Algorithms of direct output-feedback adaptive control of a linear system with finite time tuning
https://doi.org/10.17586/2226-1494-2025-25-1-33-41
Abstract
A problem of direct model reference adaptive control of parametrically uncertain systems with inaccessible for measurement state is considered in this paper. With the purpose of adaptive tuning of the controller parameters, a modification of the gradient adaptation algorithm with finite time convergence is proposed. The modification is implemented by periodic recalculation of the adjustable parameters and further their replacement in the integrators of the gradient adaptation algorithm. Preliminary calculation is accomplished under condition of interval excitation based on prediction of the adaptation algorithm dynamics; hence the controller parameters are identified precisely. The control problem is solved with the use of augmented error approach and certainty equivalence principle. Analysis of the closed-loop system is made using the Lyapunov functions method. The modification ensures parametric convergence under interval excitation condition which is weaker than the persistent excitation one, sensitive to variations of the unknown parameters, and, in comparison with the variety of analogous solutions, does not require the dynamic order increasing. The other distinguishing feature of the algorithm is opportunity of its use in schemes of both indirect and direct adaptation.
About the Authors
D. N. Gerasimov
ITMO University
Russian Federation
Russian Federation
Dmitry N. Gerasimov — PhD, Associate Professor, Associate Professor, Senior Researcher
Saint Petersburg, 197101
D. L. Podoshkin
ITMO University
Russian Federation
Russian Federation
Dmitry L. Podoshkin — PhD Student
Saint Petersburg, 197101
V. O. Nikiforov
ITMO University
Russian Federation
Russian Federation
Vladimir O. Nikiforov — D.Sc., Professor, Vice-Rector for Scientific Affairs
Saint Petersburg, 197101
References
1. Ioannou P.A., Sun J. Robust Adaptive Control. NJ: Prentice-Hall, 1996. 825 p.
2. Narendra K.S., Annaswamy A.M. Stable Adaptive Systems. NJ: Prentice Hall, 1989. 494 p.
3. Lion P. M. Rapid identification of linear and nonlinear systems // AIAA Journal. 1967. V. 5. N 10. P. 1835–1842. https://doi.org/10.2514/3.4313
4. Kreisselmeier G. Adaptive observers with exponential rate of convergence // IEEE Transactions on Automatic Control. 1977. V. 22. N 1. P. 2–8. https://doi.org/10.1109/TAC.1977.1101401
5. Andrievsky B.R., Fradkov A.L., Stotsky A.A. Shunt Compensation for Indirect Sliding-Mode Adaptive Control // IFAC Proceedings Volumes. 1996. V. 29. N 1. P. 5132–5137. https://doi.org/10.1016/S1474-6670(17)58495-5
6. Fradkov A., Andrievsky B., Combined adaptive controller for UAV guidance // European Journal of Control. 2005. V. 11. N 1. P. 71–79. https://doi.org/10.3166/ejc.11.71-79
7. de Mathelin M., Lozano R. Robust adaptive identification of slowly time-varying parameters with bounded disturbances // Automatica. 1999. V. 35. N 7. P. 1291–1305. https://doi.org/10.1016/S0005-1098(99)00026-6
8. Narendra K.S., Han Z. A new approach to adaptive control using multiple models // International Journal of Adaptive Control and Signal Processing. 2012. V. 26. N 8. P. 778–799. https://doi.org/10.1002/acs.2269
9. Gerasimov D.N., Koshelev K.P., Belyaev M.E., Nikiforov V.O. Algorithm of adaptive output control of linear system with improved parametric convergence. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2018, vol. 18, no. 5, pp. 771–779 (in Russian). https://doi.org/10.17586/2226-1494-2018-18-5-771-779
10. Aranovskiy S., Bobtsov A., Ortega R., Pyrkin A. Performance enhancement of parameter estimators via dynamic regressor extension and mixing // IEEE Transactions on Automatic Control. 2017. V. 62. N 7. P. 3546–3550. https://doi.org/10.1109/TAC.2016.2614889
11. Krause J., Khargonekar P. Parameter information content of measurable signals in direct adaptive control // IEEE Transactions on Automatic Control. 1987. V. 32. N 9. P. 802–810. https://doi.org/10.1109/TAC.1987.1104722
12. Ortega R. An on-line least-squares parameter estimator with finite convergence time // Proceedings of the IEEE. 1988. V. 76. N 7. P. 847–848. https://doi.org/10.1109/5.7153
13. Adetola V., Guay M. Finite-time parameter estimation in adaptive control of nonlinear systems // IEEE Transactions on Automatic Control. 2008. V. 53. N 3. P. 807–811. https://doi.org/10.1109/TAC.2008.919568
14. Rios H., Efimov D., Moreno J. A., Perruquetti W., Rueda-Escobedo J. G. Time-Varying Parameter Identification Algorithms: Finite and Fixed-Time Convergence // IEEE Transactions on Automatic Control. 2017. V. 62. N 7. P. 3671–3678. https://doi.org/10.1109/TAC.2017.2673413
15. Wang J., Efimov D., Aranovskiy S., Bobtsov A. Fixed-time estimation of parameters for non-persistent excitation // European Journal of Control. 2020. V. 55. P. 24–32. https://doi.org/10.1016/j.ejcon.2019.07.005
16. Holloway J., Krstic M. Prescribed-time output feedback for linear systems in controllable canonical form // Automatica. 2019. V. 107. P. 77–85. https://doi.org/10.1016/j.automatica.2019.05.027
17. Ortega R., Gerasimov D.N., Barabanov N.E., Nikiforov V.O. Adaptive control of linear multivariable systems using dynamic regressor extension and mixing estimators: removing the high-frequency gain assumptions // Automatica. 2019. V. 110. P. 108589. https://doi.org/10.1016/j.automatica.2019.108589
18. Gerasimov D.N., Ortega R., Nikiforov V.O. Adaptive control of multivariable systems with reduced knowledge of high frequency gain: application of dynamic regressor extension and mixing estimators // IFAC-PapersOnLine. 2018. V. 51. N 15. P. 886–890. https://doi.org/10.1016/j.ifacol.2018.09.108
19. Fomin V.N., Fradkov A.L., Iakubovich V.A. Adaptive control of dynamic objects. Moscow, Nauka Publ., 1981, 447 p.
20. Monopoli R. V. Model reference adaptive control with an augmented error signal // IEEE Transactions on Automatic Control. 1974. V. 19. N 5. P. 474–484. https://doi.org/10.1109/TAC.1974.1100670
21. Nikiforov V.O., Gerasimov D.N. Adaptive Regulation: Reference Tracking and Disturbance Rejection. Springer-Verlag, 2022. 358 p. https://doi.org/10.1007/978-3-030-96091-9
22. Ortega R., Nikiforov V., Gerasimov D. On modified parameter estimators for identification and adaptive control. A unified framework and some new schemes // Annual Reviews in Control. 2 0 2 0 . V. 50. P. 278–293. https://doi.org/10.1016/j.arcontrol.2020.06.002
Review
For citations:
Gerasimov D.N., Podoshkin D.L., Nikiforov V.O. Algorithms of direct output-feedback adaptive control of a linear system with finite time tuning. Scientific and Technical Journal of Information Technologies, Mechanics and Optics. 2025;25(1):33-41. (In Russ.) https://doi.org/10.17586/2226-1494-2025-25-1-33-41
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