Preview

Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series

Advanced search

About the exact determination of the solution to linear completely regular differential-algebraic systems with delay

https://doi.org/10.29235/1561-2430-2024-60-3-203-215

Abstract

We study the problem of exact reconstruction of the solution from measurements of the observed output for linear autonomous completely regular differential-algebraic systems with commensurate delays. The reconstruction process is implemented using a finite observer, which is the output of a linear autonomous retarded system type with commensurate concentrated and distributed delays and a predetermined finite spectrum. The criterion for the existence of such an observer is obtained.

About the Author

V. E. Khartovskii
Yanka Kupala State University of Grodno
Belarus

Vadim E. Khartovskii – Dr. Sc. (Physics and Mathematics), Associate Professor, Head of the Department of Logistics and Methods of Control

22, Ozheshko Str., 230023, Grodno



References

1. Luenberger D. G. An introduction to observers. IEEE Transactions on Automatic Control, 1971, vol. 16, no. 6, pp. 596– 602. https://doi.org/10.1109/tac.1971.1099826

2. Sename O. New trends in design of observers for time-delay systems. Kybernetika, 2001, vol. 37, no. 4, pp. 427–458.

3. Zheng G., Bejarano F. J. Observer design for linear singular time-delay systems. Automatica, 2017, vol. 80, no. 6, pp. 1–9. https://doi.org/10.1016/j.automatica.2017.01.025

4. Hu G. D. A Separation Property of the Observer-Based Stabilizing Controller for Linear Delay Systems. Siberian Mathematical Journal, 2021, vol. 62, no. 4, pp. 763–772. https://doi.org/10.1134/S0037446621040182

5. Hu G. D. An observer-based stabilizing controller for linear neutral delay systems. Siberian Mathematical Journal, 2022, vol. 63, no. 4, pp. 789–800. https://doi.org/10.1134/s003744662204019x

6. Il’In A. V., Budanova A. V., Fomichev V. V. Synthesis of observers for asymptotically observable time delay systems. Doklady Akademii nauk, 2013, vol. 87, no. 1, pp. 129–132 (in Russian). https://doi.org/10.7868/s0869565213040051

7. Brivadis L., Andrieu V., Serres U., Gauthier J.-P. Luenberger Observers for Infinite-Dimensional Systems, Back and Forth Nudging, and Application to a Crystallization Process. SIAM Journal on Control and Optimization, 2021, vol. 59, no. 2, pp. 857–886. https://doi.org/10.1137/20m1329020

8. Metel’skii A. V. Construction of Observers for a Delay Differential System with One-Dimensional Output. Differential Equations, 2019, vol. 55, no. 3, pp. 390–403. https://doi.org/10.1134/s0012266119030121

9. Khartovskii V. E. Synthesis of observers for linear systems of neutral type. Differential Equations, 2019, vol. 55, no. 3, pp. 404–417. https://doi.org/10.1134/s0012266119030133

10. Khartovskii V. E. Asymptotic estimates of solutions of linear time-invariant systems of the neutral type with commensurable delays. Differential Equations, 2019, vol. 55, no. 12, pp. 1649–1664. https://doi.org/10.1134/s0012266119120115

11. Metel’skii A. V., Khartovskii V. E. Finite observer design for linear systems of neutral type. Automation and Remote Control, 2019, vol. 80, no. 12, pp. 2152–2169. https://doi.org/10.1134/s0005117919120051

12. Metel’skii A. V., Khartovskii V. E. Exact reconstruction of the solution for linear neutral type systems. Differential Equations, 2021, vol. 57, no. 2, pp. 251–271. https://doi.org/10.1134/s0012266121020130

13. Khartovskii V. E. Control of Linear Systems of Neutral Type: Qualitative Analysis and Implementation of Feedback. Grodno, GrSU, 2022. 500 p. (in Russian).

14. Khartovskii V. E. Designing asymptotic observers for linear completely regular differential algebraic systems with delay. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 2023, vol. 61, pp. 114–136 (in Russian). https://doi.org/10.35634/2226-3594-2023-61-07

15. Khartovskii V. E. Estimation of the solution of asymptotically observable linear completely regular differentialalgebraic systems with delay. Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp’yuternye Nauki, 2023, vol. 33, no. 2, pp. 329–347 (in Russian). https://doi.org/10.35634/vm230210

16. Khartovskii V. E. On some problems of controllability and observability for differential-algebraic systems with aftereffect. Trudy Instituta matematiki = Proceedings of the Institute of Mathematics, 2021, vol. 29, no. 1–2, pp. 126–137 (in Russian).

17. Metel’skii A. V. Spectral reduction, complete damping, and stabilization of a delay system by a single controller. Differential Equations, 2013, vol. 49, no. 11, pp. 1405–1422. https://doi.org/10.1134/s0012266113110086

18. Watanabe K. Finite spectrum assignment and observer for multivariable systems with commensurate delays. IEEE Transactions on Automatic Control, 1986, vol. 31, no. 6, pp. 543–550. https://doi.org/10.1109/tac.1986.1104336


Review

Views: 144


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 1561-2430 (Print)
ISSN 2524-2415 (Online)