Skip to main content
SpringerLink
Log in

Disturbance Decoupling in Finite Automata

  • Conference paper
  • First Online:
Language and Automata Theory and Applications (LATA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10792))

  • 460 Accesses

Abstract

The paper addresses the disturbance decoupling problem by dynamic measurement feedback for finite automata. The mathematical technique called the pair algebra of partitions is used. The paper gives sufficient solvability conditions and a procedure to construct the required feedback.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    For the specific case \(\pi _\lambda =\mathbf 1 \), Theorem 5 has been proved in [9], in this case the appropriate partition and the corresponding function are \(\delta \)-invariant.

References

  1. Lhommeau, M., Hardouin, L., Cottenceau, B.: Disturbance decoupling of timed event graphs by output feedback controller. In: Proceedings of the 6th Workshop on DES, Zaragoza, Spain, vol. 6, pp. 203–208 (2002)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  3. Kotta, U., Mullari, T.: Discussion on: unified approach to the problem of full decoupling via output feedback. Eur. J. Control 16, 326–328 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cheng, D.: Disturbance decoupling of Boolean control networks. IEEE Trans. Autom. Control 56, 2–10 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Yang, M., Li, R., Chu, T.: Controller design for disturbance decoupling of Boolean control networks. Automatica 49, 273–277 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. Katz, R.: Max-plus (a,b)-invariant spaces and control of timed discrete-event systems. IEEE TAC 52(2), 229–241 (2007)

    MathSciNet  MATH  Google Scholar 

  7. Kaldmäe, A., Kotta, U., Shumsky, A., Zhirabok, A.: Measurement feedback disturbance decoupling in discrete-time nonlinear systems. Automatica 49, 2887–2891 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kaldmäe, A., Kotta, U., Shumsky, A., Zhirabok, A.: Measurement feedback disturbance decoupling in discrete-event systems. Int. J. Robust Nonlinear Control 25, 3330–3348 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hartmanis, J., Stearns, R.: The Algebraic Structure Theory of Sequential Machines. Prentice-Hall, Upper Saddle River (1966)

    MATH  Google Scholar 

  10. Berdjag, D., Cocquempot, V., Christophe, C., Shumsky, A., Zhirabok, A.: Algebraic approach for model decomposition: application to fault detection and isolation in discrete-event systems. Int. J. Appl. Math. Comput. Sci. 21, 109–125 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  11. Danilov, V., Kolesov, N., Podkopaev, B.: Algebraic model of hardware monitoring of automata. Autom. Remote Control 36, 118–125 (1975)

    MathSciNet  MATH  Google Scholar 

  12. Kaldmäe, A., Kotta, U., Shumsky, A., Zhirabok, A.: Faulty plant reconfiguration based on disturbance decoupling methods. Asian J. Control 8, 858–867 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  13. Zhirabok, A., Shumsky, A.: Method of fault accommodation in finite automata. Autom. Remote Control 71, 122–132 (2010)

    MathSciNet  Google Scholar 

  14. Nijmeijer, H., van der Schaft, A.: Nonlinear Dynamical Control Systems. Springer, Heidelberg (1990). https://doi.org/10.1007/978-1-4757-2101-0

    Book  MATH  Google Scholar 

  15. Isidori, A.: Nonlinear Control Systems. Springer, Heidelberg (1995). https://doi.org/10.1007/978-1-84628-615-5

    Book  MATH  Google Scholar 

Download references

Acknowledgments

This work was supported by the Russian Scientific Foundation (project 16-19-00046).

Author information

Authors and Affiliations

  1. Far Easter Federal University, Vladivostok, 690950, Russia

    Alexey Zhirabok & Alexey Shumsky

  2. Institute of Applied Mathematics, Far Eastern Branch of Russian Academy of Sciences, Vladivostok, 690041, Russia

    Alexey Shumsky

  3. Institute of Marine Technology Problem, Far Eastern Branch of Russian Academy of Sciences, Vladivostok, 690950, Russia

    Alexey Zhirabok

Authors
  1. Alexey Zhirabok
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexey Shumsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexey Zhirabok .

Editor information

Editors and Affiliations

  1. Bar-Ilan University, Ramat Gan, Israel

    Shmuel Tomi Klein

  2. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  3. Ariel University, Ariel, Israel

    Dana Shapira

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Zhirabok, A., Shumsky, A. (2018). Disturbance Decoupling in Finite Automata. In: Klein, S., Martín-Vide, C., Shapira, D. (eds) Language and Automata Theory and Applications. LATA 2018. Lecture Notes in Computer Science(), vol 10792. Springer, Cham. https://doi.org/10.1007/978-3-319-77313-1_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-77313-1_9

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-77312-4

  • Online ISBN: 978-3-319-77313-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation