Robust Nonlinear Consensus Seeking

In this paper we propose a new stochastic consensus algorithm based on the introduction of a nonlinear transformation aimed at robustification with respect to noise influence. The introduced nonlinear transformation is selected according to the methodology of stochastic approximation and robust statistics. The proposed algorithm represents a general nonlinear stochastic consensus seeking scheme, not yet treated in the literature. It is proved, under general conditions, that the algorithm converges almost surely to consensus. The choice of the nonlinearity ensuring better robustness properties compared to the linear algorithm, in the sense of better convergence rate and lower sensitivity of the asymptotic consensus value, is discussed. Illustrative simulation results, demonstrating the obtained advantages, are also provided.

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