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오늘 본 자료
Reaching a Nonlinear Consensus: Polynomial Stochastic Operators
Mansoor Saburov,Khikmat Saburov 제어·로봇·시스템학회 2014 International Journal of Control, Automation, and Vol.12 No.6
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.
ON LEBESGUE NONLINEAR TRANSFORMATIONS
Ganikhodjaev, Nasir,Muhitdinov, Ramazon,Saburov, M. Korean Mathematical Society 2017 대한수학회보 Vol.54 No.2
In this paper, we introduce a quadratic stochastic operators on the set of all probability measures of a measurable space. We study the dynamics of the Lebesgue quadratic stochastic operator on the set of all Lebesgue measures of the set [0, 1]. Namely, we prove the regularity of the Lebesgue quadratic stochastic operators.
On Lebesgue nonlinear transformations
Nasir Ganikhodjaev,Ramazon Muhitdinov,M. Saburov 대한수학회 2017 대한수학회보 Vol.54 No.2
In this paper, we introduce a quadratic stochastic operators on the set of all probability measures of a measurable space. We study the dynamics of the Lebesgue quadratic stochastic operator on the set of all Lebesgue measures of the set $[0,1]$. Namely, we prove the regularity of the Lebesgue quadratic stochastic operators.