ISSN 0021-3454 (print version)
ISSN 2500-0381 (online version)
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vol 67 / April, 2024
Article

DOI 10.17586/0021-3454-2023-66-4-266-275

UDC 681.51

ALGORITHM OF ADAPTIVE ESTIMATION OF PARAMETERS FOR A CLASS OF NONLINEAR NON-STATIONARY SYSTEMS

A. A. Pyrkin
ITMO University, Saint Petersburg, 197101, Russian Federation; Full Professor


A. A. Bobtsov
ITMO University, Saint Petersburg, 197101, Russian Federation; Head of the School of Computer Technologies and Control, Professor at the Faculty of Control Systems and Robotics, Head of the Adaptive and Nonlinear Control Systems Lab


H. T. Nguyen
ITMO University, Saint Petersburg, 197101, Russian Federation; postgraduate


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Abstract. The problem of identification of unknown parameters for a class of non-stationary nonlinear systems is considered. It is assumed that non-stationary parameters can be represented as outputs of linear generators with unknown state matrices and initial conditions. The system state variables are supposed to be available for measurement. At the first step of the developed algorithm, the problem of parametrization of the initial dynamic model is solved to obtain a linear static regression model. At the second step of the algorithm, the unknown constant parameters of the linear regression model are estimated. Then the synthesis of observers for non-stationary parameters is performed. Presented results of computer simulation demonstrate the proposed algorithm efficiency.
Keywords: non-stationary nonlinear systems, identification of parameters, regression model

References:
  1. Bobtsov A.A., Nagovitsina A.G. Automation and Remote Control, 2006, no. 12(67), pp. 2010–2020.
  2. Bobtsov A.A., Grigoriev V.V., Nagovitsina A.G. Mekhatronika, Avtomatizatsiya, Upravlenie, 2007, no. 1, pp. 8–14. (in Russ.)
  3. Dung Kh.B., Pyrkin A.A., Bobtsov А.А., Vedyakov А.А. Journal of Instrument Engineering, 2021, no. 6(64), pp. 459–468. (in Russ.)
  4. Le V.T., Korotina M.M., Bobtsov A.A., Aranovskiy S.V., Vo Q.D. Mekhatronika, Avtomatizatsiya, Upravlenie, 2019, no. 5(20), pp. 259–265. (in Russ.)
  5. Wang J., Le Vang T., Pyrkin A.A., Kolyubin S.A., Bobtsov A.A. Automation and Remote Control, 2018, no. 12, pp. 2159–2168.
  6. Dung Kh.B., Pyrkin A.A., Bobtsov А.А., Vedyakov А.А. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2021, no. 3(21), pp. 374–379. (in Russ.)
  7. Bobtsov A.A., Nikolaev N.A., Ortega Martinez R., Slita O.V., Kozachok O.A. Mekhatronika, Avtomatizatsiya, Upravlenie, 2022, no. 6(23), pp. 283–288. (in Russ.)
  8. Bobtsov A.A., Lyamin A.V., Sergeev K.A. Journal of Instrument Engineering, 2001, no. 4, pp. 3–7. (in Russ.)
  9. Quoc D.V., Bobtsov A.A. Automation and Remote Control, 2020, no. 12(81), pp. 2220–2229.
  10. Tsykunov A.M. Automation and Remote Control, 1996, no. 2, pp. 117–125. (in Russ.)
  11. Kleiman E.G., Mochalov I.A. Automation and Remote Control, 1994, no. 2(55), pp. 149–163.
  12. Ortega R., Bobtsov A., Nikolaev N., Schiffer J., Dochain D. Automatica, 2021, vol. 129, рр. 109635.
  13. Miroshnik I.V., Nikiforov V.O. Sintez lineynykh sistem avtomaticheskogo upravleniya (Synthesis of Linear Automatic Control Systems), St. Petersburg, 2000, 76 р. (in Russ.)
  14. Aranovskiy S., Bobsov A., Ortega R., Pyrkin A. IEEE Transactions on Automatic Control, 2017, no. 7(62), pp. 3546–3550.
  15. Pyrkin A., Bobtsov A., Ortega R., Isidori A. Automatica, 2023, vol. 147, рр. 110677.