Identification of neuro-fractional Hammerstein systems: a hybrid frequency-/time-domain approach

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

“…There exist two main differences between the identification of the traditional Hammerstein system and the continuous‐time fractional‐order Hammerstein one: (i) in the case of input‐output regression‐based identification, data preprocessing techniques are essential for the continuous‐time Hammerstein identification, whereas such techniques are not required for the traditional Hammerstein identification; (ii) in contrast to the traditional Hammerstein identification, which estimates only the unknown coefficient vector, the fractional‐order Hammerstein identification includes the estimation of not only the coefficient vector but also the unknown fractional orders. This issue was addressed by the authors in their previous works …”

“…"> A1. The fractional‐order α and dimension of the states n are supposed to be known or may be identified via the approach previously proposed by the authors …”

“… In this paper, the joint state and parameter estimation is established on the basis of adaptive observer. In contrast with the work of Rahmani and Farrokhi, the global stability of the identification algorithm is ensured by introducing auxiliary input‐output filtered signals into differential equation of the observer. Moreover, in comparison with optimization‐based algorithms, including many of the references cited earlier, herein, stable identification laws are obtained via the use of the Lyapunov stability theory. In order to obtain a robust identification against outliers, a Gaussian Lyapunov function is introduced.…”

“…It is noteworthy that two main strategies have been presented in the literature on Hammerstein state‐space identification: (i) identification algorithms that are under the assumption of the system states being known and (ii) hierarchical methods based on the cost function minimization problem, which commonly bring the system back to its discrete‐time input‐output representation . Recently, the authors proposed an observer‐based state‐space identification using an auxiliary model‐based observer . Although, in the authors' previous work, joint state and parameter estimation is performed without the need for signal filtering techniques, the drawback of this method is its serious sensitivity to initial conditions.…”

“…This issue was addressed by the authors in their previous works. 18,27,28 In practice, measured data are usually contaminated by different types of noises and outliers. Outliers are defined as large deviations from the standard data range and may be referred to as large perturbations, impulsive noises, missing data, or non-Gaussian noises.…”