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Reaching a Nonlinear Consensus: Polynomial Stochastic Operators

Mansoor Saburov* and Khikmat Saburov
International Journal of Control, Automation, and Systems, vol. 12, no. 6, pp.1276-1282, 2014

Abstract : 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.

Keyword : Multidimension stochastic hypermatrix, nonlinear consensus, polynomial operator.

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