The Maximum Correntropy Criterion-Based Identification for Fractional-Order Systems under Stable Distribution Noises

Abstract

This paper studies the identification for fractional-order systems (FOSs) under stable distribution noises. First, the generalized operational matrix of block pulse functions is used to convert the identified system into an algebraic one. Then, the conventional least mean square (LMS) criterion is replaced by the maximum correntropy criterion (MCC) to restrain the effect of noises, and a MCC-based algorithm is designed to perform the identification. To verify the superiority of the proposed method, the identification accuracy is examined when the noise follows different types of stable distributions. In addition, the impact of parameters of stable distribution on identification accuracy is discussed. It is shown that when the impulse of noise increases, the identification error becomes larger, but the proposed algorithm is always superior to its LMS counterpart. Moreover, the location parameter of stable distribution noise has a significant impact on the identification accuracy.