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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| Format: | Proceeding Paper |
| Language: | English |
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2016
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| Online Access: | http://irep.iium.edu.my/54406/ http://irep.iium.edu.my/54406/1/NCTS%20---%20IREP.pdf |
| _version_ | 1848784406233219072 |
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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. |
| first_indexed | 2025-11-14T16:36:44Z |
| format | Proceeding Paper |
| id | iium-54406 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T16:36:44Z |
| publishDate | 2016 |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |