Method of Estimation of Parameters of Linear Regression Model with Linearly Dependent Elements
https://doi.org/10.17586/0021-3454-2024-67-8-670-677
Abstract
The problem of online estimation of parameters of linear regression models in the presence of linearly dependent elements in the regressor is considered. To solve the problem, a method is proposed that allows estimating the parameters corresponding to independent elements of the regressor. The method includes two stages. At the first stage, the original regression model with unknown vector parameters is transformed into a model with a new unknown vector method. Thus, the problem of measuring parameters leads to the problem of synthesizing an observer. At the second stage, an adaptive observer of the new vector of variables is synthesized, which allows simultaneously estimating the desired vector of parameters.
About the Authors
A. O. Ovcharov
ITMO University,
Russian Federation
Russian Federation
Alexey O. Ovcharov – Post-Graduate Student; Faculty of Control Systems and Robotics; Head of a Laboratory
St. Petersburg
A. A. Vedyakov
ITMO University
Russian Federation
Russian Federation
Alexey A. Vedyakov – PhD, Associate Professor; Faculty of Control Systems and Robotics; Associate Professor
St. Petersburg
References
1. Simpkins C. Robotics & Automation Magazine, IEEE, 2012, vol. 19, pp. 95–96, DOI: 10.1109/MRA.2012.2192817.
2. Ioannou P. and Sun J. Robust adaptive control, Courier Corporation, 2012, 821 p.
3. Aranovskiy S., Bobtsov A., Ortega R., and Pyrkin A. IEEE Transactions on Automatic Control, 2017, no. 7(62), pp. 3546–3550.
4. Aeyels D. and Sepulchre R. Kybernetika, 1994, no. 6(30), pp. 715–723.
5. Praly L. Convergence of the gradient algorithm for linear regression models in the continuous and discrete time cases, PSL Research University, Mines ParisTech, Research Report, Feb. 2017, https://hal.archives-ouvertes.fr/hal-01423048.
6. Barabanov N. and Ortega R. Systems and Control Letters, 2017, vol. 109, pp. 24–29, DOI: 10.1016/j.sysconle.2017.09.005.
7. Efimov D., Barabanov N., and Ortega R. 2018 IEEE Conference on Decision and Control (CDC), IEEE, 2018, pp. 7243–7248.
8. Efimov D., Barabanov N., and Ortega R. International Journal of Adaptive Control and Signal Processing, 2019, no. 12(33), pp. 1885–1900, DOI: https://doi.org/10.1002/acs.2997.
9. Vedyakov A.A., Vediakova A.O., Bobtsov A.A., and Pyrkin A.A. International Journal of Adaptive Control and Signal Processing, 2019, no. 12(33), pp. 1857–1867, DOI: 10.1002/acs.3034.
10. Chowdhary G. and Johnson E.N. AIAA Guidance, Navigation, and Control Conference, 2010, no. 4, pp. 3674–3679, DOI: 10.2514/6.2010-7540.
11. Chowdhary G., Yucelen T., Mühlegg M., and Johnson E.N. International Journal of Adaptive Control and Signal Processing, 2013, no. 4(27), pp. 280–301, DOI: 10.1002/acs.2297.
12. Chowdhary G., Mühlegg M., and Johnson E. International Journal of Control, 2014, no. 8(87), pp. 1583–1603, DOI: 10.1080/00207179.2014.880128.
13. Kamalapurkar R., Reish B., Chowdhary G., and Dixon W.E. IEEE Transactions on Automatic Control, 2017, no. 7(62), pp. 3594–3601, DOI: 10.1109/TAC.2017.2671343.
14. Pan Y., Pan L., and Yu H. Proc. 2015 Chinese Automation Congress, CAC 2015, 2016, pp. 232–236, DOI: 10.1109/CAC.2015.7382502.
15. Pan Y. and Yu H. IEEE Transactions on Automatic Control, 2016, no. 9(61) pp. 2603–2609, DOI: 10.1109/TAC.2015.2495232.
16. Pan Y., Sun T., Liu Y., and Yu H. Neural Networks, 2017, vol. 95, pp. 134–142, DOI: 10.1016/j.neunet.2017.08.005.
17. Basu Roy S., Bhasin S., Kar and I.N. IEEE Transactions on Automatic Control, 2018, no. 1(63), pp. 283–290, DOI: 10.1109/TAC.2017.2725955.
18. Basu Roy S., Bhasin S., and Kar I.N. Asian Journal of Control, 2020, no. 1(22), pp. 1–10, DOI: 10.1002/asjc.1877.
19. Gerasimov D., Ortega R., and Nikiforov V. IFAC-PapersOnLine, 2018, no. 15(51), pp. 886–890, DOI: 10.1016/j.ifacol.2018.09.108.
20. Ortega R., Aranovskiy S., Pyrkin A.A., Astolfi A., and Bobtsov A.A. http://arxiv.org/abs/1908.05125, Aug. 2019.
21. Wang J., Efimov D., and Bobtsov A.A. IEEE Transactions on Automatic Control, 2020, no. 4(65), pp. 1731–1738, DOI: 10.1109/TAC.2019.2932960.
22. Ovcharov A., Vedyakov A., Kazak S., and Pyrkin A. International Journal of Adaptive Control and Signal Processing, 2022, no. 6(36), pp. 1305–1325, DOI: https://doi.org/10.1002/acs.3382.
23. Basu Roy S. and Bhasin S. International Journal of Adaptive Control and Signal Processing, 2019, no. 12(33), pp. 1759–1774, DOI: https://doi.org/10.1002/acs.3046.
Review
For citations:
Ovcharov A.O., Vedyakov A.A. Method of Estimation of Parameters of Linear Regression Model with Linearly Dependent Elements. Journal of Instrument Engineering. 2024;67(8):670-677. (In Russ.) https://doi.org/10.17586/0021-3454-2024-67-8-670-677
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