Skip to main content
Log in

Redundancy Relations for the Diagnosis of Hybrid Systems

  • Systems Analysis and Operations Research
  • Published:
Journal of Computer and Systems Sciences International Aims and scope

Abstract

In the concept of analytical redundancy, the problem of the functional diagnosis of hybrid systems is studied. The solution of this problem assumes checking the redundancy relations between the inputs and outputs of the system. A method for constructing the redundancy relations that includes transformation of the operational and controlling subsystems and then reduction of the operational subsystem to a form without feedbacks is proposed. The problem is solved using the pair algebra of partitions, algebra of functions, and differential-algebraic methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E. Y. Chow and A. S. Willsky, “Analytical redundancy and the design of robust failure detection systems,” IEEE Trans. Automat. Contr. 29, 603–614 (1984).

    Article  MathSciNet  MATH  Google Scholar 

  2. L. A. Mironovskii, “Functional diagnosis of dynamic systems,” Avtom. Telemekh., No. 8, 120–128 (1980).

    MathSciNet  Google Scholar 

  3. M. Blanke, M. Kinnaert, J. Lunze, and M. Staroswiecki, Diagnosis and Fault Tolerant Control (Springer, Berlin, 2003).

    Book  MATH  Google Scholar 

  4. J. Chen and R. Patton, Robust Model–Based Fault Diagnosis for Dynamic Systems (Kluwer, Boston, 1999).

    Book  MATH  Google Scholar 

  5. J. Gertler, Fault Detection and Diagnosis in Engineering Systems (Marcel Dekker, New York, 1998).

    Google Scholar 

  6. A. Shumsky, “Robust analytical redundancy relations for fault diagnosis in nonlinear systems,” Asian J. Control. 4, 159–170 (2002).

    Article  Google Scholar 

  7. V. Filaretov, M. Vukobratovic, and A. Zhirabok, “Parity relation approach to fault diagnosis in manipulation robots,” Mechatronics 13, 141–152 (2003).

    Article  Google Scholar 

  8. A. Medvedev, “Parity space method: a continuous time approach,” in Proceedings of the American Control Conference ACC, Baltimore, 1994, pp. 662–665.

    Google Scholar 

  9. G. Comtet–Varga, C. Christophe, V. Cocquempot, and M. Staroswiecki, “FDI for the induction motor using elimination theory,” in Proceedings of the European Control Conference, Germany, Karlsrue, 1999, CD ROM.

    Google Scholar 

  10. A. Shumsky, “Redundancy relations for fault diagnosis in nonlinear uncertain systems,” Int. J. Appl. Math. Comput. Sci. 17, 477–489 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  11. A. E. Shumskii, “Functional diagnosis of the nonlinear dynamic delay systems,” Autom. Remote Control 70, 502 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  12. A. N. Zhirabok and A. E. Shumskii, Algebraic Analysis Methods for Nonlinear Dynamical Systems (Dal’nauka, Vladivostok, 2008) [in Russian].

    Google Scholar 

  13. A. Shumsky and A. Zhirabok, “Unified approach to the problem of full decoupling via output feedback,” Eur J. Control. 16, 313–325 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  14. http://webmathematica.cc.ioc.ee/webmathematica/NLControl/main/index.html.

  15. J. Hartmanis and R. Stearns, The Algebraic Structure Theory of Sequential Machines (Prentice–Hall, New York, 1966).

    MATH  Google Scholar 

  16. A. Isidori, Nonlinear Control Systems, 3d ed. (Springer, Berlin, 1995).

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. N. Zhirabok.

Additional information

Original Russian Text © A.N. Zhirabok, A.E. Shumsky, 2018, published in Izvestiya Akademii Nauk, Teoriya i Sistemy Upravleniya, 2018, No. 4.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhirabok, A.N., Shumsky, A.E. Redundancy Relations for the Diagnosis of Hybrid Systems. J. Comput. Syst. Sci. Int. 57, 594–607 (2018). https://doi.org/10.1134/S1064230718040159

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064230718040159

Navigation