Ergodic theory of nonlinear markov operators with applications in nonlinear consensus problems

A consensus problem of multi-agent systems has been considered a dual problem to Markov chains. Historically, an idea of reaching consensus through linear repeated averaging was introduced by DeGroot (see [1]) for a structured time-invariant and synchronous environment. Since that time, the consensu...

Full description

Bibliographic Details
Main Author:	Saburov, Mansoor
Format:	Conference or Workshop Item
Language:	English
Published:	2016
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/54406/ http://irep.iium.edu.my/54406/1/NCTS%20---%20IREP.pdf

id	iium-54406
recordtype	eprints
spelling	iium-544062017-01-17T04:31:06Z http://irep.iium.edu.my/54406/ Ergodic theory of nonlinear markov operators with applications in nonlinear consensus problems Saburov, Mansoor QA Mathematics A consensus problem of multi-agent systems has been considered a dual problem to Markov chains. Historically, an idea of reaching consensus through linear repeated averaging was introduced by DeGroot (see [1]) 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. In [2], Chatterjee and Seneta considered a generalization of DeGroot’s model for the structured time-varying synchronous environment. Based on the ergodic theory of non-homogeneous Markov chains, the theory of linear consensus problems for structured time-varying environment was established very well [2]. In this plenary talk, we shall present the ergodic theory of nonlinear Markov chains which enables to study the nonlinear consensus problems for the structured time-invariant as well as time-varying synchronous environment. This theory was developed in the series of papers [3, 4, 5, 6]. This work was supported by Ministry of Higher Education (MOHE) grant FRGS14-141-0382. 2016-08-15 Conference or Workshop Item PeerReviewed application/pdf en http://irep.iium.edu.my/54406/1/NCTS%20---%20IREP.pdf Saburov, Mansoor (2016) Ergodic theory of nonlinear markov operators with applications in nonlinear consensus problems. In: 2016 NCTS Workshop on Dynamical Systems & 2016 China, Hong Kong, Taiwan joint conference on dynamical systems, 15-18 Aug 2016, Taiwan. (Unpublished)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 Ergodic theory of nonlinear markov operators with applications in nonlinear consensus problems
description	A consensus problem of multi-agent systems has been considered a dual problem to Markov chains. Historically, an idea of reaching consensus through linear repeated averaging was introduced by DeGroot (see [1]) 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. In [2], Chatterjee and Seneta considered a generalization of DeGroot’s model for the structured time-varying synchronous environment. Based on the ergodic theory of non-homogeneous Markov chains, the theory of linear consensus problems for structured time-varying environment was established very well [2]. In this plenary talk, we shall present the ergodic theory of nonlinear Markov chains which enables to study the nonlinear consensus problems for the structured time-invariant as well as time-varying synchronous environment. This theory was developed in the series of papers [3, 4, 5, 6]. This work was supported by Ministry of Higher Education (MOHE) grant FRGS14-141-0382.
format	Conference or Workshop Item
author	Saburov, Mansoor
author_facet	Saburov, Mansoor
author_sort	Saburov, Mansoor
title	Ergodic theory of nonlinear markov operators with applications in nonlinear consensus problems
title_short	Ergodic theory of nonlinear markov operators with applications in nonlinear consensus problems
title_full	Ergodic theory of nonlinear markov operators with applications in nonlinear consensus problems
title_fullStr	Ergodic theory of nonlinear markov operators with applications in nonlinear consensus problems
title_full_unstemmed	Ergodic theory of nonlinear markov operators with applications in nonlinear consensus problems
title_sort	ergodic theory of nonlinear markov operators with applications in nonlinear consensus problems
publishDate	2016
url	http://irep.iium.edu.my/54406/ http://irep.iium.edu.my/54406/1/NCTS%20---%20IREP.pdf
first_indexed	2023-09-18T21:16:59Z
last_indexed	2023-09-18T21:16:59Z
_version_	1777411628657016832

Ergodic theory of nonlinear markov operators with applications in nonlinear consensus problems

Similar Items