Further Results on Model Structure Validation for Closed Loop System Identification

In this paper, further results on the problem of the model structure validation for closed loop system identification are proposed. One probabilistic model uncertainty is derived from some statistical properties of the parameter estimation. The uncertainties bound of the model parameter is constructed in the probability sense by using the inner product form of the asymptotic covariance matrix. Further a new technique for estimating bias and variance contributions to the model error is suggested. One bound described as an inequality corresponds to a condition on the model error. Due to this proposed bound, model structure validation process can be transformed to verify whether the model error obeys this inequality. Finally the simulation example results confirm the identification theoretical results.