Abstract
In this paper one way is proposed to construct asymptotic and non-asymptotic confidence regions in the problem of closed loop model validation deeply. These two asymptotic and non-asymptotic confidence regions correspond to the infinite and finite data points. Firstly one asymptotic confidence region is derived from some statistical properties on noise. The uncertainties bound of the model parameter is constructed in the probability sense by using the inner product form of the asymptotic covariance matrix, then a new technique for estimating bias and variance contributions to the model error is suggested. Secondly we modify sign perturbed sums (SPS) method to construct non-asymptotic confidence regions under a finite number of data points, where some modifications are studied for closed loop system. Finally the simulation example results confirm the identification theoretical results.
Highlights
The automatic control system includes two basic structures: one open loop and other closed loop
As there does not exist any feedback in open loop structure, so the plant output affects the input less
The whole theory of system identification can be divided into four categories, i.e. experiment design [1], model structure selection [2], model parameter identification [3] and model structure validation test [4]
Summary
The automatic control system includes two basic structures: one open loop and other closed loop. As there does not exist any feedback in open loop structure, so the plant output affects the input less. In closed open structure, the error signals coming from the input and feedback output generate one correction action and make the output converge to some given value. In the direct data driven method, the modeling process is not needed and the controller is directly designed by using the input-output data. There are three common identification methods for closed loop system identification, i.e. direct approach, indirect approach and joint input-output approach, where the feedback is neglected in direct approach and the plant model is identified directly using the input-output data. In the indirect approach for closed loop system identification, the feedback effect is considered and the input-output from the whole closed loop condition are used to identify the plant model.
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