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/ http://irep.iium.edu.my/54402/1/ICDEA%20---%20IREP.pdf

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recordtype	eprints
spelling	iium-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 PeerReviewed 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)
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
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/ http://irep.iium.edu.my/54402/1/ICDEA%20---%20IREP.pdf
first_indexed	2023-09-18T21:16:59Z
last_indexed	2023-09-18T21:16:59Z
_version_	1777411628207177728

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

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