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(Unpublished)
Abstract
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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