Time delay system identification based on optimization approaches

In this paper, the problem of estimating the time delay and dynamic parameters of monovariable time delay discrete is addressed. This problem involves both the estimation of the time delay and the dynamic parameters from input-output data. In fact, we have considered our previous method which consists in minimizing a quadratic criterion using either the gradient method or the Levenberg-Marquardt method. The used criterion is deduced from a formulation allowing to define the time delay and the dynamic parameters in the same estimated vector and to build the corresponding observation vector. In order to improve the performance of this approach, we advocate the use of the quasi-Newton approach based on the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. Simulation results are presented to illustrate the performance of the new solution.