Reaching nonlinear consensus via non-autonomous polynomial stochastic operators

• Main Authors: Saburov, Mansoor, Saburov, Khikmat
• Format: Conference or Workshop Item
• Language: English; English; English; English
• Published: IOP Publishing 2017
• Subjects: QA Mathematics
• Online Access: http://irep.iium.edu.my/57120/1/The%20Nonlinear%20Consensus%20---%20JOP.pdf; http://irep.iium.edu.my/57120/7/57120_Reaching%20nonlinear%20concensus_SCOPUS.pdf; http://irep.iium.edu.my/57120/13/57120_reaching%20nonlinear%20consensus.pdf; http://irep.iium.edu.my/57120/19/57120%20Reaching%20nonlinear%20consensus%20via%20non-autonomous%20WOS.pdf; http://irep.iium.edu.my/57120/; http://iopscience.iop.org/article/10.1088/1742-6596/819/1/012009

This paper is a continuation of our previous studies on nonlinear consensus which uni�es and generalizes all previous results. We consider a nonlinear protocol for a structured time-varying synchronous multi-agent system. We present an opinion sharing dynamics of the multi-agent system as a trajectory of non-autonomous polynomial stochastic operators associated with multidimensional stochastic hyper-matrices. We show that the multi-agent system eventually reaches to a nonlinear consensus if either one of the following two conditions is satisfied: (i) every member of the group people has a positive subjective distribution on the given task after some revision steps or (ii) all entries of some multidimensional stochastic hyper-matrix are positive.