delo diplomskega seminarja
Andraž De Luisa (Author), Aljoša Peperko (Mentor)

Abstract

Namen tega diplomskega dela je predstavitev dveh različnih metod za kontrolo prometa, enostranske in dvostranske, ter analiza njune stabilnosti. Matematična modela, ki metodi opisujeta, bomo zapisali kot sistema homogenih linearnih diferencialnih enačb ter s pomočjo lastnih vrednosti in lastnih vektorjev preučili njuno stabilnost. Obravnavali bomo tako splošni primer, z neomejenim številom vozil v sistemu, kot tudi različne robne pogoje. Teoretične ugotovitve bomo nazadnje podkrepili še z računalniškimi simulacijami.

Keywords

matematika;kontrola prometa;PID regulator;problem lastnih vrednosti;sistemi diferencialnih enačb;neskončne matrike;

Data

Language: Slovenian
Year of publishing:
Typology: 2.11 - Undergraduate Thesis
Organization: UL FS - Faculty of Mechanical Engineering
Publisher: [A. De Luisa]
UDC: 517.9
COBISS: 18723417 Link will open in a new window
Views: 994
Downloads: 195
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Other data

Secondary language: English
Secondary title: Eigenvalue and eigenvector analysis of stability for a line of traffic
Secondary abstract: This thesis describes two different methods for the control of traffic flow, the car-following model and the bilateral control model, and presents an analysis of their stability. The mathematical models that describes them can be written as systems of homogeneous linear differential equations and their stability analysed by studying their eigenvalues and eigenvectors. We will discuss a general case, with an infinite number of vehicles, and some boundary traffic conditions. We will then further substantiate the theoretical claims with computer simulations.
Secondary keywords: mathematics;traffic control;PID controller;eigenvalue problem;systems of differential equations;infinite matrices;
Type (COBISS): Final seminar paper
Study programme: 0
Embargo end date (OpenAIRE): 1970-01-01
Thesis comment: Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages: 29 str.
ID: 11223557