Skip to main content
Log in

Discrete time neuro sliding mode control with a task-specific output error

  • Original Article
  • Published:
Neural Computing & Applications Aims and scope Submit manuscript

Abstract

The problem of obtaining the error at the output of a neuro sliding mode controller is analyzed in this paper. The controller operates in discrete time and the method presented describes an error measure that can be used if the task to be achieved is to drive the system under control to a predefined sliding regime. Once the task-specific output error is calculated, the neurocontroller parameters can be tuned so that the task is achieved. The paper postulates the strategy for discrete time representation of uncertain nonlinear systems belonging to a particular class. The performance of the proposed technique has been clarified on a third order nonlinear system, and the parameters of the controller are adjusted by using the error backpropagation algorithm. It is observed that the prescribed behavior can be achieved with a simple network configuration.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.

Similar content being viewed by others

References

  1. Rumelhart DE, Hinton GE, Williams RJ (1986) Learning internal representations by error propagation. In: Rumelhart DE, McClelland JL (eds) Parallel distributed processing: explorations in the microstructure of cognition, vol. 1. MIT Press, Cambridge, MA

  2. Jordan MI, Rumelhart DE (1992) Forward models: supervised learning with a distal teacher. Cog Sci 16:307–354

    Article  Google Scholar 

  3. Psaltis D, Sideris A, Yamamura AA (1988) A multilayered neural network controller. IEEE Contr Sys Mag 17–20

  4. Narendra KS, Parthasarathy K (1990) Identification and control of dynamical systems using neural networks. IEEE Trans Neur Net 1:4–27

    Article  Google Scholar 

  5. Efe MO, Kaynak O (1999) A comparative study of neural network structures in identification of nonlinear systems. Mechatronics 9:287–300

    Article  Google Scholar 

  6. Miller WT, Sutton RS, Werbos PJ (1991) Neural networks for control. MIT Press, Cambridge, MA

  7. Hung JY, Gao W, Hung JC (1993) Variable structure control: a survey. IEEE Trans Industr Elect 40:2–22

    Article  MATH  Google Scholar 

  8. Young KD, Utkin VI, Özgüner Ü (1999) A control engineer’s guide to sliding mode control. IEEE Trans Contr Sys Technol 7:328–342

    Article  Google Scholar 

  9. Sanner RM, Slotine J-JE (1992) Gaussian networks for direct adaptive control. IEEE Trans Neur Net 3:837–863

    Article  Google Scholar 

  10. Hsu L, Real JA (1997) Dual mode adaptive control using Gaussian neural networks. In: Proceedings of the 36th Conference on Decision and Control, (CDC), New Orleans, LA, December 1997

  11. Ertugrul M, Kaynak O (2000) Neuro sliding mode control of robotic manipulators. Mechatronics 10:239–263

    Article  Google Scholar 

  12. Gao W, Wang Y, Homaifa A (1995) Discrete-time variable structure control systems. IEEE Trans Indust Electr 42:117–122

    Article  Google Scholar 

  13. Sarpturk SZ, Istefanopulos Y, Kaynak O (1987) On the stability of discrete-time sliding mode control systems. IEEE Trans Auto Cont 32:930–932

    MATH  Google Scholar 

  14. Pieper JK, Surgenor BW (1992) Optimal discrete sliding mode control with application. In: Proceedings of the First IEEE Conference on Control Applications, September 1992

  15. Sira-Ramirez H (1991) Non-linear discrete variable structure systems in quasi-sliding mode. Int J Cont 54:1171–1187

    MathSciNet  MATH  Google Scholar 

  16. Chen X, Fukuda T (1997) Computer-controlled continuous-time variable structure systems with sliding modes. Int J Cont 67:619–639

    Article  MathSciNet  MATH  Google Scholar 

  17. Misawa EA (1997) Discrete-time sliding mode control for nonlinear systems with unmatched uncertainties and uncertain control vector. Trans ASME J Dyn Sys Meas Cont 119:503–512

    MATH  Google Scholar 

  18. Park KB (2000) Discrete-time sliding mode controller for linear time-varying systems with uncertainty. Elect Lett 36:2111–2112

    Article  Google Scholar 

  19. Chen X, Fukuda T, Young KD (2001) Adaptive quasi-sliding-mode tracking control for discrete uncertain input-output systems. IEEE Trans Indust Elect 48:216–224

    Article  Google Scholar 

  20. Tesfaye A, Tomizuka M (1993) Sliding control of discretized continuous systems via the Euler operator. In: Proceedings of the 32nd Conference on Decision and Control, San Antonio, TX, December 1993

  21. Xu H, Sun F, Sun Z (1996) The adaptive sliding mode control based on a fuzzy neural network for manipulators. In: Proceedings of the IEEE International Conference on Systems, Man and Cybernetics 3:1942–1946

  22. Fang Y, Chow TWS, Li XD (1999) Use of a recurrent neural network in discrete sliding-mode control. IEEE Proc Cont Theor App 146:84–90

    Article  Google Scholar 

  23. Muñoz D, Sbarbaro D (2000) An adaptive sliding-mode controller for discrete nonlinear systems. IEEE Trans Indust Elect 47:574–581

    Article  Google Scholar 

  24. Haykin S (1994) Neural networks. Prentice-Hall, Englewood Cliffs, NJ

  25. Slotine J-JE, Li W (1991) Applied nonlinear control. Prentice-Hall, Englewood Cliffs, NJ

  26. Roy RG, Olgaç N (1997) Robust nonlinear control via moving sliding surfaces—n-th order case. In: Proceedings of the 36th Conference on Decision and Control, San Diego, CA, December 1997

  27. Yılmaz C, Hürmüzlü Y (2000) Eliminating the reaching phase from variable structure control. Trans ASME J Dyn Sys Meas Cont 122:753–757

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mehmet Önder Efe.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Efe, M.Ö. Discrete time neuro sliding mode control with a task-specific output error. Neural Comput & Applic 13, 211–220 (2004). https://doi.org/10.1007/s00521-004-0406-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-004-0406-3

Keywords

Navigation