim rješenjima korišten je programski paket Matlab.

Abstract (english)

Hopfield neural networks are a class of dynamic neural networks with a wide field of application in solving various optimization problems. Also many algebraic problems can be formulated as an optimization problem and solved using the Hopfield neural network. This paper deals with problems of quadratic programming, inverting a matrix and solving linear matrix equations, which are then applied to the synthesis of linear regulators inverted pendulum.

Gradient algorithm is used during learning phase of Hopfield neural network. The control system of inverted pendulum is tested by a series of simulations with different angles of deflection of the inverted position. Simulation results show that Hopfield neural network gives

satisfactory solutions in the area where the system can be operated with linear regulator. Matlab is used for the implementation of Hopfield neural networks and comparison of the results with the exact solutions.

• Keywords: Hopfieldova neuronska mreža; optimizacija; gradijentni algoritam
• Keywords (english): Hopfield neural network; optimization; gradient algorithm
• Language: croatian
• URN:NBN: urn:nbn:hr:235:815353
• Study programme: Title: Mechanical Engineering; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka strojarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka strojarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-05-22 19:04:20