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Robust Evolving Granular Feedback Linearization

  • Lucas OliveiraEmail author
  • Anderson Bento
  • Valter Leite
  • Fernando Gomide
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (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.

Keywords

Robust control Evolving systems Feedback linearization 

Notes

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.

References

  1. 1.
    Angelov, P.: Autonomous Learning Systems: From Data Streams to Knowledge in Real-time, 1st edn. Wiley, Hoboken (2013)Google Scholar
  2. 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)CrossRefGoogle Scholar
  3. 3.
    Van de Water, H., Willems, J.: The certainty equivalence property in stochastic control theory. IEEE Trans. Autom. Control 26(5), 1080–1087 (1981)MathSciNetCrossRefGoogle Scholar
  4. 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)MathSciNetCrossRefGoogle Scholar
  5. 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)CrossRefGoogle Scholar
  6. 6.
    Dorf, R.C., Bishop, R.H.: Modern Control Systems, 9th edn. Prentice-Hall Inc., Upper Saddle River (2000)zbMATHGoogle Scholar
  7. 7.
    Esfandiari, F., Khalil, H.K.: Output feedback stabilization of fully linearizable systems. Int. J. Control 56(5), 1007–1037 (1992)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Freidovich, L.B., Khalil, H.K.: Performance recovery of feedback-linearization-based designs. IEEE Trans. Autom. Control 53(10), 2324–2334 (2008)MathSciNetCrossRefGoogle Scholar
  9. 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)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Isidori, A.: Nonlinear Control Systems, 3rd edn. Springer, London (1995)CrossRefGoogle Scholar
  11. 11.
    Khalil, H.: Nonlinear Systems, 3rd edn. Prentice Hall, Upper Saddle River (2002)zbMATHGoogle Scholar
  12. 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)CrossRefGoogle Scholar
  13. 13.
    Lima, E., Hell, M., Ballini, R., Gomide, F.: Evolving Fuzzy Modeling Using Participatory Learning, pp. 67–86. Wiley, Hoboken (2010)Google Scholar
  14. 14.
    Ljung, L.: System Identification: Theory for the User, 2nd edn. Prentice-Hall Inc., Upper Saddle River (1999)zbMATHGoogle Scholar
  15. 15.
    Lughofer, E.: Evolving Fuzzy Systems, 1st edn. Springer, Heidelberg (2011)zbMATHGoogle Scholar
  16. 16.
    Oliveira, L., Leite, V., Silva, J., Gomide, F.: Granular evolving fuzzy robust feedback linearization. In: Evolving and Adaptive Intelligent Systems, Ljubljana, June 2017Google Scholar
  17. 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)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Passino, K.: Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Syst. Mag. 22(3), 52–67 (2002)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Passino, K., Yurkovich, S.: Fuzzy Control, 1st edn. Addison-Wesley, Boston (1997)Google Scholar
  20. 20.
    Sastry, S.: Nonlinear Systems - Analysis, Stability and Control, 1st edn. Springer, Heidelberg (1999)zbMATHGoogle Scholar
  21. 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 2018Google Scholar
  22. 22.
    Slotine, J., Li, W.: Applied Nonlinear Control, 1st edn. Prentice Hall, Upper Saddle River (1991)zbMATHGoogle Scholar
  23. 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)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Lucas Oliveira
    • 1
    • 2
    Email author
  • Anderson Bento
    • 2
  • Valter Leite
    • 2
  • Fernando Gomide
    • 1
  1. 1.Department of Computer Engineering and Automation, School of Electrical and Computer EngineeringUniversity of CampinasCampinasBrazil
  2. 2.Department of Mechatronics EngineeringFederal Center for Technological Education of Minas GeraisDivinópolisBrazil

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