System identification: Parameter and time-delay estimation for Wiener nonlinear systems with delayed input

In this paper, a novel optimization approach to estimate the time delay and the parameters of Wiener time-delay systems is proposed. The proposed method consists first in defining a cost function and second in selecting an appropriate algorithm to solve it. However, any used cost function for the purpose of Wiener time-delay system identification presents several difficulties in terms of nonlinearity and inaccessible measurements. In fact, the hierarchical approach, the rounding property and the auxiliary model approach are suggested as solutions to overcome these difficulties. These solutions allow us to transform the cost function to be minimized into two simple cost functions that are minimized using the conjugate gradient algorithm with different choices of its main parameters. Simulation results are presented to illustrate the performance of the proposed approach.