Tuned Parameter Analysis of Weighted Recursive Least Squares Identifier with Structured Uncertainty

다국어 초록 (Multilingual Abstract)

ABSTRACTSome problems for analyzing the existence and uniqueness of the tuned parameter vec-
tor in a discrete-time Weighted Recursive Least Squares identifier with structured un-
certainty are discussed in this paper. The model to be estimated is an ARX model
with random disturbance.Using Power Spectrum Analysis, the persistent excitation condition is given by the
positiveness of the auto-correlation function matrix for the regressor. Several properties
for model error between the true system model and the estimated one are also dis-
cussed.The rank of the auto-correlation matrix depends on the structural aspect and the
spectrum behavior of all external signals. For the noise free case, it is verified that the
regressor can be partitioned into a pseudo-Sylvester matrix and an auxiliary regressor
and so some results for testing the rank of the auto-correlation matrix is presented
based on these relations. For the over-modeling case, it is easily shown that the re-
gressor can not be persistent exciting, even though the input has enough frequencies
and then, the tuned parameter vector can not be uniquely determined.When there exists the disturbance with sufficient spectra or the white noise, it is
also given that if the number of the input spectral lines is equal to, or larger than the
degree of the numerator polynomial in the estimated model, the regressor is always per-
sistently exciting, independently of model error.

다국어 초록 (Multilingual Abstract)

Some problems for analyzing the existence and uniquenress of the tuned parameter vector in a discrete-time Weighted Recurive Least Squares identifier with structured uncertainty are discussed in this paper. The mode1 to be estimated is an ARX model with random disturbance.
Using Power Spectrum Analysis, the persistent excitation condition is given by the positiveness of the auto-correlation function matrix for the regressor. Several properties for model error between the true system model and the estimated one are also discussed. The rank of the auto-correlation matrix depends on the structural aspect and the spectrum behavior of all external signals. For the noise free case, it is verified that the regresfor can be partitioned into a pseudo-Sylvester matrix and an auxiliary regresor and so some results for testing the rank of the auto-crrelation matrix is presented based on these relations. For the over-modeling case, if is easily shown that the re-grosser can not be persistent exciting, even though the input has enough frequencies and then, the tuned parameter vector can not be uniquely determined.
When there exists the disturbance with sufficient spectra or the white noise, it is also given that if the number of the input spectral lines is equal to, or larger than the degree of the numerator polynomial in the estimated mode1, tile regressor is always persisten1y exciting, independently of model error.