Identifiability implies robust, globally exponentially convergent on-line parameter estimation

Abstract

AbstractIn this paper we propose a new parameter estimator that ensures global exponential convergence of linear regression models requiring only the necessary assumption of identifiability of the regression equation, which we show is equivalent to interval excitation of the regressor vector. An extension to – separable and monotonic – nonlinear parameterisations is also given. The estimators are shown to be robust to additive measurement noise and – not necessarily slow-parameter variations. Moreover, a version of the estimator that is robust with respect to sinusoidal disturbances with unknown internal model is given. Simulation results that illustrate the performance of the estimator compared with other algorithms are given.Keywords: Parameter estimationidentifiabilityrobustnessinterval excitation AcknowledgmentsThe authors are grateful to S. Aranovskiy for help in the derivations of Section 5.2.Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 To simplify the notation we consider the case of scalar y, as will become clear below, the extension to the matrix case is straightforward.2 To simplify the notation, we omit throughout the subsection the subindex i.3 To avoid cluttering the notation, we restrict our presentation to the CT case, since as shown in Ortega, Gromov, et al. (Citation2021) the extension to DT follows verbatim.4 To simplify the notation we omit the subindex i.Additional informationFundingThe work of Lei was supported by the National Natural Science Foundation of China under Grant No. 62203386, and Zhejiang Provincial Natural Science Foundation of China under Grant No. LZ23F030008.