Relaxation of Conditions for Convergence of Dynamic Regressor Extension and Mixing Procedure

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription or Fee Access

Abstract

A generalization of the dynamic regressor extension and mixing procedure is proposed, which, unlike the original procedure, first, guarantees a reduction of the unknown parameter identification error if the requirement of regressor semi-finite excitation is met, and second, it ensures exponential convergence of the regression function (regressand) tracking error to zero when the regressor is semi-persistently exciting with a rank one or higher.

About the authors

A. I Glushchenko

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences

Email: aiglush@ipu.ru
Moscow, Russia

K. A Lastochkin

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences

Author for correspondence.
Email: lastconst@yandex.ru
Moscow, Russia

References

  1. Ortega R., Nikiforov V., Gerasimov D. On Modified Parameter Estimators for Identification and Adaptive Control. A Unified Framework and Some New Schemes // Annual Reviews in Control. 2020. V. 50. P. 278-293.
  2. Aranovskiy S., Bobtsov A., Ortega R., Pyrkin A. Performance Enhancement of Parameter Estimators via Dynamic Regressor Extension and Mixing // IEEE Trans. Automat. Control. 2016. V. 62, No. 7. P. 3546-3550.
  3. Glushchenko A.I., Petrov V.A., Lastochkin K.A. I-DREM: Relaxing the Square Integrability Condition // Autom. Remote Control. 2021. V. 82. No. 7. P. 1233-1247.
  4. Korotina M., Romero J.G., Aranovskiy S., Bobtsov A., Ortega R. A New On-Line Exponential Parameter Estimator without Persistent Excitation // Sys. Control Letters. 2022. V. 159. P. 1-10.
  5. Wang L., Ortega R., Bobtsov A., Romero J.G., Yi B. Identifiability implies robust, globally exponentially convergent on-line parameter estimation: Application to model reference adaptive control // arXiv preprint arXiv:2108.08436. 2021. P. 1-16.
  6. Wang J., Efimov D., Aranovskiy S., Bobtsov A. Fixed-Time Estimation of Parameters for Non-Persistent Excitation // European J. Control. 2020. V. 55. P. 24-32.
  7. Yi B., Ortega R. Conditions for convergence of dynamic regressor extension and mixing parameter estimators using LTI filters // IEEE Trans. Automat. Control. 2022. P. 1-6.
  8. Aranovskiy S., Ushirobira R., Korotina M., Vedyakov A. On preserving-excitation properties of Kreisselmeiers regressor extension scheme // IEEE Trans. Automat. Control. 2022. P. 1-6.
  9. Sastry S., Bodson M. Adaptive Control - Stability, Convergence, and Robustness. N.J.: Prentice Hall, 1989.
  10. Kreisselmeier G., Rietze-Augst G. Richness and Excitation on an Interval-with Application to Continuous-Time Adaptive Control // IEEE Trans. Automat. Control. 1990. V. 35. No. 2. P. 165-171.
  11. Roy S.B., Bhasin S. Novel Model Reference Adaptive Control Architecture Using Semi-Initial Excitation-Based Switched Parameter Estimator // Int. J. Adaptive Control Signal Proc. 2019. V. 33. No. 12. P. 1759-1774.
  12. Glushchenko A., Lastochkin K. Robust Time-Varying Parameters Estimation Based on I-DREM Procedure // IFAC-PapersOnLine. 2022. V. 55. No. 12. P. 91-96.
  13. Ovcharov A., Vedyakov A., Kazak S., Bespalov V., Pyrkin A., Bobtsov A. Flux Observer for The Levitated Ball with Relaxed Excitation Conditions // Proc. European Control Conf. 2021. P. 2334-2339.
  14. Ovcharov A., Vedyakov A., Kazak S., Pyrkin A. Overparameterized model parameter recovering with finite-time convergence // Int. J. Adapt. Control. Signal Process. 2022. P. 1305-1325.
  15. Tihonov A.N. Solution of incorrectly formulated problems and the regularization method // Soviet Math. 1963. V. 4. P. 1035-1038.
  16. Hansen P.C. The Truncated SVD as a Method For Regularization // BIT Num. Math. 1987. V. 27. No. 4. С. 534-553.
  17. Meyer C.D. Matrix Analysis and Applied Linear Algebra. Siam, 2000.
  18. Glushchenko A.I., Lastochkin K.A., Petrov V.A. Normalization of Regressor Excitation in the Dynamic Extension and Mixing Procedure // Autom. Remote Control. 2022. Vol. 83. No. 1. P. 17-31.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2023 The Russian Academy of Sciences