On Persistent Noise in Distributed Averaging Dynamics
(2024)Department of Automatic Control
- Abstract
- In this thesis general formulas for calculating variance and total variance for the dynamics of distributed averaging in discrete time are presented. These formulas are derived by building on previous notions and ideas of stability measures and convergence. In doing so, a framework for quantifying stability of distributed averaging models through variance and total variance is provided. In addition, this framework extends to give select conditional formulas. Much of the focus of the thesis is directed at the total variance of the deviations of nodes from the average state of nodes in a network. This measurement can also be described as the sum of squared deviations of nodes from the average state of nodes.
By analyzing formulas derived... (More) - In this thesis general formulas for calculating variance and total variance for the dynamics of distributed averaging in discrete time are presented. These formulas are derived by building on previous notions and ideas of stability measures and convergence. In doing so, a framework for quantifying stability of distributed averaging models through variance and total variance is provided. In addition, this framework extends to give select conditional formulas. Much of the focus of the thesis is directed at the total variance of the deviations of nodes from the average state of nodes in a network. This measurement can also be described as the sum of squared deviations of nodes from the average state of nodes.
By analyzing formulas derived in this framework, statements regarding network topology are made. Previously known facts, such as conditions for emergence of a steady state are also included into the framework. Select formulas from the framework for total variance are used to numerically calculate total variance over time. This is also compared to the sum of squared deviations of nodes from the average state of nodes over time in an arbitrarily chosen network. As a partial conclusion from this, the validity of the framework is reaffirmed. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9150924
- author
- Johansson Elmér, Hans
- supervisor
-
- Giacomo Como LU
- Emma Tegling LU
- organization
- year
- 2024
- type
- H3 - Professional qualifications (4 Years - )
- subject
- report number
- TFRT-6228
- other publication id
- 0280-5316
- language
- English
- id
- 9150924
- date added to LUP
- 2024-05-22 16:10:20
- date last changed
- 2024-05-22 16:10:20
@misc{9150924,
abstract = {{In this thesis general formulas for calculating variance and total variance for the dynamics of distributed averaging in discrete time are presented. These formulas are derived by building on previous notions and ideas of stability measures and convergence. In doing so, a framework for quantifying stability of distributed averaging models through variance and total variance is provided. In addition, this framework extends to give select conditional formulas. Much of the focus of the thesis is directed at the total variance of the deviations of nodes from the average state of nodes in a network. This measurement can also be described as the sum of squared deviations of nodes from the average state of nodes.
By analyzing formulas derived in this framework, statements regarding network topology are made. Previously known facts, such as conditions for emergence of a steady state are also included into the framework. Select formulas from the framework for total variance are used to numerically calculate total variance over time. This is also compared to the sum of squared deviations of nodes from the average state of nodes over time in an arbitrarily chosen network. As a partial conclusion from this, the validity of the framework is reaffirmed.}},
author = {{Johansson Elmér, Hans}},
language = {{eng}},
note = {{Student Paper}},
title = {{On Persistent Noise in Distributed Averaging Dynamics}},
year = {{2024}},
}