Adaptive observer for state variables of a time-varying nonlinear system with unknown constant parameters and delayed measurements
https://doi.org/10.17586/2226-1494-2023-23-4-850-853
Abstract
Unknown constant parameters estimation problem for a nonlinear time-varying system with delayed measurements is considered. The objective of this work is to design an adaptive observer for a nonlinear time-varying system. The observer must provide asymptotic convergence of the unknown constant parameters estimates to their true values. The main idea behind the method is to perform the parametrization of initial dynamical system based on GPEBO (Generalized Parameter Estimation Based Observer) technology and to build a linear regression model. The identifcation of linear regression model unknown parameters is performed using least square method with forgetting factor. This work develops the previously published approach for the case of nonlinear time-varying systems with delayed measurements. New parameters estimation algorithm can be applied for technical tasks, such as technical condition control and automatic control systems design.
Supporting agencies: This work was supported by Russian Science Foundation, project no. 22-21-00499, https://rscf.ru/project/22-21-00499.
About the Authors
A. A. Bobtsov
ITMO University
Russian Federation
Russian Federation
Alexey A. Bobtsov — D.Sc., Professor, Director of School of Computer Technologies and Control
sc 8046819200
Saint Petersburg, 197101
N. A. Nikolaev
ITMO University
Russian Federation
Russian Federation
Nikolay A. Nikolaev — PhD, Associate Professor, Associate Professor
sc 13105019100
Saint Petersburg, 197101
O. A. Kozachek
ITMO University
Russian Federation
Russian Federation
Olga A. Kozachek — Engineer
sc 57219308287
Saint Petersburg, 197101
O. V. Oskina
ITMO University
Russian Federation
Russian Federation
Olga V. Oskina — Student, Engineer
sc 57353555800
Saint Petersburg, 197101
References
1. Kozachek O., Bobtsov A., Nikolaev N. Adaptive observer of state variables of a nonlinear time varying system with unknown constant parameters. arXiv, 2023, arXiv:2305.15504. (in Russian). https://doi.org/10.48550/arXiv.2305.15504
2. Ortega R., Bobtsov A., Nikolaev N., Schiffer J., Dochain D. Generalized parameter estimation-based observers: Application to power systems and chemical–biological reactors // Automatica. 2021. V. 129. P. 109635. https://doi.org/10.1016/j.automatica.2021.109635
3. Tranninger M., Seeber R., Zhuk S., Steinberger M., Horn M. Detectability analysis and observer design for linear time varying systems // IEEE Control Systems Letters. 2020. V. 4. N 2. P. 331–336. https://doi.org/10.1109/lcsys.2019.2927549
4. Tranninger M., Zhuk S., Steinberger M., Fridman L., Horn M. Non-uniform stability, detectability, and, sliding mode observer design for time varying systems with unknown inputs // arXiv. 2018. arXiv:1809.06460. https://doi.org/10.48550/arXiv.1809.06460
5. Bobtsov A., Nikolaev N., Slita O., Kozachek O., Oskina O. Adaptive observer for a LTV system with partially unknown state matrix and delayed measurements // Proc. of the 14th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT). 2022. P. 165–170. https://doi.org/10.1109/ICUMT57764.2022.9943429
6. Rugh W.J. Linear System Theory. Prentice-Hall, Inc., 1996. 581 p.
7. Ljung L. System identifcation // Signal Analysis and Prediction. Birkhäuser, Boston, MA, 1998. P. 163–173. https://doi.org/10.1007/978-1-4612-1768-8_11
8. Sastry S., Bodson M. Adaptive Control: Stability, Convergence and Robustness. New Jersey: Prentice-Hall, 1989. 377 p.
Review
For citations:
Bobtsov A.A., Nikolaev N.A., Kozachek O.A., Oskina O.V. Adaptive observer for state variables of a time-varying nonlinear system with unknown constant parameters and delayed measurements. Scientific and Technical Journal of Information Technologies, Mechanics and Optics. 2023;23(4):850-853. (In Russ.) https://doi.org/10.17586/2226-1494-2023-23-4-850-853
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