A Robust Consensus Seeking Algorithm

In this paper we propose a new robust consensus algorithm based on the introduction of a nonlinear transformation selected according to the methodology of robust statistics. Compared to the standard linear consensus scheme, the proposed algorithm provides significant improvements from the point of view of noise influence on the limit state value at consensus, and the convergence rate. It is proved that the algorithm almost surely convergences to a finite consensus point, belonging to the set of zeros of the regression function. The choice of the nonlinearities in the algorithm is discussed from the robust statistics point of view. Some illustrative simulation results are provided demonstrating the theoretically anticipated advantages of the proposed algorithm.