Interval Observers for Continuous-Time Systems with Parametric Uncertainties

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription or Fee Access

Abstract

In this paper, interval observers are designed for linear dynamic systems described by continuous-time models with exogenous disturbances, measurement noises, and parametric uncertainties.
Jordan canonical form-based relations are presented for an interval observer that estimates the set of admissible values of a given linear function of the system state vector. The theoretical results are
illustrated by a practical example.

About the authors

A. N. Zhirabok

Institute of Marine Technology Problems, Far Eastern Branch, Russian Academy of Sciences; Institute of Automation and Control Processes, Far Eastern Branch, Russian Academy of Sciences

Email: zhirabok@mail.ru
Vladivostok, Russia; Vladivostok, Russia

A. V. Zuev

Institute of Marine Technology Problems, Far Eastern Branch, Russian Academy of Sciences; Institute of Automation and Control Processes, Far Eastern Branch, Russian Academy of Sciences

Email: alvzuev@yandex.ru
Vladivostok, Russia; Vladivostok, Russia

V. F. Filaretov

Institute of Automation and Control Processes, Far Eastern Branch, Russian Academy of Sciences

Email: filaretov@inbox.ru
Vladivostok, Russia

A. E. Shumskiy

Institute of Marine Technology Problems, Far Eastern Branch, Russian Academy of Sciences

Email: a.e.shumsky@yandex.con
Vladivostok, Russia

- Kim chkhun ir

Institute of Marine Technology Problems, Far Eastern Branch, Russian Academy of Sciences

Author for correspondence.
Email: kim.ci@dvfu.ru
Vladivostok, Russia

References

  1. Efimov D., Raissi T., Perruquetti W., Zolghadri A. Estimation and control of discrete-time LPV systems using interval observers // 52nd IEEE Conf. on Decision and Control. Florence, Italy. 2013. P. 5036-5041.
  2. Chebotarev S., Efimov D., Raissi T., Zolghadri A.Interval observers for continuous-time LPV systems with L1/L2 performance // Automatica. 2015. V. 51. P. 82-89.
  3. Efimov D., Polyakov A., Richard J. Interval observer design for estimation and control of time-delay descriptor systems // Eur. J. Control. 2015. V. 23. P. 26-35.
  4. Kolesov N., Gruzlikov A., Lukoyanov E. Using fuzzy interacting observers for fault diagnosis in systems with parametric uncertainty // Proc. XII-th Inter. Symp. Intelligent Systems, INTELS'16, 5-7 October 2016, Moscow, Russia. P. 499-504.
  5. Кремлев А.С., Чеботарев С.Г. Синтез интервального наблюдателя для линейной системы с переменными параметрами // Изв. вузов. Приборостроение. 2013. Т. 56. №. 4. C. 42-46.
  6. Mazenc F., Bernard O. Asymptotically stable interval observers for planar systems with complex poles // IEEE Trans. Automatic Control. 2010. V. 55. № 2. P. 523-527.
  7. Blesa J., Puig V., Bolea Y. Fault detection using interval LPV models in an open-flow canal // Control Engineering Practice. 2010. V. 18. P. 460-470.
  8. Zheng G., Efimov D., Perruquetti W. Interval state estimation for uncertain nonlinear systems // IFAC Nolcos 2013. Toulouse, France, 2013.
  9. Zhang K., Jiang B., Yan X., Edwards C. Interval sliding mode based fault accommodation for non-minimal phase LPV systems with online control application // Int. J. Control. 2019. https://doi.org/10.1080/00207179.2019.1687932
  10. Ефимов Д.В., Раисси Т. Построение интервальных наблюдателей для динамических систем с неопределенностями // АиТ. 2016. № 2. С. 5-49.
  11. Khan A., Xie W., Zhang L., Liu L. Design and applications of interval observers for uncertain dynamical systems // IET Circuits Devices Syst. 2020. V. 14. P. 721-740.
  12. Жирабок А.Н. Самокоррекция ошибок в дискретных динамических системах // АиТ. 2006. № 6. С. 41-53.
  13. Жирабок А.Н., Зуев А.В., Ким Чхун Ир. Метод построения интервальных наблюдателей для стационарных линейных систем // Известия РАН. Теория и системы управления. 2022. № 4. С. 22-32.
  14. Жирабок А.Н., Зуев А.В., Филаретов В.Ф., Шумский А.Е., Ким Чхун Ир. Каноническая форма Жордана в задачах диагностирования и оценивания // АиТ. 2022. № 9. С. 49-67.
  15. Жирабок А.Н., Шумский А.Е., Павлов С.В. Диагностирование линейных динамических систем непараметрическим методом // АиТ. 2017. № 7. С. 3-21.
  16. Low X., Willsky A., Verghese G. Optimally robust redundancy relations for failure detection in uncertain systems // Automatica. 1996. V. 22. P. 333-344.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2023 The Russian Academy of Sciences