An Optimal Two Stage Identification Algorithm for Discrete Hammerstein Time Delay Systems

This paper deals with the problem of identification of Hammerstein time delay systems. In fact, we propose a Hierarchical optimization based approach allowing to estimate simultaneously the time delay, the linear dynamic parameters and the nonlinear static parameters of such systems. This approach consists, firstly, in decomposing a complex nonlinear cost function into two simple cost functions and secondly, in using the gradient method to minimize each function (HH-G). The convexity condition to authorize the use of the rounding property is also developed and the convergence analysis of the proposed algorithm indicates that the parameter estimation errors converge to zero under persistent excitation conditions and the estimated time delay converge to a finite value. The simulation results are presented to illustrate the effectiveness of the proposed method.