Nonlinear robustified stochastic consensus seeking

In this paper we propose a novel stochastic consensus seeking 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 provides a significant improvement over the linear algorithms from the point of view of robustness to noise, ensuring better convergence rate and lower sensitivity of the limit state value at consensus. One of the main contributions of the paper is the proof that the algorithm converges almost surely to consensus under general conditions. A detailed analysis of the limit state value at consensus is provided together with an insight into achievable convergence rate. Illustrative simulation results are also provided, demonstrating great advantages of the proposed algorithm compared to the existing consensus schemes.