Hybrid identification method for fractional-order nonlinear systems based on the multi-innovation principle

Aiming at the identification problems arising for fractional-order Hammerstein-Wiener system parameter coupling, namely, the difficulty of estimating the fractional order, low algorithm accuracy and slow convergence, an alternate identification method based on the principle of multiple innovations is proposed. First, a discrete model of a fractional-order Hammerstein-Wiener system is constructed. Second, an information matrix composed of fractional-order variables is used as the system input, combined with the multi-innovation principle, and the multi-innovation recursive gradient descent algorithm and the multi-innovation Levenberg-Marquardt algorithm are used to alternately estimate the parameters and fractional order of the model. The algorithms are executed cyclically and alternately presuppose each other. Finally, the convergence of the overall algorithm is theoretically analyzed, and the fractional-order Hammerstein-Wiener nonlinear system model is used to carry out numerical simulation experiments to verify the effectiveness of the algorithm. Moreover, we apply the proposed algorithm to an actual flexible manipulator system and perform fractional-order modeling and identification with high accuracy. Compared with the methods proposed by other scholars, the method proposed in this paper is more effective.