Hierarchical gradient based identification of discrete-time delay systems

In this paper, we apply a hierarchical identification principle to identify simultaneously the unknown time delay and dynamic parameters of discrete-time delay systems. In our approach, we separate the nonlinear cost function into two simple cost functions and present a gradient iterative algorithm for estimating directly the time delay and the parameters. The cost function used to estimate the time delay is an integer nonlinear programming problem (IP) and the solution of the integer version of a nonlinear optimization problem is obtained by rounding the solution for its continuous relaxation (CP). Furthermore, we give an appropriate choice of the convergence factor. Finally, the effectiveness of this method has been illustrated through simulation.