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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| Format: | Proceeding Paper |
| Language: | English |
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2016
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| Online Access: | http://irep.iium.edu.my/54402/ http://irep.iium.edu.my/54402/1/ICDEA%20---%20IREP.pdf |
| _version_ | 1848784405425815552 |
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| author | Saburov, Mansoor |
| author_facet | Saburov, Mansoor |
| author_sort | Saburov, Mansoor |
| building | IIUM Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-14T16:36:43Z |
| format | Proceeding Paper |
| id | iium-54402 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T16:36:43Z |
| publishDate | 2016 |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 Proceeding Paper 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) |
| spellingShingle | QA Mathematics Saburov, Mansoor Applications of non-autonomous discrete dynamical systems into nonlinear consensus problems |
| title | 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_short | Applications of non-autonomous discrete dynamical
systems into nonlinear consensus problems |
| title_sort | applications of non-autonomous discrete dynamical
systems into nonlinear consensus problems |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/54402/ http://irep.iium.edu.my/54402/1/ICDEA%20---%20IREP.pdf |