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International Conference on Computational Intelligence

Fuzzy Days 1999: Computational Intelligence pp 382–390Cite as

Center Manifold Theory Approach to the Stability Analysis of Fuzzy Control Systems

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1625))

Abstract

The paper proposes a stability analysis method based on the application of the center manifold theory belonging to the state-space methods to the stability analysis of fuzzy control systems. The methods considers a linearized mathematical model of the second order nonlinear plant, and its only constraint is in the smooth character of the right-hand term of the state-space equations of the controlled plant. The method is exemplified by applying it to the stability analysis of a state feedback fuzzy control system meant for the position control of an electrohydraulic servosystem.

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References

  1. Bretthauer, G., Opitz, H.-P.: Stability of Fuzzy Systems-A Survey. Proceedings of Second EUFrT’94 European Congress, Aachen, Vol. 1 (1994) 283–290

    Google Scholar 

  2. Aracil, J., Ollero, A., Garcia-Cerezo, A.: Stability Indices for the Global Analysis of Expert Control Systems. IEEE Transactions on Systems, Man, and Cybernetics, Vol. 195 (1989) 998–1007

    Article  Google Scholar 

  3. Garcia-Cerezo, A., Ollero, A.: Stability of Fuzzy Control Systems by Using Nonlinear System Theory. Proceedings of IFAC/IFIP/IMACS Symposium on Artificial Intelligence in Real-Time Control, Delft (1992) 171–176

    Google Scholar 

  4. Driankov, D., Hellendoom, H., Reinfrank, M.: An Introduction to Fuzzy Control, Springer-Verlag, Berlin Heidelberg New York (1993)

    MATH  Google Scholar 

  5. Doboli, S., Precup, R.-E.: The Application of a Stability Analysis Method to Fuzzy Control Systems. Proceedings of Sixth IFSA’97 World Congress, Prague, Vol. 3 (1997) 452–457

    Google Scholar 

  6. Opitz, H.-P.: Fuzzy Control and Stability Criteria. Proceedings of First EUFIT’93 European Congress, Aachen, Vol. 1 (1993) 130–136

    Google Scholar 

  7. Böhm, R., Krebs, V.: Ein Ansatz zur Stabilitätsanalyse und Synthese von Fuzzy-Regelungen. Automatisierungstechnik, Vol. 418 (1993) 288–293

    MATH  Google Scholar 

  8. Bindel, T., Mikut, R.: Entwurf, Stabilitätsanalyse und Erprobung von Fuzzy-Reglern am Beispiel einer Durchflussregelung. Automatisierungstechnik, Vol. 435 (1995) 249–255

    Google Scholar 

  9. Böhm, R., Bosch, M.: Stabilitätsanalyse von Fuzzy-Mehrgrössenregelungen mit Hilfe der Hyperstabilitätstheorie. Automatisierungstechnik, Vol. 434 (1995) 181–186

    Google Scholar 

  10. Precup, R.-E., Preitl, S.: Popov-Type Stability Analysis Method for Fuzzy Control Systems. Proceedings of Fifth EUFIT’97 European Congress, Aachen, Vol. 2 (1997) 1306–1310

    Google Scholar 

  11. Kiendl, H., Rüger, J.: Verfahren zum Entwurf unt Stabilitätsnachweis von Fuzzy-Regelungssystemen. Workshop “Fuzzy Control” des GMA-UA 1.4.2, Dortmund, Forshungsberichte der Fakultät für ET 0392 (1992) 1–9

    Google Scholar 

  12. Kiendl, H., Rüger, J.: Verfahren zum Entwurf unt Stabilitätsnachweis von Regelungssys-temen mit Fuzzy-Reglern. Automatisierungstechnik, Vol. 415 (1993) 138–144

    Google Scholar 

  13. Scheel, T.: Verallgemeinerte Integrate Ljapunov Funktionen und ihre Anwendung zur Stabilitätsanalyse von Fuzzy-Systeme. Workshop “Fuzzy Control” des GMA-UA 1.4.2, Dortmund, Forshungsberichte der Fakultät für ET 0295 (1995) 99–113

    Google Scholar 

  14. Kiendl, H.: Stabilitätsanalyse von mehrschleifigen Fuzzy-Regelungssystemen mit Hilfe der Methode der Harmonischen Balance. Workshop “Fuzzy Control” des GMA-UA 1.4.2, Dortmund, Forshungsberichte der Fakultät für ET 0392 (1992) 315–321

    Google Scholar 

  15. Kiendl, H.: Harmonic Balance for Fuzzy Control Systems. Proceedings of First EUFIT’93 European Congress, Aachen, Vol. 1 (1993) 127–141

    Google Scholar 

  16. Boll, M, Bornemann, J., Dörrscheidt, F.: Anwendung der harmonischen Balance auf Regelkreise mit unsymmetrischen Fuzzy-Komponenten und konstante Eingangsgrössen. Workshop “Fuzzy Control” des GMA-UA 1.4.2, Dortmund, Forshungsberichte der Fakultät für ET 0194 (1994) 70–84

    Google Scholar 

  17. Nijmeijer, H., van der Schaft, A.: Nonlinear Dynamical Control Systems. Springer-Verlag, Berlin Heidelberg New York (1990)

    MATH  Google Scholar 

  18. Isidori, A.: Nonlinear Control Systems. Springer-Verlag, Berlin Heidelberg New York (1989)

    MATH  Google Scholar 

  19. Gartner, H., Astolfi, A.: Stability Study of a Fuzzy Controlled Mobile Robot. Technical Report, Automatic Control Laboratory, ETH Zürich (1995)

    Google Scholar 

  20. Galichet, S., Foulloy, L.: Fuzzy Controllers: Synthesis and Equivalences. IEEE Transactions on Fuzzy Systems, Vol. 32 (1995) 140–148

    Article  Google Scholar 

  21. Schröder, M., Klawonn, F., Kruse, R.: Sequential Optimization of Multidimensional Controllers Using Genetic Algorithms and Fuzzy Situations, In: Herrera, F., Verdegay, J.L. (eds.): Genetic Algorithms and Soft Computing, Springer-Verlag, Berlin Heidelberg New York (1996)

    Google Scholar 

  22. Precup, R.-E., Preitl, S.: Fuzzy Control of an Electrohydraulic Servosystem under Nonlinearity Constraints.. Proceedings of First EUFIT93 European Congress, Aachen, Vol. 3 (1993) 1524–1530

    Google Scholar 

  23. Lohmann, B.: Order Reduction and Determination of Dominant State Variables of Nonlinear Systems. Proceedings of First MATHMOD Conference, Vienna (1994)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Automation, “Politehnica” University of Timisoara, Bd. V. Parvan 2, RO-1900, Timisoara, Romania

    Radu-Emil Precup, Stefan Preitl & Stefan Solyom

Authors
  1. Radu-Emil Precup
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  2. Stefan Preitl
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  3. Stefan Solyom
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Editor information

Editors and Affiliations

  1. Computer Science I, University of Dortmund, D-44221, Dortmund, Germany

    Bernd Reusch

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© 1999 Springer-Verlag Berlin Heidelberg

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Precup, RE., Preitl, S., Solyom, S. (1999). Center Manifold Theory Approach to the Stability Analysis of Fuzzy Control Systems. In: Reusch, B. (eds) Computational Intelligence. Fuzzy Days 1999. Lecture Notes in Computer Science, vol 1625. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48774-3_44

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  • DOI: https://doi.org/10.1007/3-540-48774-3_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66050-7

  • Online ISBN: 978-3-540-48774-6

  • eBook Packages: Springer Book Archive

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