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Interval Observers for Continuous-Time Systems with Parametric Uncertainties

  • LINEAR SYSTEMS
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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.

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REFERENCES

  1. Efimov, D., Raissi, T., Perruquetti, W., and Zolghadri, A., Estimation and Control of Discrete-Time LPV Systems Using Interval Observers, Proc. 52nd IEEE Conf. on Decision and Control, Florence, 2013, pp. 5036–5041.

  2. Chebotarev, S., Efimov, D., Raissi, T., and Zolghadri, A., Interval Observers for Continuous-Time LPV Systems with L1/L2 Performance, Automatica, 2015, vol. 51, pp. 82–89.

    Article  Google Scholar 

  3. Efimov, D., Polyakov, A., and Richard, J., Interval Observer Design for Estimation and Control of Time-Delay Descriptor Systems, Eur. J. Control, 2015, vol. 23, pp. 26–35.

    Article  MathSciNet  Google Scholar 

  4. Kolesov, N., Gruzlikov, A., and Lukoyanov, E., Using Fuzzy Interacting Observers for Fault Diagnosis in Systems with Parametric Uncertainty, Proc. 12th Inter. Symp. Intelligent Systems (INTELS’16), October 5–7, 2016, Moscow, pp. 499–504.

  5. Kremlev, A.S. and Chebotarev, S.G., Synthesis of Interval Observer for Linear System with Variable Parameters, Journal of Instrument Engineering, 2013, vol. 56, no. 4, pp. 42–46.

    Google Scholar 

  6. Mazenc, F. and Bernard, O., Asymptotically Stable Interval Observers for Planar Systems with Complex Poles, IEEE Trans. Automatic Control, 2010, vol. 55, no. 2, pp. 523–527.

    Article  MathSciNet  Google Scholar 

  7. Blesa, J., Puig, V., and Bolea, Y., Fault Detection Using Interval LPV Models in an Open-Flow Canal, Control Engineering Practice, 2010, vol. 18, pp. 460–470.

    Article  Google Scholar 

  8. Zheng, G., Efimov, D., and Perruquetti, W., Interval State Estimation for Uncertain Nonlinear Systems, Proc. IF AC NOLCOS 2013, Toulouse, 2013.

  9. Zhang, K., Jiang, B., Yan, X., and 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. Efimov, D. and Raissi, T., Design of Interval State Observers for Uncertain Dynamical Systems, Autom. Remote Control, 2016, vol. 77, no. 2, pp. 191–225.

    Article  MathSciNet  Google Scholar 

  11. Khan, A., **e, W., Zhang, L., and Liu, L., Design and Applications of Interval Observers for Uncertain Dynamical Systems, IET Circuits Devices Syst., 2020, vol. 14, pp. 721–740.

    Article  Google Scholar 

  12. Zhirabok, A., Self-correction of Errors in Discrete Dynamic Systems, Autom. Remote Control, 2006, vol. 67, no. 6, pp. 868–879.

    Article  MathSciNet  Google Scholar 

  13. Zhirabok, A.N., Zuev, V.V., and Ir, K.C., Method to Design Interval Observers for Linear Time-Invariant Systems, J. Comput. Syst. Sci. Int., 2022, vol. 61, no. 4, pp. 485–495.

    Article  MathSciNet  Google Scholar 

  14. Zhirabok, A., Zuev, A., Filaretov, V., Shumsky, A., and Kim Chkhun Ir, Jordan Canonical Form in Diagnosis and Estimation Problems, Autom. Remote Control, 2022, vol. 83, no. 9, pp. 1355–1370.

    Article  MathSciNet  Google Scholar 

  15. Zhirabok, A., Shumsky, A., and Pavlov, S., Diagnosis of Linear Dynamic Systems by the Nonparametric Method, Autom. Remote Control, 2017, vol. 78, no. 7, pp. 1173–1188.

    Article  MathSciNet  Google Scholar 

  16. Low, X., Willsky, A., and Verghese, G., Optimally Robust Redundancy Relations for Failure Detection in Uncertain Systems, Automatica, 1996, vol. 22, pp. 333–344.

    Google Scholar 

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Funding

This work was supported by the Russian Science Foundation, project no. 23-29-00191, https://rscf.ru/project/23-29-00191/.

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Authors and Affiliations

  1. Far Eastern Federal University, Vladivostok, Russia

    A. N. Zhirabok, A. V. Zuev, A. E. Shumsky & Kim Chkhun Ir

  2. Institute of Marine Technology Problems, Far Eastern Branch, Russian Academy of Sciences, Vladivostok, Russia

    A. N. Zhirabok & A. V. Zuev

  3. Institute of Automation and Control Processes, Far Eastern Branch, Russian Academy of Sciences, Vladivostok, Russia

    V. F. Filaretov

Authors
  1. A. N. Zhirabok
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  2. A. V. Zuev
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  3. V. F. Filaretov
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  4. A. E. Shumsky
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  5. Kim Chkhun Ir
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Corresponding authors

Correspondence to A. N. Zhirabok, A. V. Zuev, V. F. Filaretov, A. E. Shumsky or Kim Chkhun Ir.

Additional information

This paper was recommended for publication by N.N. Bakhtadze, a member of the Editorial Board

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Zhirabok, A.N., Zuev, A.V., Filaretov, V.F. et al. Interval Observers for Continuous-Time Systems with Parametric Uncertainties. Autom Remote Control 84, 1137–1147 (2023). https://doi.org/10.1134/S0005117923110085

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  • DOI: https://doi.org/10.1134/S0005117923110085

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