Skip to main content

Robust Evolving Granular Feedback Linearization

  • Conference paper
  • First Online:

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1000))

Abstract

This paper develops an adaptive feedback linearization approach to control nonlinear systems under model mismatch conditions. The approach uses the participatory learning modeling algorithm to estimate the nonlinearities from data streams online, and the certainty equivalence principle to compute the control signal. Simulation experiments with the classic surge tank level control benchmark show that evolving robust granular feedback linearization outperforms exact feedback linearization.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
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

Learn about institutional subscriptions

References

  1. Angelov, P.: Autonomous Learning Systems: From Data Streams to Knowledge in Real-time, 1st edn. Wiley, Hoboken (2013)

    Google Scholar 

  2. Banerjee, S., Chakrabarty, A., Maity, S., Chatterjee, A.: Feedback linearizing indirect adaptive fuzzy control with foraging based online plant model estimation. Appl. Soft Comput. 11(4), 3441–3450 (2011)

    Article  Google Scholar 

  3. Van de Water, H., Willems, J.: The certainty equivalence property in stochastic control theory. IEEE Trans. Autom. Control 26(5), 1080–1087 (1981)

    Article  MathSciNet  Google Scholar 

  4. DeJesus, E.X., Kaufman, C.: Routh-Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations. Phys. Rev. A 35, 5288–5290 (1987)

    Article  MathSciNet  Google Scholar 

  5. Dinh, T.Q., Marco, J., Yoon, J.I., Ahn, K.K.: Robust predictive tracking control for a class of nonlinear systems. Mechatronics 52, 135–149 (2018)

    Article  Google Scholar 

  6. Dorf, R.C., Bishop, R.H.: Modern Control Systems, 9th edn. Prentice-Hall Inc., Upper Saddle River (2000)

    MATH  Google Scholar 

  7. Esfandiari, F., Khalil, H.K.: Output feedback stabilization of fully linearizable systems. Int. J. Control 56(5), 1007–1037 (1992)

    Article  MathSciNet  Google Scholar 

  8. Freidovich, L.B., Khalil, H.K.: Performance recovery of feedback-linearization-based designs. IEEE Trans. Autom. Control 53(10), 2324–2334 (2008)

    Article  MathSciNet  Google Scholar 

  9. Ho, M.T., Datta, A., Bhattacharyya, S.P.: An elementary derivation of the Routh-Hurwitz criterion. IEEE Trans. Autom. Control 43(3), 405–409 (1998)

    Article  MathSciNet  Google Scholar 

  10. Isidori, A.: Nonlinear Control Systems, 3rd edn. Springer, London (1995)

    Book  Google Scholar 

  11. Khalil, H.: Nonlinear Systems, 3rd edn. Prentice Hall, Upper Saddle River (2002)

    MATH  Google Scholar 

  12. Leite, D., Palhares, R., Campos, V., Gomide, F.: Evolving granular fuzzy model-based control of nonlinear dynamic systems. IEEE Trans. Fuzzy Syst. 23(4), 923–938 (2015)

    Article  Google Scholar 

  13. Lima, E., Hell, M., Ballini, R., Gomide, F.: Evolving Fuzzy Modeling Using Participatory Learning, pp. 67–86. Wiley, Hoboken (2010)

    Google Scholar 

  14. Ljung, L.: System Identification: Theory for the User, 2nd edn. Prentice-Hall Inc., Upper Saddle River (1999)

    MATH  Google Scholar 

  15. Lughofer, E.: Evolving Fuzzy Systems, 1st edn. Springer, Heidelberg (2011)

    MATH  Google Scholar 

  16. Oliveira, L., Leite, V., Silva, J., Gomide, F.: Granular evolving fuzzy robust feedback linearization. In: Evolving and Adaptive Intelligent Systems, Ljubljana, June 2017

    Google Scholar 

  17. Park, J., Seo, S., Park, G.: Robust adaptive fuzzy controller for nonlinear system using estimation of bounds for approximation errors. Fuzzy Sets Syst. 133(1), 19–36 (2003)

    Article  MathSciNet  Google Scholar 

  18. Passino, K.: Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Syst. Mag. 22(3), 52–67 (2002)

    Article  MathSciNet  Google Scholar 

  19. Passino, K., Yurkovich, S.: Fuzzy Control, 1st edn. Addison-Wesley, Boston (1997)

    Google Scholar 

  20. Sastry, S.: Nonlinear Systems - Analysis, Stability and Control, 1st edn. Springer, Heidelberg (1999)

    MATH  Google Scholar 

  21. Silva, J., Oliveira, L., Gomide, F., Leite, V.: Avaliação experimental da linearização por realimentação granular evolutiva. In: Proceedings Fifth Brazilian Conference on Fuzzy Systems, Fortaleza, CE, Brazil, June 2018

    Google Scholar 

  22. Slotine, J., Li, W.: Applied Nonlinear Control, 1st edn. Prentice Hall, Upper Saddle River (1991)

    MATH  Google Scholar 

  23. Wang, L.: Stable adaptive fuzzy controllers with application to inverted pendulum tracking. IEEE Trans. Syst. Man Cybern. Part B 26(5), 677–691 (1996)

    Article  Google Scholar 

Download references

Acknowledgments

The authors acknowledge the Brazilian National Council for Scientific and Technological Development (CNPq) for grant 305906/2014-3, and the Federal Center for Technological Education of Minas Gerais (CEFET-MG) for their support.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lucas Oliveira .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Oliveira, L., Bento, A., Leite, V., Gomide, F. (2019). Robust Evolving Granular Feedback Linearization. In: Kearfott, R., Batyrshin, I., Reformat, M., Ceberio, M., Kreinovich, V. (eds) Fuzzy Techniques: Theory and Applications. IFSA/NAFIPS 2019 2019. Advances in Intelligent Systems and Computing, vol 1000. Springer, Cham. https://doi.org/10.1007/978-3-030-21920-8_40

Download citation

Publish with us

Policies and ethics