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

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 (Unpublished)

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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.

Item Type: Conference or Workshop Item (Keynote)
Additional Information: 6769/54406
Uncontrolled Keywords: Ergodic Theory, nonlinear Markov operators, nonlinear consensus problems
Subjects: Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button): Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User: Dr Mansoor Saburov
Date Deposited: 17 Jan 2017 12:31
Last Modified: 17 Jan 2017 12:31
URI: http://irep.iium.edu.my/id/eprint/54406

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