Hierarchical Identification of Hammerstein- Wiener time-delay systems with maximum likelihood and gradient descent algorithm

In this paper, the parameter estimation for Hammerstein-Wiener nonlinear systems with unknown delay is studied. Based on the hierarchical identification principle and two-step identification, the maximum likelihood recursive algorithm is used to identify the parameters of the system, and the gradient descent method is used to identify the time delay. Finally, the algorithm is verified by a numerical example, and the simulation results show that the algorithm has the characteristics of fast convergence speed and high identification accuracy.