Smoothed functional algorithm with norm-limited update vector for identification of continuous-time fractional-order Hammerstein Models

This article proposes an identification method of continuous-time fractional-order Hammerstein model using smoothed functional algorithm with a norm-limited update vector (NL-SFA). In particular, the standard smoothed functional algorithm (SFA) based method is modified by implementing a limit function in the update vector of the standard SFA based method to solve the issue of high tendency of divergence during the identification process. As a result of this, the proposed NL-SFA based method is applied to identify the variables of the linear and non-linear subsystems in the Hammerstein model. While most of the actual linear subsystems can be naturally expressed in a continuous-time domain, the implementation of the fractional-order could also reduce the computational complexity in finding a more accurate reduced-order model. Moreover, three experiments of the Hammerstein model identification based on a numerical example, an actual twin-rotor system, and an actual flexible manipulator system were carried out in this study to verify the effectiveness of the proposed NL-SFA-based method. The numerical and experimental results were analyzed to correspond to the measurement of the objective function and variable identification error and time-domain and frequency-domain responses. Conclusively, the proposed NL-SFA-based method can provide stable convergence and significantly better accuracy of the Hammerstein model in the numerical example, the actual twin-rotor system, and the flexible manipulator system compared to the standard SFA. Moreover, the proposed NL-SFA also provides slightly competitive identification accuracy with the existing norm-limited simultaneous perturbation stochastic approximation (NL-SPSA) and the average multi-verse optimizer sine cosine algorithm (AMVO-SCA) based methods.