Analiza stabilnosti prometa s pomočjo lastnih vrednosti in lastnih vektorjev : delo diplomskega seminarja

De Luisa, Andraž (author), Peperko, Aljoša (mentor)

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.

• Language: Slovenian
• Keywords: kontrola prometa, PID regulator, problem lastnih vrednosti, sistemi diferencialnih enačb, neskončne matrike
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2019
• PID: 20.500.12556/RUL-110362
• UDC: 517.9
• COBISS.SI-ID: 18723417
• Publication date in RUL: 14.09.2019

Secondary language

• Language: English
• Title: Eigenvalue and eigenvector analysis of stability for a line of traffic

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.

• Keywords: traffic control, PID controller, eigenvalue problem, systems of differential equations, infinite matrices