Skip to main content
SpringerLink
Log in

Normalization of Regressor Excitation in the Dynamic Extension and Mixing Procedure

  • LINEAR SYSTEMS
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

We propose an approach to the normalization of the excitation of the identification loop regressor constructed based on the dynamic extension and mixing procedure. With a constant estimation loop gain, applying this approach allows one to have the same upper bound on the parametric identification error for scalar regressors with various degrees of excitation, a feature that is a significant advantage for practice. The approach developed is compared with the well-known regressor amplitude normalization method, and it is shown that the classical normalization method does not have the above-mentioned property. As a validation of our theoretical conclusions, the results of comparative mathematical modeling are presented for the classical gradient estimation loop, loops with amplitude regressor normalization, and loops with the proposed regressor excitation normalization.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.

Similar content being viewed by others

REFERENCES

  1. Ljung, L., System Identification: Theory for the User, Englewood Cliffs, N.J.: Prentice-Hall, 1987. Translated under the title: Identifikatsiya sistem. Teoriya dlya pol’zovatelya, Moscow: Nauka, 1991.

    MATH  Google Scholar 

  2. Narendra, K.S. and Annaswamy, A.M., Persistent excitation in adaptive systems, Int. J. Control, 1987, vol. 45, no. 1, pp. 127–160.

    Article  MathSciNet  Google Scholar 

  3. Holtz, J., Sensorless control of induction machines—with or without signal injection? IEEE Trans. Ind. Electron., 2006, vol. 53, no. 1, pp. 7–30.

    Article  Google Scholar 

  4. Wang, J., Efimov, D., Aranovskiy, S., and Bobtsov, A., Fixed-time estimation of parameters for non-persistent excitation, Eur. J. Control, 2020, vol. 55, pp. 24–32.

    Article  MathSciNet  Google Scholar 

  5. Wang, J., Efimov, D., and Bobtsov, A., On robust parameter estimation in finite-time without persistence of excitation, IEEE Trans. Autom. Control, 2019, vol. 65, no. 4, pp. 1731–1738.

    Article  MathSciNet  Google Scholar 

  6. Ortega, R., Bobtsov, A., and Nikolaev, N., Parameter identification with finite-convergence time alertness preservation, IEEE Control Syst. Lett., 2021, pp. 1–6.

  7. Chowdhary, G., Mühlegg, M., and Johnson, E., Exponential parameter and tracking error convergence guarantees for adaptive controllers without persistency of excitation, Int. J. Control, 2014, vol. 87, no. 8, pp. 1583–1603.

  8. Cho, N., Shin, H., Kim, Y., and Tsourdos, A., Composite model reference adaptive control with parameter convergence under finite excitation, IEEE Trans. Autom. Control, 2017, vol. 63, no. 3, pp. 811–818.

    Article  MathSciNet  Google Scholar 

  9. Lee, H.I., Shin, H.S., and Tsourdos, A., Concurrent learning adaptive control with directional forgetting, IEEE Trans. Autom. Control, 2019, vol. 64, no. 12, pp. 5164–5170.

    Article  MathSciNet  Google Scholar 

  10. Aranovskiy, S., Bobtsov, A., Ortega, R., and Pyrkin, A., Performance enhancement of parameter estimators via dynamic regressor extension and mixing, IEEE Trans. Autom. Control, 2016, vol. 62, no. 7, pp. 3546–3550.

    Article  MathSciNet  Google Scholar 

  11. Bobtsov, A., Pyrkin, A., Ortega, R., and Vedyakov, A., A state observer for sensorless control of magnetic levitation systems, Automatica, 2018, vol. 97, pp. 263–270.

    Article  MathSciNet  Google Scholar 

  12. Ortega, R., Bobtsov, A., Nikolaev, N., Schiffer, J., and Dochain, D., Generalized parameter estimation-based observers: application to power systems and chemical-biological reactors, , 2020, pp. 1–13.

  13. Ortega, R., Gromov, V., Nuno, E., Pyrkin, A., and Romero, J., Parameter estimation of nonlinearly parameterized regressions without overparameterization: application to adaptive control, Automatica, 2021, vol. 127, p. 109544.

    Article  MathSciNet  Google Scholar 

  14. Glushchenko, A., Petrov, V., and Lastochkin, K., Regression filtration with resetting to provide exponential convergence of MRAC for plants with jump change of unknown parameters, , 2021, pp. 1–12.

  15. Ioannou, P. and Sun, J., Robust Adaptive Control, New York: Dover, 2013.

    MATH  Google Scholar 

  16. Sastry, S. and Bodson, M., Adaptive Control—Stability, Convergence, and Robustness, Englewood Cliffs, N.J.: Prentice Hall, 1989.

    MATH  Google Scholar 

  17. Schatz, S.P., Yucelen, T., Gruenwal, B., and Holzapfel, F., Application of a novel scalability notion in adaptive control to various adaptive control frameworks, AIAA Guid. Navig. Control Conf. (2015), pp. 1–17.

  18. Aranovskiy, S., Belov, A., Ortega, R., Barabanov, N., and Bobtsov, A., Parameter identification of linear time-invariant systems using dynamic regressor extension and mixing, Int. J. Adapt. Control Signal Process., 2019, vol. 33, no. 6, pp. 1016–1030.

    Article  MathSciNet  Google Scholar 

  19. Yi, B. and Ortega, R., Conditions for convergence of dynamic regressor extension and mixing parameter estimator using LTI filters, , 2020, pp. 1–6.

  20. Aranovskiy, S., Ushirobira, R., Korotina, M., and Vedyakov, A., On preserving-excitation properties of a dynamic regressor extension scheme, INRIA Int. Rep., 2019„ pp. 1–6.

  21. Glushchenko, A.I., Petrov, V.A., and Lastochkin, K.A., I-DREM: relaxing the square integrability condition, Autom. Remote Control, 2021, vol. 82, pp. 1233–1247.

    Article  Google Scholar 

Download references

Funding

This work was financially supported in part by the Russian Foundation for Basic Research, project no. 18-47-310003 r_a.

Author information

Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997, Russia

    A. I. Glushchenko & K. A. Lastochkin

  2. Ugarov Staryi Oskol Technological University, Branch of National University of Science and Technology “MISiS”, Staryi Oskol, Belgorod oblast, 309516, Russia

    V. A. Petrov

Authors
  1. A. I. Glushchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. A. Lastochkin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. A. Petrov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to A. I. Glushchenko, K. A. Lastochkin or V. A. Petrov.

Additional information

Translated by V. Potapchouck

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Glushchenko, A.I., Lastochkin, K.A. & Petrov, V.A. Normalization of Regressor Excitation in the Dynamic Extension and Mixing Procedure. Autom Remote Control 83, 17–31 (2022). https://doi.org/10.1134/S0005117922010027

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117922010027

Keywords

Search

Navigation