Identification of fractional Hammerstein systems with the conformable fractional derivative

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SummaryIn this article, we study parameter estimation problems for fractional commensurate Hammerstein systems utilizing the conformable fractional derivative. Two algorithms are investigated: first, the Poisson moment functions (PMF) method, aiming to transfer the fractional derivative of the measurement signal into PMF using the fractional Laplace transform and convolution; second, a proposed new instrumental variable algorithm, which is based on the conformable fractional derivative. Both algorithms have been analyzed and shown to be consistent. A comprehensive complexity analysis is provided for each algorithm. Furthermore, a kind of special time‐varying systems are discussed under the conformable fractional derivative. Finally, an example is given to illustrate the effectiveness of the proposed algorithms.