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...

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Main Author: Saburov, Mansoor
Format: Proceeding Paper
Language:English
Published: 2016
Subjects:
Online Access:http://irep.iium.edu.my/54406/
http://irep.iium.edu.my/54406/1/NCTS%20---%20IREP.pdf
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author Saburov, Mansoor
author_facet Saburov, Mansoor
author_sort Saburov, Mansoor
building IIUM Repository
collection Online Access
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.
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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 Proceeding Paper 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)
spellingShingle QA Mathematics
Saburov, Mansoor
Ergodic theory of nonlinear markov operators with applications in nonlinear consensus problems
title 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_short 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
topic QA Mathematics
url http://irep.iium.edu.my/54406/
http://irep.iium.edu.my/54406/1/NCTS%20---%20IREP.pdf