Reaching a nonlinear consensus: polynomial stochastic operators

• Main Authors: Saburov, Mansoor, Saburov, Khikmat
• Format: Article
• Language: English; English; English
• Published: Springer 2014
• Subjects: QA Mathematics
• Online Access: http://irep.iium.edu.my/38828/1/38828_Reaching%20a%20nonlinear%20consensus.pdf; http://irep.iium.edu.my/38828/2/38828_Reaching%20a%20nonlinear%20consensus_SCOPUS.pdf; http://irep.iium.edu.my/38828/3/38828_Reaching%20a%20nonlinear%20consensus_WOS.pdf; http://irep.iium.edu.my/38828/; http://link.springer.com/article/10.1007/s12555-014-0061-0
• Institution: Universiti Islam Antarabangsa Malaysia

We provide a general nonlinear protocol for a structured time-varying and synchronous multi-agent system. We present an opinion sharing dynamics of the multi-agent system as a trajectory of a polynomial stochastic operator associated with a multidimensional stochastic hypermatrix. We show that the multi-agent system eventually reaches to a consensus if either one of the following two conditions is satisfied: (i) every member of the group people has a positive subjective opinion on the given task after some revision steps or (ii) all entries of a multidimensional stochastic hypermatrix are positive. Numerical results are also presented.