Skip to main content

New developments in dynamical adaptive backstepping control

  • Conference paper
  • First Online:
Nonlinear control in the year 2000 volume 2

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 259))

Abstract

We consider a number of dynamical adaptive backstepping control algorithms for the class of observable non-minimum phase nonlinear continuous uncertain systems (triangular and non-triangular), as well as systems with disturbances which can be converted to the parametric semi-strict feedback form. Nonlinear, sliding and second-order sliding control laws are developed. Adaptive backstepping algorithms with tuning functions, and modular parameter identification approaches are presented. BACK, a Maple symbolic algebra package, has been developed as a tool for the design of dynamical adaptive nonlinear controllers for regulation and tracking tasks.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bartolini G., A. Ferrara, L. Giacomini and E. Usai (1996) A combined backstepping/second order sliding mode approach to control a class of nonlinear systems, Proc. IEEE International Workshop on Variable Structure Systems, Tokyo, Japan, 205–210

    Google Scholar 

  2. Bartolini, G., A. Ferrara and E. Usai (1997) Applications of a suboptimal discontinuous control algorithm for uncertain second order systems, Int. J. Robusk Nonlinear Control, 7, 299–320

    Article  MATH  MathSciNet  Google Scholar 

  3. Bartolini, G., A. Ferrara and E. Usai (1997) Output Tracking Control of Uncertain Nonlinear Second-Order Systems, Automatica, 33, 2203–2212

    Article  MATH  MathSciNet  Google Scholar 

  4. Bartolini, G., A. Ferrara and E. Usai (1998) Chattering avoidance by second-order sliding mode control, IEEE Trans. Automat. Contr., 43, 241–246

    Article  MATH  MathSciNet  Google Scholar 

  5. Blankenship, G. L., R. Ghanadan, H. G. Kwatny, C. LaVigna and V. Polyakov, (1995) Tools for integrated modelling, design, and nonlinear control, IEEE Control Systems Mag., 15, 65–79

    Article  Google Scholar 

  6. Corless, M., and G. Leitmann (1981) Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamical systems, IEEE Trans. Automat. Contr., 26, 1139–1144

    Article  MATH  MathSciNet  Google Scholar 

  7. Freeman, R. A., and P. V. Kokotović (1996) Tracking controllers for systems linear in unmeasured states, Automatica, 32, 735–746

    Article  MATH  Google Scholar 

  8. de Jager, B. (1996) Symbolic analysis and design for (nonaffiX-Mozilla-Status: 0009 systems, Proc. 13th IFAC World Congress, San Francisco, F, 289–294)

    Google Scholar 

  9. Glumineau, A. and L. Graciani (1996) Symbolic nonlinear analysis and control package, Proc. 13th IFAC World Congress, San Francisco, F, 295–298

    Google Scholar 

  10. Jiang, Z. P. and L. Praly (1991) Iterative designs of adaptive controllers for systems with nonlinear integrators, Proc. 30th IEEE Conference on Decision and Control, Brighton, UK, 2482–2487

    Google Scholar 

  11. Kanellakopoulos, I., P.V. Kokotović and A. S. Morse (1991) Systematic Design of Adaptive Controllers for Feedback Linearizable Systems, IEEE Trans. Automat. Contr., 36, 1241–1253

    Article  MATH  Google Scholar 

  12. Koshkouei, A. J. and A.S.I. Zinober (1999) Adaptive Sliding Backstepping Control of Nonlinear Semi-Strict Feedback Form Systems, Proc. 7th IEEE Mediterranean Control Conference, Haifa

    Google Scholar 

  13. Koshkouei, A.J. and A.S.I. Zinober (2000) Adaptive Output Tracking Backstepping Sliding Mode Control of Nonlinear Systems, Proc. 3rd IFAC Symposium on Robust Control Design, Prague

    Google Scholar 

  14. Koshkouei, A.J. and A.S.I. Zinober (2000), Adaptive Backstepping Control of Nonlinear Systems with Unmatched Uncertainty, submitted to CDC2000, Sydney

    Google Scholar 

  15. Kravaris, C. and S. Palanki (1988) AIChE Journal, 34, 1119–1127

    Article  MathSciNet  Google Scholar 

  16. Krstić, M., I. Kanellakopoulos and P.V. Kokotović (1992) Adaptive Nonlinear Control without Overparametrization, Systems and Control Letters, 19, 177–185

    Article  MathSciNet  Google Scholar 

  17. Krstić, M., I. Kanellakopoulos, and P.V. Kokotović (1995) Nonlinear and Adaptive Control Design, New York: John Wiley & Sons

    Google Scholar 

  18. Marino, R. and P. Tomei (1995) Nonlinear Control Design, London: Prentice-Hall

    MATH  Google Scholar 

  19. Rios-Bolívar, M. (1997) Adaptive Backstepping and Sliding Mode Control of Uncertain Nonlinear Systems, PhD dissertation, Applied Mathematics, University of Sheffield

    Google Scholar 

  20. Rios-Bolívar, M., H. Sira-Ramírez and A. S. I. Zinober (1995) Output Tracking Control via Adaptive Input-Output Linearization: A Backstepping Approach, Proc. 34th IEEE CDC, New Orleans, 2, 1579–1584

    Google Scholar 

  21. Rios-Bolívar, M. and A.S.I. Zinober (1994) Sliding mode control for uncertain linearizable nonlinear systems: A backstepping approach, Proc. 3rd IEEE Workshop on Robust Control via Variable Structure and Lyapunov Techniques, Benevento, Italy, 78–85

    Google Scholar 

  22. Rios-Bolívar, M. and A.S.I. Zinober (1997a) Dynamical adaptive backstepping control design via symbolic computation, Proc. 3rd European Control Conference, Brussels

    Google Scholar 

  23. Rios-Bolívar, M. and A.S.I. Zinober (1997b) Dynamical adaptive sliding mode output tracking control of a class of nonlinear systems, Int. J. Robust and Nonlinear Control, 7, 387–405

    Article  MATH  Google Scholar 

  24. Rios-Bolívar, M., and A.S.I. Zinober (1998) A symbolic computation toolbox for the design of dynamical adaptive nonlinear control, Appl. Math. and Comp. Sci., 8, 73–88

    MATH  Google Scholar 

  25. Rios-Bolívar, E.M. and Zinober, A.S.I. (1999) Dynamical adaptive sliding mode control of observable minimum-phase uncertain nonlinear systems, in “Variable structure systems, sliding mode and nonlinear control”, ed K.D. Young and Ü. Özgüner, Springer-Verlag, London, 211–235

    Google Scholar 

  26. Rios-Bolívar, M., A.S.I. Zinober and H. Sira-Ramírez (1996) Dynamical Sliding Mode Control via Adaptive Input-Output Linearization: A Backstepping Approach, in: Robust Control via Variable Structure and Lyapunov Techniques (F. Garofalo and L. Glielmo, Eds.), Springer-Verlag, 15–35

    Google Scholar 

  27. Rios-Bolívar M., A.S.I. Zinober and H. Sira-Ramírez (1997) Dynamical Adaptive Sliding Mode Output Tracking Control of a Class of Nonlinear Systems, Int. J. Robust and Nonlinear Control, 7, 387–405

    Article  MATH  Google Scholar 

  28. Rothfuss, R. and M. Zeitz (1996) A toolbox for symbolic nonlinear feedback design”, Proc. 13th IFAC World Congress, San Francisco, F, 283–288

    Google Scholar 

  29. Sira-Ramírez, H. and M. Delgado Passivity Based Regulation of Nonlinear Continuous Processes (to be published in Advances in Control)

    Google Scholar 

  30. Sira-Ramírez, H. and O. Llanes-Santiago (1994) Dynamical Feedback Strategies in the Regulation of Nonlinear Chemical Processes, IEEE Trans. Control Systems Technology, 2, 11–21

    Article  Google Scholar 

  31. Slotine, J-J. E. and W. Li (1991) Applied Nonlinear Control, Prentice-Hall, London

    MATH  Google Scholar 

  32. Sontag, E. D. (1989) Smooth stabilization implies coprime factorization, IEEE Trans. Automat. Contr., 34, 435–443

    Article  MATH  MathSciNet  Google Scholar 

  33. Yao, B. and M. Tomizuka (1997) Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form, Automatica, 33, 893–900

    Article  MATH  MathSciNet  Google Scholar 

  34. Zinober, A.S.I., J.C. Scarratt, A. Ferrara, L. Giacomini and E.M. Rios-Bolívar (1999) Dynamical adaptive first and second order sliding mode control of nonlinear non-triangular uncertain systems, Proc. 7th IEEE Mediterranean Control Conference, Haifa

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Alberto Isidori Françoise Lamnabhi-Lagarrigue Witold Respondek

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag London Limited

About this paper

Cite this paper

Zinober, A.S.I., Scarratt, J.C., Mills, R.E., Koshkouei, A.J. (2001). New developments in dynamical adaptive backstepping control. In: Isidori, A., Lamnabhi-Lagarrigue, F., Respondek, W. (eds) Nonlinear control in the year 2000 volume 2. Lecture Notes in Control and Information Sciences, vol 259. Springer, London. https://doi.org/10.1007/BFb0110326

Download citation

  • DOI: https://doi.org/10.1007/BFb0110326

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-364-5

  • Online ISBN: 978-1-84628-569-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics