This work focuses on the online identification of discrete-time input-output models, also called infinite impulse response (IIR) or autoregressive moving average (ARMA) models, using recursive least squares (RLS).
The key insights are:
It introduces the notion of equivalence between input-output models of different orders. Two models are equivalent if they produce the same outputs under the same inputs and initial conditions.
It analyzes the case where the order of the identified model is higher than the true system. In this case, the regressor of RLS is not persistently exciting, so standard convergence guarantees do not apply.
It shows that, under persistent excitation of a modified regressor, the identified higher-order model converges to the higher-order model that is equivalent to the true system and minimizes the regularization term of RLS.
It provides necessary and sufficient conditions for the reducibility of an input-output model, i.e., the existence of an equivalent lower-order model. This is related to the case of model order mismatch.
The analysis provides insights into the behavior of RLS-based identification when the model order is not known a priori, which is common in practical applications.
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by Brian Lai,De... о arxiv.org 04-18-2024
https://arxiv.org/pdf/2404.10850.pdfГлибші Запити