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Active noise control (ANC) algorithms are generally designed to obtain the attenuation of gaussian noise signals using suitable adaptive signal processing algorithms. The rejection of non-gaussian impulsive noise signals represents a much more critical task, with respect to which standard ANC algorithms generally fail to provide a satisfactory solution, due to convergence and instability problems. This paper proposes a novel ANC algorithm for the attenuation of impulsive noise, based on the online estimation of an alpha-stable model of the noise probabilistic description. Simulation analysis shows that the presented approach provides some improvement with respect to competitor methods.