Skip to main content
Log in

Neural net robot controller: Structure and stability proofs

  • Published:
Journal of Intelligent and Robotic Systems Aims and scope Submit manuscript

Abstract

A multilayer neural net (NN) controller for a general serial-link robot arm is developed. The structure of the NN controller is derived using a filtered error approach. It is argued that standard backpropagation tuning, when used for real-time closed-loop control, can yield unbounded NN weights if: (1) the net can not exactly reconstruct a certain required control function, (2) there are bounded unknown disturbances in the robot dynamics, or (3) the robot arm has more than one link (i.e. nonlinear case). On-line weight tuning algorithms including correction terms to backpropagation, plus an added robustifying signal, guarantee tracking as well as bounded weights. The correction terms involve a second-orderforward-propagated wave in the backprop network.

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

Similar content being viewed by others

References

  1. Alcorta, E. and Sánchez, E. N.: On-line Function Approximation via Neural Networks, Preprint, 1992.

  2. Bartle, R. G.:The Elements of Real Analysis, Wiley, New York, 1964.

    Google Scholar 

  3. Chu, S. R. and Shoureshi, R.: Neural-based adaptive nonlinear system identification,Intelligent Control Systems DSC-45, ASME Winter Annual Meeting, 1992.

  4. Craig, J. J.:Adaptive Control of Robot Manipulators, Addison-Wesley, Reading, MA, 1988.

    Google Scholar 

  5. Cybenko, G.: Approximation by superpositions of a sigmoidal functions,Math. Control, Signals, Systems 2(4) (1989), 303–314.

    Google Scholar 

  6. Dawson, D. M., Qu, Z., Lewis, F. L. and Dorsey, J. F.: Robust control for the tracking of robot motion,Int. J. Control 52(3) 19??, 581–595.

    Google Scholar 

  7. Goodwin, G. C.: Can we identify adaptive control?Proc. Eur. Control Conf. July 1991, pp. 1714–1725.

  8. Goodwin, G. C. and Sin, K. S.:Adaptive Filtering, Prediction, and Control, Prentice-Hall, New Jersey, 1984.

    Google Scholar 

  9. Horn, B., Hush, D. and Abdallah, C.: The state space recurrent neural network for robot identification,Adv. Control Issues for Robot Manipulators, DSC-39, ASME Winter Annual Meeting, 1992.

  10. Hornik, K., Stinchombe, M. and White, H.: Multilayer feedforward networks are universal approximators,Neural Networks 2 (1989), 359–366.

    Google Scholar 

  11. Iiguni, Y., Sakai, H. and Tokumaru, H.: A nonlinear regulator design in the presence of system uncertaities using multilayer neural networks,IEEE Trans. Neural Networks 2(4) (1991), 410–417.

    Google Scholar 

  12. Kraft, L. G. and Campagna, D. P.: A summary comparison of CMAC neural network and traditional adaptive control systems, in W. T. Miller, R. S. Sutton and P. J. Werbos (eds),Neural Networks for Control, MIT Press, Cambridge, 1991, pp. 143–169.

    Google Scholar 

  13. Landau, Y. D.:Adaptive Control:The Model Reference Approach, Marcel Dekker, New York, 1979.

    Google Scholar 

  14. Lewis, F. L., Abdallah, C. T. and Dawson, D. M.:Control of Robot Manipulators, Macmillan, New York, 1993.

    Google Scholar 

  15. Lewis, F. L., Liu, K. and Yesildirek, A.: Neural net robot controller with guaranteed performance, 1993, in press.

  16. Liu, K. and Lewis, F. L.: Robust control techniques for general dynamic systems,J. Intel. Robotic Syst. 6 (1992), 33–49.

    Google Scholar 

  17. Miller, W. T., Sutton, R. S. and Werbos, P. J. (eds):Neural Networks for Control, MIT Press, Cambridge, 1991.

    Google Scholar 

  18. Narendra, K. S.: Adaptive control using neural networks, in W. T. Miller, R. S. Sutton and P. J. Werbos (eds),Neural Networks for Control, MIT Press, Cambridge, 1991, pp. 115–142.

    Google Scholar 

  19. Narendra, K. S. and Annaswamy, A. M.: A new adaptive law for robust adaptation without persistent excitation,IEEE Trans. Automat. Control AC-32(2) (1987), 134–145.

    Google Scholar 

  20. Narendra, K. S. and Parthasarathy, K.: Identification and control of dynamical systems using neural networks,IEEE Trans. Neural Networks 1 (Mar. 1990), 4–27.

    Google Scholar 

  21. Olvera, J., Guan, X. and Manry, M. T.: Theory of Monomial Networks,Proc. Symp. Implicit and Nonlinear Systems, Dec. 1992, pp. 96–101.

  22. Ozaki, T., Suzuki, T., Furuhashi, T., Okuma, S. and Uchikawa, Y.: Trajectory control of robotic manipulators,IEEE Trans. Ind. Elec. 38 (June 1991), 195–202.

    Google Scholar 

  23. Pao, Y. H.:Adaptive Pattern Recognition and Neural Networks, Addison-Wesley, Reading, MA, 1989.

    Google Scholar 

  24. Park, J. and Sandberg, I. W.: Universal approximation using radial-basis-function networks,Neural Comp. 3 (1991), 246–257.

    Google Scholar 

  25. Polycarpou, M. M. and Ioannu, P. A.: Identification and control using neural network models: design and stability analysis, Tech. Report 91-09-01, Dept. Elect. Eng. Sys., Univ. S. Cal., Sep. 1991.

  26. Polycarpou, M. M. and Ioannu, P. A.: Neural networks as on-line approximators of nonlinear systems,Proc. IEEE Conf. Decision and Control, Tuscon, Dec. 1992, pp. 7–12.

  27. Poggio, T. and Girosi, F.: A theory of networks with for approximation and learning, Tech. Report Memo No 1140, Artif. Intel. Lab, MIT, 1989.

  28. Sadegh, N.: Nonlinear identification and control via neural networks,Control Systems with Inexact Dynamics Models,DSC-33, ASME Winter Annual Meeting, 1991.

  29. Sanner, R. M. and Slotine, J.-J. E.: Stable adaptive control and recursive identification using radial gaussian networks,Proc. IEEE Conf. Decision and Control, Brighton, 1991.

  30. Sastry, S. S. and Bodson, M.:Adaptive Control, Prentice-Hall, New Jersey, 1989.

    Google Scholar 

  31. Slotine, J.-J. E. and Li, W.: Adaptive manipulator control: a case study,IEEE Trans. Automat. Control 33(11) (1988), 995–1003.

    Google Scholar 

  32. Slotine, J.-J. E. and Li, W.:Applied Nonlinear Control, Prentice-Hall, New Jersey, 1991.

    Google Scholar 

  33. Yabuta, T. and Yamada, T.: Neural network controller characteristics with regard to adaptive control,IEEE Trans. Syst., Man. Cybern. 22(1) (1992), 170–176.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lewis, F.L., Yeşildirek, A. & Liu, K. Neural net robot controller: Structure and stability proofs. J Intell Robot Syst 12, 277–299 (1995). https://doi.org/10.1007/BF01262965

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01262965

Key words

Navigation