We study a class of recursive least-squares estimators in an errors-in-variables setting where disturbances affect both the regressor and the regressand variables. We prove the existence and stability of an optimal steady state and robustness with respect to the disturbances in form of input-to-state and input–output stability relative to the unperturbed steady-state trajectories. Depending on the choice of some design parameters, different specific estimators can be realized within the considered class, each of which is associated with a different underlying optimization problem and with different excitation requirements for the unperturbed regressor. As expected, we find that persistence of excitation is associated with uniform, in fact exponential, convergence. In addition, we also show that choices of the design parameters are possible for which convergence and robustness hold without persistence of excitation and with the same asymptotic gain, the only difference being a loss of uniformity in the convergence rate.

Generalized recursive least squares: Stability, robustness, and excitation / Bin M. - In: SYSTEMS & CONTROL LETTERS. - ISSN 1872-7956. - ELETTRONICO. - 161:March 2022(2022), pp. 105144.1-105144.1. [10.1016/j.sysconle.2022.105144]

Generalized recursive least squares: Stability, robustness, and excitation

Bin M
Primo
2022

Abstract

We study a class of recursive least-squares estimators in an errors-in-variables setting where disturbances affect both the regressor and the regressand variables. We prove the existence and stability of an optimal steady state and robustness with respect to the disturbances in form of input-to-state and input–output stability relative to the unperturbed steady-state trajectories. Depending on the choice of some design parameters, different specific estimators can be realized within the considered class, each of which is associated with a different underlying optimization problem and with different excitation requirements for the unperturbed regressor. As expected, we find that persistence of excitation is associated with uniform, in fact exponential, convergence. In addition, we also show that choices of the design parameters are possible for which convergence and robustness hold without persistence of excitation and with the same asymptotic gain, the only difference being a loss of uniformity in the convergence rate.
2022
Generalized recursive least squares: Stability, robustness, and excitation / Bin M. - In: SYSTEMS & CONTROL LETTERS. - ISSN 1872-7956. - ELETTRONICO. - 161:March 2022(2022), pp. 105144.1-105144.1. [10.1016/j.sysconle.2022.105144]
Bin M
File in questo prodotto:
File Dimensione Formato  
published.pdf

accesso aperto

Descrizione: published version
Tipo: Versione (PDF) editoriale
Licenza: Licenza per Accesso Aperto. Creative Commons Attribuzione (CCBY)
Dimensione 448.68 kB
Formato Adobe PDF
448.68 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/916876
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact