Robust identification of MISO neuro-fractional-order Hammerstein systems

This paper introduces a multiple-input-single-output (MISO) neuro-fractional-order Hammerstein (NFH) model with a Lyapunov-based identification method, which is robust in the presence of outliers. The proposed model is composed of a multiple-input-multiple-output radial basis function neural network in series with a MISO linear fractional-order system. The state-space matrices of the NFH are identified in the time domain via the Lyapunov stability theory using input-output data acquired from the system. In this regard, the need for the system state variables is eliminated by introducing the auxiliary input-output filtered signals into the identification laws. Moreover, since practical measurement data may contain outliers, which degrade performance of the identification methods (eg, least-square-based methods), a Gaussian Lyapunov function is proposed, which is rather insensitive to outliers compared with commonly used quadratic Lyapunov function. In addition, stability and convergence analysis of the presented method is provided. Comparative example verifies superior performance of the proposed method as compared with the algorithm based on the quadratic Lyapunov function and a recently developed input-output regression-based robust identification algorithm.