Joint Parameter and Time-Delay Identification Algorithm and Its Convergence Analysis for Wiener Time-Delay Systems

New developments for parameter and time-delay identification are presented for discrete nonlinear systems with delayed input. The proposed approach is based on overparametrization approach which involves subsuming the delay term into an extended numerator polynomial of the linear block of Wiener time-delay system. On this basis, the parameter identification problem can be then solved using recursive least squares-based optimization techniques and then, the delay is calculated directly based on the extended numerator polynomial identified: For a noise-free system, all extended numerator parameters are equal to zero. However in the noisy-output case, it is necessary to introduce an upper bound and the extended parameters whose values are smaller than a threshold level should be identified as zero. Then, the delay is determined as the first number of null extended parameter values. In addition, the convergence of the identified parameter vector is studied. The performances of the proposed identification algorithms are illustrated through simulation examples.