Skip to main content
SpringerLink
Log in

NN-based output tracking for more general stochastic nonlinear systems with unknown control coefficients

  • Research Article
  • Published:
International Journal of Automation and Computing Aims and scope Submit manuscript

Abstract

This paper considers the output tracking problem for more general classes of stochastic nonlinear systems with unknown control coefficients and driven by noise of unknown covariance. By utilizing the radial basis function neural network approximation method and backstepping technique, we successfully construct a controller to guarantee the solution process to be bounded in probability. The tracking error signal is 4th-moment semi-globally uniformly ultimately bounded (SGUUB) and can be regulated into a small neighborhood of the origin in probability. A simulation example is given to demonstrate the effectiveness of the control scheme.

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

Access this article

Log in via an institution

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. R. Z. Has’minskii. Stochastic Stability of Differential Equations. Norwell: Kluwer Academic Publisher, 1980.

    Book  Google Scholar 

  2. M. Krstic, H. Deng. Stabilization of Nonlinear Uncertain Systems, New York, USA: Springer, 1998.

    MATH  Google Scholar 

  3. H. Deng, M. Krstic, R. J.Williams. Stabilization of stochastic nonlinear systems driven by noise of unknown covariance. IEEE Transactions on Automatic Control, vol. 46, no. 8, pp. 1237–1253, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  4. Z. J. Wu, X. J. Xie, S. Y. Zhang. Adaptive backstepping controller design using stochastic small-gain theorem. Automatica, vol. 43, no. 4, pp. 608–620, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  5. W. S. Chen. Output-feedback adaptive stochastic nonlinear stabilization using neural networks. Journal of Systems Engineering and Electronics, vol. 21, no. 1, pp. 81–87, 2010.

    Article  Google Scholar 

  6. N. Duan, X. J. Xie. Further results on output-feedback stabilization for a class of stochastic nonlinear systems. IEEE Transactions on Automatic Control, vol. 56, no. 5, pp. 1208–1213, 2011.

    Article  MathSciNet  Google Scholar 

  7. Y. G. Liu, Z. G. Pan, S. J. Shi. Output feedback control design for strict-feedback stochastic nonlinear systems under a risk-sensitive cost. IEEE Transactions on Automatic Control, vol. 48, no. 3, pp. 509–513, 2003.

    Article  MathSciNet  Google Scholar 

  8. S. J. Liu, J. F. Zhang, Z. P. Jiang. Decentralised adaptive output-feedback stabilization for large-scale stochastic nonlinear systems. Automatica, vol. 43, no. 2, pp. 238–251, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  9. H. B. Ji, H. S. Xi. Adaptive output-feedback tracking of stochastic nonlinear systems. IEEE Transactions on Automatic Control, vol. 51, no. 2, pp. 355–360, 2006.

    Article  MathSciNet  Google Scholar 

  10. J. Li, W. S. Chen, J. M. Li. Adaptive NN output-feedback stabilization for a class of stochastic nonlinear strictfeedback systems. ISA Transactions, vol. 48, no. 4, pp. 468–475, 2009.

    Article  Google Scholar 

  11. R. D. Nussbaum. Some remarks on the conjecture in parameter adaptive control. System and Control Letters, vol.3, no. 5, pp. 243–246, 1983.

    Article  MathSciNet  MATH  Google Scholar 

  12. C. J. Qian, W. Lin. Practical output tracking of nonlinear systems with uncontrollable unstable linearization. IEEE Transactions on Automatic Control, vol. 47, no. 1, pp. 21–35, 2002.

    Article  MathSciNet  Google Scholar 

  13. S. S. Ge, J. Wang. Robust adaptive tracking for timevarying uncertain nonlinear systems with unknown control coefficients. IEEE Transactions on Automatic Control, vol. 48, no. 8, pp. 1463–1469, 2003.

    Article  MathSciNet  Google Scholar 

  14. Z. Y. Sun, Y. G. Liu. Adaptive practical output tracking control for high-order nonlinear uncertain systems. Acta Automatica sinica, vol. 34, no. 8, pp. 984–989, 2008.

    Article  MathSciNet  Google Scholar 

  15. Q. D. Wang, C. L. Wei. Output tracking of nonlinear systems with unknown control coefficients and nonlinear parameterization. In Proceedings of the Chinese Control and Decision Conference, Shanghai, China, pp. 4193–4203, 2008.

    Google Scholar 

  16. J. Tian, X. J. Xie. Adaptive state-feedback stabilization for high-order stochastic nonlinear systems with time-varying control coefficients. In Proceedings of the 27th Chinese Control Conference, IEEE, Hunan, China, pp. 757–761, 2007.

    Google Scholar 

  17. J. Tian, X. J. Xie. Adaptive state-feedback stabilization for high-order stochastic non-linear systems with uncertain control coefficients. International Journal of Control, vol. 80, no. 9, pp. 1503–1516, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  18. X. J. Xie, N. Duan. Output tracking of high-order stochastic nonlinear systems with application to benchmark mechanical system. IEEE Transactions on Automatic Control, vol. 55, no. 5, pp. 1197–1202, 2010.

    Article  MathSciNet  Google Scholar 

  19. S. S. Yu, A. M. Annaswamy. Adaptive control of nonlinear dynamic systems using θ-adaptive neural networks. Automatica, vol. 33, no. 11, pp. 1975–1995, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  20. A. S. Pznyak, W. Yu, E. N. Sanchez, J. P. Perez. Stability analysis of dynamic neural network control. Expert Systems with Applications, vol. 14, no. 2, pp. 227–236, 1998.

    Article  Google Scholar 

  21. S. S. Ge, C. Wang. Direct adaptive NN control of a class of nonlinear systems. IEEE Transactions on Neural Networks, vol. 13, no. 1, pp. 214–221, 2002.

    Article  Google Scholar 

  22. W. S. Chen, R. H. Li. Adaptive output-feedback control for MIMO nonlinear systems with time-varying delays using neural networks. Journal of systems Engineering and Electronics, vol. 21, no. 5, pp. 850–858, 2010.

    Article  Google Scholar 

  23. H. B. Du, H. B. Shao, P. J. Yao. Adaptive neural network control for a class of low-triangular structured nonlinear systems. IEEE Transactions on Neural Networks, vol. 17, no. 2, pp. 509–514, 2006.

    Article  Google Scholar 

  24. W. S. Chen, C. J. Li, J. S. Wu. Globally stable adaptive robust tracking control using RBF neural networks as feedforward compensators. Neural Computing and Applications, vol. 21, no. 2, pp. 351–363, 2012.

    Article  Google Scholar 

  25. Y. T. Wen, X. M. Ren. Neural networks-based adaptive control for nonlinear time-varying delays systems with unknown control direction. IEEE Transactions on Neural Networks, vol. 22, no. 10, pp. 1599–1612, 2011.

    Article  Google Scholar 

  26. S. S. Ge, C. Wang. Adaptive NN control of uncertain nonlinear pure-feedback systems. Automatica, vol. 38, no. 4, pp. 671–682, 2002.

    Article  MathSciNet  MATH  Google Scholar 

  27. H. E. Psillakis, A. T. Alexandridis. NN-based adaptive tracking control of uncertain nonlinear systems disturbed by unknown covariance noise. IEEE Transactions on Neural Networks, vol. 18, no. 6, pp. 1830–1835, 2007.

    Article  Google Scholar 

  28. W. S. Chen, C. J. Li, J. M. Li, R. H. Li. Adaptive NN backstepping output-feedback control for stochastic nonlinear strict-feedback systems with time-varying delays. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 40, no. 3, pp. 939–950, 2010.

    Article  Google Scholar 

  29. Q. Zhou, P. Shi. A new approach to network-based H1 control for stochastic systems. International Journal of Robust and Nonlinear Control, vol. 22, no. 9, pp. 1036–1059, 2012.

    Article  MathSciNet  MATH  Google Scholar 

  30. Q. Zhou, P. Shi, S. Y. Xu, H. Y. Li. Observer-based adaptive neural network control for nonlinear stochastic systems with time delay. IEEE Transactions on Neural Networks and Learning Systems, vol. 24, no. 1, pp. 71–80, 2013.

    Article  Google Scholar 

  31. R. M. Sanner, J. J. E. Slotine. Gaussian networks for direct adaptive control. IEEE Transactions on Neural Networks, vol. 3, no. 6, pp. 837–863, 1992.

    Article  Google Scholar 

  32. S. Battilotti, A. De Santis. Stabilization in probability of nonlinear stochastic systems with guaranteed region of attraction and target set. IEEE Transactions on Automatic Control, vol. 48, no. 9, pp. 1585–1595, 2003.

    Article  MathSciNet  Google Scholar 

  33. M. Krstic, I. Kanellakopoulos, P. V. Kokotovic. Nonlinear and Adaptive Control Design, New York, USA: Wiley, 1995.

    MATH  Google Scholar 

  34. Z. C. Zhang, Y. Q. Wu. Globally asymptotic stabilization for nonlinear time-delay systems with ISS inverse dynamics. International Journal of Automation and Computing, vol. 9, no. 6, pp. 634–640, 2012.

    Article  Google Scholar 

  35. G. D. Zhao, N. Duan. A continuous state feedback controller design for high-order nonlinear systems with polynomial growth nonlinearities. International Journal of Automation and Computing, vol. 10, no. 4, pp. 267–274, 2013.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electrical Engineering & Automation, Jiangsu Normal University, Xuzhou, 221116, China

    Na Duan & Hui-Fang Min

Authors
  1. Na Duan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hui-Fang Min
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Na Duan.

Additional information

This work was supported by National Natural Science Foundation of China (Nos. 61573172, 61305149 and 61403174), 333 High-level Talents Training Program in Jiangsu Province (No.BRA2015352) and Program for Fundamental Research of Natural Sciences in Universities of Jiangsu Province (No. 15KJB510011).

Recommended by Associate Editor Ding-Li Yu

Na Duan received the Ph.D. degree from Institute of Automation, Qufu Normal University. Now she is an associate professor of Jiangsu Normal University, China.

Her research interests include nonlinear adaptive control and stochastic nonlinear control.

ORCID iD: 0000-0001-7152-0036

Hui-Fang Min received the M. Sc. degree from School of Electrical Engineering and Automation, Jiangsu Normal University, China in 2015. She is currently a Ph.D. degree candidate at School of Automation, Nanjing University of Science and Technology.

Her research interests include nonlinear adaptive control and stochastic nonlinear control.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Duan, N., Min, HF. NN-based output tracking for more general stochastic nonlinear systems with unknown control coefficients. Int. J. Autom. Comput. 14, 350–359 (2017). https://doi.org/10.1007/s11633-015-0936-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11633-015-0936-4

Keywords

Search

Navigation