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The method of excitation normalization of the regressor, which is used in theestimation loop to solve the plant identification problem, is proposed. It isbased on the dynamic regressor extension and mixing procedure. Its applicationallows to obtain the same upper bound of the parameter identification error forthe scalar regressors with different excitation level, using a constant valueof the adaptation rate for all of them. This fact is a significant advantagefrom the practical point of view. Comparison of the developed method with theknown one of the regressor amplitude normalization is conducted. It is shownthat the classical approach does not have the above-stated property. Tovalidate the theoretical conclusions made, the results of the comparativemathematical modeling of three loops are presented: 1) the classical gradientone, 2) the one with the normalization of the regressor amplitude, 3) theproposed one with the normalization of the regressor excitation.

Normalization of regressor excitation as a part of dynamic regressor extension and mixing procedure