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A new on-line exponential parameter estimator without persistent excitation

Abstract : In this paper we propose a new algorithm that estimates on-line the parameters of a classical vector linear regression equation Y = Ωθ, where Y ∈ R n , Ω ∈ R n×q are bounded, measurable signals and θ ∈ R q is a constant vector of unknown parameters, even when the regressor Ω is not persistently exciting. Moreover, the convergence of the new parameter estimator is global and exponential and is given for both, continuous-time and discrete-time implementations. As an illustration example we consider the problem of parameter estimation of a linear timeinvariant system, when the input signal is not sufficiently exciting, which is known to be a necessary and sufficient condition for the solution of the problem with standard gradient or least-squares adaptation algorithms.
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https://hal-centralesupelec.archives-ouvertes.fr/hal-03463648
Contributor : Stanislav Aranovskiy Connect in order to contact the contributor
Submitted on : Thursday, December 2, 2021 - 3:32:44 PM
Last modification on : Wednesday, March 16, 2022 - 3:51:08 AM
Long-term archiving on: : Thursday, March 3, 2022 - 7:46:56 PM

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M. Korotina, J.G. G Romero, Stanislav Aranovskiy, A. Bobtsov, R. Ortega. A new on-line exponential parameter estimator without persistent excitation. Systems and Control Letters, Elsevier, 2022, 159, pp.105079. ⟨10.1016/j.sysconle.2021.105079⟩. ⟨hal-03463648⟩

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