Auxiliary model maximum likelihood gradient‐based iterative identification for feedback nonlinear systems

Abstract This article considers the iterative identification problems for a class of feedback nonlinear systems with moving average noise. The model contains both the dynamic linear module and the static nonlinear module, which brings challenges to the identification. By utilizing the key term separation technique, the unknown parameters from both linear and nonlinear modules are included in a parameter vector. Furthermore, an auxiliary model maximum likelihood gradient‐based iterative algorithm is derived to estimate the unknown parameters. In addition, an auxiliary model maximum likelihood stochastic gradient algorithm is derived as a comparison. The numerical simulation results indicate that the auxiliary model maximum likelihood gradient‐based iterative algorithm can effectively estimate the parameters of the feedback nonlinear systems and get more accurate parameter estimates than the auxiliary model maximum likelihood stochastic gradient algorithm.