Multistage for identification of Wiener time delay systems based on hierarchical gradient approach

This paper deals with the problem of identification of Wiener systems with unknown integer time delay. This problem presents several difficulties, since it consists in estimating simultaneously the integer time delay, the parameters of the linear dynamic subsystem and the parameters of the non-linear static block. To overcome these difficulties, we propose a new approach to identify the Wiener time delay systems based on the Hierarchical gradient identification principle. This proposed method consists, first, in decoupling the original optimization problem into three simple separate criteria jointly optimized and second, in using the gradient algorithm to minimize each function. The analysis gives us insight into the properties of this algorithm and develops condition that must be satisfied to ensure the convergence and to guarantee the use of rounding property. Simulation results are presented to illustrate the performance of the proposed method.