DOI 10.17586/0021-3454-2023-66-10-828-833
UDC 681.51
ADAPTIVE OBSERVERS FOR NONLINEAR SYSTEMS BASED ON DYNAMIC EXTENSION AND MIXING PROCEDURE
ITMO University, Faculty of Control Systems and Robotics;
A. A. Vedyakov
ITMO University, Saint Petersburg, 197101, Russian Federation; Associate Professor
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Reference for citation: Bespalov V. V., Vedyakov А. А. Adaptive observers for nonlinear systems based on dynamic extension and mixing procedure. Journal of Instrument Engineering. 2023. Vol. 66, N 10. P. 828—833 (in Russian). DOI: 10.17586/0021-3454-2023-66-10-828-833.
Abstract. The problem of synthesizing an adaptive observer of state variables of nonlinear dynamic systems is considered. Correct estimation of state vector components under parametric uncertainty is a rather complex process necessary e.g. for solving several problems of systems control and diagnostic. Synthesis of the proposed adaptive observer consists of two steps. In the first one, a parameterization of the nonlinear dynamical system, which can be transformed to a state affine form, is performed. In the second step, the unknown parameters are estimated based on the gradient descent method, and a gradient-based observer for the state variables is designed.
Abstract. The problem of synthesizing an adaptive observer of state variables of nonlinear dynamic systems is considered. Correct estimation of state vector components under parametric uncertainty is a rather complex process necessary e.g. for solving several problems of systems control and diagnostic. Synthesis of the proposed adaptive observer consists of two steps. In the first one, a parameterization of the nonlinear dynamical system, which can be transformed to a state affine form, is performed. In the second step, the unknown parameters are estimated based on the gradient descent method, and a gradient-based observer for the state variables is designed.
Keywords: adaptive observer, nonlinear system parameterization, affine state form, global convergence, parameter estimation
Acknowledgement: The work was carried out with the support of the Ministry of Science and Higher Education of the Russian Federation, state assignment passport 2019-0898.
References:
Acknowledgement: The work was carried out with the support of the Ministry of Science and Higher Education of the Russian Federation, state assignment passport 2019-0898.
References:
- Kazantzis N. and Kravaris C. Proceedings of the 36th IEEE Conference on Decision and Control, San Diego, CA, USA, 1997, vol. 5, pp. 4802–4807, DOI: 10.1109/CDC.1997.649779.
- Andrieu V. and Praly L. SIAM Journal on Control and Optimization, 2006, no. 45(2), pp. 432–456.
- Ortega R., Bobtsov A., Pyrkin A., Aranovskiy S. Systems & Control Letters, 2015, vol. 85, pp. 84–94, ISSN 0167-6911, https://doi.org/10.1016/j.sysconle.2015.09.008.
- Ortega R., Bobtsov A., Nikolaev N., Schiffer J. Automatica, 2021, vol. 129, рр. 109635, ISSN 0005-1098, https://doi.org/10.1016/j.automatica.2021.109635.
- Pyrkin A., Bobtsov A., Ortega R., Vedyakov A., Aranovskiy S. Systems & Control Letters, 2019, vol. 133, рр. 104519, ISSN 0167-6911, https://doi.org/10.1016/j.sysconle.2019.104519.
- Sastry S., Bodson M. Adaptive Control: Stability, Convergence and Robustness, Englewood Cliffs, NJ, Prentice Hall, 1989.
- Kreisselmeier G., Rietze-Augst G. IEEE Trans. Automat. Control, 1990, no. 35(2), pp. 165–171.
- Afanasyev V.N., Kolmanovsky V.B., Nosov V.R. Matematicheskaya teoriya konstruirovaniya sistem upravleniya (Mathematical Theory of Design of Control Systems), Moscow, 2003, ISBN: 5-06-004162-X. (in Russ.)
