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Robust Backstepping Control of Robotic Systems Using Neural Networks

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Abstract

Neural network (NN) controllers for the robust back stepping control of robotic systems in both continuous and discrete-time are presented. Control action is employed to achieve tracking performance for unknown nonlinear system. Tuning methods are derived for the NN based on delta rule. Novel weight tuning algorithms for the NN are obtained that are similar to ε-modification in the case of continuous-time adaptive control. Uniform ultimate boundedness of the tracking error and the weight estimates are presented without using the persistency of excitation (PE) condition. Certainty equivalence is not used and regression matrix is not computed. No learning phase is needed for the NN and initialization of the network weights is straightforward. Simulation results justify the theoretical conclusions.

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References

  1. Åström, K. J. and Wittenmark, B.: Adaptive Control, Addison-Wesley, Reading, MA, 1989.

    Google Scholar 

  2. Commuri, S., Jagannathan, S., and Lewis, F. L.: CMAC NN control of robot manipulators, J. Robotic Systems 14(6) (1997), 465–482.

    Google Scholar 

  3. Dawson, D. W., Qu, Z., and Hu, J.: Robust trasking control of an induction motor, in: Proc. of American Control Conf., 1993, pp. 648–652.

  4. Goodwin, G. C. and Sin, K. S.: Adaptive Filtering, Prediction, and Control, Prentice-Hall, Englewood Cliffs, NJ, 1984.

    Google Scholar 

  5. Jagannathan, S. and Lewis, F. L.: Robust implicit self tuning regulator, Automatica 12(12) (1996).

  6. Jagannathan, S. and Lewis, F. L.: Multilayer discrete-time neural net controller with guaranteed performance, IEEE Trans. Neural Networks 7(1) (1996), 107–130.

    Google Scholar 

  7. Jagannathan, S. and Lewis, F. L.: Discrete-time neural net controller with guaranteed performance, IEEE Trans Automat. Control 41(11) (1996), 1693–1699.

    Google Scholar 

  8. Jagannathan, S.: Adaptive control of a class of feedback linearizable nonlinear systems using neural networks, in: Proc. of the IEEE Conf. on Robotics and Automation, Vol. 1, April 1996, pp. 258–263.

  9. Kanellakopoulos, I.: A discrete-time adaptive nonlinear system, IEEE Trans. Automat. Control 39(11) (1994), 2362–2365.

    Google Scholar 

  10. Kokotovic, P. V.: Bode lecture: The joy of feedback, IEEE Control Systems Magazine 3 (June 1992), 7–17.

    Google Scholar 

  11. Kwan, C. M. and Lewis, F. L.: Robust backstepping control of nonlinear systems using neural networks, in: European Control Conf., 1994.

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

    Google Scholar 

  13. Landau, I. D.: Evolution of adaptive control, ASME J. Dynamic Syst. Measurements Control 115 (June 1993), 381–391.

  14. Lewis, F. L., Liu, K., and Yesilderik, A.: Multilayer neural robot controller with guaranteed performance, IEEE Trans. Neural Networks 6(3) (1995), 703–715.

    Google Scholar 

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

    Google Scholar 

  16. Ljung, L. and Söderström, T.: Theory and Practice of Recursive Identification, MIT Press, Cambridge, MA, 1993.

    Google Scholar 

  17. 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 

  18. Narendra, K. S. and Annaswamy, A. M.: Stable Adaptive Systems, Prentice-Hall, Englewood Cliffs, NJ, 1989.

    Google Scholar 

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

    Google Scholar 

  20. Sabanovic, A., Sabanovic, N., and Ohnishi, K.: Sliding modes in power converters and motion control systems, Internat. J. Control 57 (1993), 1237–1259.

    Google Scholar 

  21. Sanner, R. M. and Slotine, J.-J.: Gaussian networks for direct adaptive control, IEEE Trans. Neural Networks 3(6) (1992), 837–863.

    Google Scholar 

  22. Slotine, J.-J. E. and Li, W.: Applied Nonlinear Control, Prentice-Hall, Englewood Cliffs, NJ, 1991.

    Google Scholar 

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Authors and Affiliations

  1. Department of Electrical Engineering, University of Texas at San Antonio, San Antonio, TX, 78249, USA

    S. Jagannathan

  2. Automation and Robotics Research Institute, 7300 Jack Newell Blvd. South, Fort Worth, Texas, 76118, USA

    F. L. Lewis

Authors
  1. S. Jagannathan
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  2. F. L. Lewis
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Jagannathan, S., Lewis, F.L. Robust Backstepping Control of Robotic Systems Using Neural Networks. Journal of Intelligent and Robotic Systems 23, 105–128 (1998). https://doi.org/10.1023/A:1008052206600

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  • DOI: https://doi.org/10.1023/A:1008052206600

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