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Applications of non-autonomous discrete dynamical systems into nonlinear consensus problems

Historically, an idea of reaching consensus through repeated averaging was introduced by DeGroot (see [1, 3]) for a structured time-invariant and synchronous environment. Since that time, the consensus which is the most ubiquitous phenomenon of multi-agent systems becomes popular in various scientif...

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Main Author: Saburov, Mansoor
Format: Conference or Workshop Item
Language:English
Published: 2016
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/54402/1/ICDEA%20---%20IREP.pdf
http://irep.iium.edu.my/54402/
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spelling my.iium.irep.544022018-05-22T01:12:52Z http://irep.iium.edu.my/54402/ Applications of non-autonomous discrete dynamical systems into nonlinear consensus problems Saburov, Mansoor QA Mathematics Historically, an idea of reaching consensus through repeated averaging was introduced by DeGroot (see [1, 3]) for a structured time-invariant and synchronous environment. Since that time, the consensus which is the most ubiquitous phenomenon of multi-agent systems becomes popular in various scientific communities, such as biology, physics, control engineering and social science. Roughly speaking, a trajectory of a row-stochastic matrix presents DeGroot’s model of the structured time-invariant synchronous environment. In [2], Chatterjee and Seneta considered a generalization of DeGroot’s model for the structured time-varying synchronous environment. A trajectory of a sequence of row-stochastic matrices (a non-homogeneous Markov chain) presents the Chatterjee- Seneta model of the structured time-varying synchronous environment. In this paper, we shall consider a nonlinear model of the structured time-varying synchronous environment which generalizes both DeGroot’s and the Chatterjee-Seneta models. Namely, by means of multidimensional stochastic hypermatrices, we present an opinion sharing dynamics of the multi-agent system as a trajectory of non-autonomous polynomial stochastic operators (nonlinear Markov operators). We show that the multiagent system eventually reaches to a consensus under suitable conditions. 2016-07-24 Conference or Workshop Item REM application/pdf en http://irep.iium.edu.my/54402/1/ICDEA%20---%20IREP.pdf Saburov, Mansoor (2016) Applications of non-autonomous discrete dynamical systems into nonlinear consensus problems. In: The 22nd International Conference on Difference Equations and Applications, 24-29 Jul 2016, Osaka, Japan. (Unpublished)
institution Universiti Islam Antarabangsa Malaysia
building IIUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider International Islamic University Malaysia
content_source IIUM Repository (IREP)
url_provider http://irep.iium.edu.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Saburov, Mansoor
Applications of non-autonomous discrete dynamical systems into nonlinear consensus problems
description Historically, an idea of reaching consensus through repeated averaging was introduced by DeGroot (see [1, 3]) for a structured time-invariant and synchronous environment. Since that time, the consensus which is the most ubiquitous phenomenon of multi-agent systems becomes popular in various scientific communities, such as biology, physics, control engineering and social science. Roughly speaking, a trajectory of a row-stochastic matrix presents DeGroot’s model of the structured time-invariant synchronous environment. In [2], Chatterjee and Seneta considered a generalization of DeGroot’s model for the structured time-varying synchronous environment. A trajectory of a sequence of row-stochastic matrices (a non-homogeneous Markov chain) presents the Chatterjee- Seneta model of the structured time-varying synchronous environment. In this paper, we shall consider a nonlinear model of the structured time-varying synchronous environment which generalizes both DeGroot’s and the Chatterjee-Seneta models. Namely, by means of multidimensional stochastic hypermatrices, we present an opinion sharing dynamics of the multi-agent system as a trajectory of non-autonomous polynomial stochastic operators (nonlinear Markov operators). We show that the multiagent system eventually reaches to a consensus under suitable conditions.
format Conference or Workshop Item
author Saburov, Mansoor
author_facet Saburov, Mansoor
author_sort Saburov, Mansoor
title Applications of non-autonomous discrete dynamical systems into nonlinear consensus problems
title_short Applications of non-autonomous discrete dynamical systems into nonlinear consensus problems
title_full Applications of non-autonomous discrete dynamical systems into nonlinear consensus problems
title_fullStr Applications of non-autonomous discrete dynamical systems into nonlinear consensus problems
title_full_unstemmed Applications of non-autonomous discrete dynamical systems into nonlinear consensus problems
title_sort applications of non-autonomous discrete dynamical systems into nonlinear consensus problems
publishDate 2016
url http://irep.iium.edu.my/54402/1/ICDEA%20---%20IREP.pdf
http://irep.iium.edu.my/54402/
_version_ 1643614546434195456
score 13.211869

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