Skip to main content
SpringerLink
Log in

A novel neural network-based adaptive control for a class of uncertain nonlinear systems in strict-feedback form

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this paper, a novel robust adaptive tracking control approach is presented for a class of strict-feedback single-input single-output nonlinear systems. By employing radial basis function neural network to account for system uncertainties, the proposed scheme is developed by combining “command filter” and “minimal learning parameter” techniques. The main advantages of the proposed controller are that: (1) the problem of “explosion of complexity” inherent in the conventional backstepping method is avoided; (2) the problem of “dimensionality curse” is solved, and only one adaptive parameter needs to be updated online. These advantages result in a much simpler adaptive control algorithm, which is convenient to implement in applications. In addition, stability analysis shows that uniform ultimate boundedness of the solution of the closed-loop system can be guaranteed. Simulation results demonstrate the effectiveness of the proposed 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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Sun, Y.L., Er, M.J.: Hybrid fuzzy control of robotics systems. IEEE Trans. Fuzzy Syst. 12, 755–765 (2004)

    Article  Google Scholar 

  2. Ye, D., Yang, G.H.: Adaptive fault-tolerant tracking control against actuator faults with application to flight control. IEEE Trans. Control Syst. Technol. 14, 1088–1096 (2006)

    Article  Google Scholar 

  3. Li, T.S., Wang, D., Feng, G., Tong, S.C.: A DSC approach to robust adaptive NN tracking control for strict-feedback nonlinear systems. IEEE Trans. Syst. Man Cybern. B Cybern. 40, 915–927 (2010)

    Article  Google Scholar 

  4. Lapierre, L., Jouvencel, B.: Robust nonlinear path-following control of an AUV. IEEE J. Ocean. Eng. 33, 89–102 (2008)

    Article  Google Scholar 

  5. Refsnes, J.E., Srensen, A.J., Pettersen, K.Y.: Model-based output feedback control of slender-body underactuated AUVs: theory and experiments. IEEE Trans. Control Syst. Technol. 16, 930–946 (2008)

    Article  Google Scholar 

  6. Chen, M., Ge, S.S., How, B.V.E.: Robust adaptive neural network control for a class of uncertain MIMO nonlinear systems with input nonlinearities. IEEE Trans. Neural Netw. 21, 796–812 (2010)

    Article  Google Scholar 

  7. Hsu, C.F., Lin, C.M., Lee, T.T.: Wavelet adaptive backstepping control for a class of nonlinear systems. IEEE Trans. Neural Netw. 17, 1175–1183 (2006)

    Article  Google Scholar 

  8. Kwan, C., Lewis, F.L.: Robust backstepping control of nonlinear systems using neural networks. IEEE Trans. Syst. Man Cybern. A Syst. Humans 30, 753–766 (2000)

    Article  Google Scholar 

  9. Zhang, Y., Peng, P.Y., Jiang, Z.P.: Stable neural controller design for unknown nonlinear systems using backstepping. IEEE Trans. Neural Netw. 11, 1347–1359 (2000)

    Article  Google Scholar 

  10. Kanellakopoulos, I., Kokotovic, P.V., Morse, A.S.: Systematic design of adaptive controllers for feedback linearizable systems. IEEE Trans. Autom. Control 36, 1241–1253 (1991)

  11. Krstic, M., Kanellakopoulos, I., Kokotovic, P.V.: Adaptive nonlinear control without overparametrization. Syst. Control Lett. 19, 177–185 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  12. Tong, S.C., Li, C.Y., Li, Y.M.: Fuzzy adaptive observer backstepping control for MIMO nonlinear systems. Fuzzy Sets Syst. 160, 2755–2775 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. Cao, Y.Y., Lin, Z.L.: Robust stability analysis and fuzzy-scheduling control for nonlinear systems subject to actuator saturation. IEEE Trans. Fuzzy Syst. 11, 57–67 (2003)

    Article  Google Scholar 

  14. Tong, S.C., He, X.L., Zhang, H.G.: A combined backstepping and small-gain approach to robust adaptive fuzzy output feedback control. IEEE Trans. Fuzzy Syst. 17, 1059–1069 (2009)

    Article  Google Scholar 

  15. Zhang, T., Ge, S.S., Hang, C.C.: Adaptive neural network control for strict-feedback nonlinear systems using backstepping design. Automatica 36, 1835–1846 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  16. Li, Y.H., Qiang, S., Zhuang, X.Y., Kaynak, O.: Robust and adaptive backstepping control for nonlinear systems using RBF neural networks. IEEE Trans. Neural Netw. 15, 693–701 (2004)

    Article  Google Scholar 

  17. Hsu, C.F.: Adaptive recurrent neural network control using a structure adaptation algorithm. Neural Comput. Appl. 18, 115–125 (2009)

    Article  Google Scholar 

  18. Li, T.S., Li, R.H., Li, J.F.: Decentralized adaptive neural control of nonlinear interconnected large-scale systems with unknown time delays and input saturation. Neurocomputing 74, 2277–2283 (2011)

    Article  Google Scholar 

  19. Peng, Z.H., Wang, D., Lan, W.Y., Sun, G.: Robust leader-follower formation tracking control of multiple underactuated surface vessels. China Ocean Eng. 26, 521–534 (2012)

    Article  Google Scholar 

  20. Li, T.S., Li, R.H., Li, J.F.: Decentralized adaptive neural control of nonlinear systems with unknown time delays. Nonlinear Dyn. 67, 2017–2026 (2012)

    Article  MATH  Google Scholar 

  21. Swaroop, D., Hedrick, J.K., Yip, P.P., Gerdes, J.C.: Dynamic surface control for a class of nonlinear systems. IEEE Trans. Autom. Control 45, 1893–1899 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  22. Na, J., Ren, X.M., Herrmann, G., Qiao, Z.: Adaptive neural dynamic surface control for servo systems with unknown dead-zone. Control Eng. Pract. 19, 1328–1343 (2011)

    Article  Google Scholar 

  23. Yip, P., Hedrick, J.K.: Adaptive dynamic surface control: a simplified algorithm for adaptive backstepping control of nonlinear systems. Int. J. Control 71, 959–979 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  24. Wang, D., Huang, J.: Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form. IEEE Trans. Neural Netw. 16, 195–202 (2005)

    Article  Google Scholar 

  25. Ge, S.S., Wang, C.: Direct adaptive NN control of a class of nonlinear systems. IEEE Trans. Neural Netw. 13, 214–221 (2002)

    Article  Google Scholar 

  26. Shin, D.H., Kim, Y.: Reconfigurable flight control system design using adaptive neural networks. IEEE Trans. Control Syst. Technol. 12, 87–100 (2004)

    Article  Google Scholar 

  27. Chen, B., Liu, X.P., Liu, K.F., Lin, C.: Direct adaptive fuzzy control of nonlinear strict-feedback systems. Automatica 45, 1530–1535 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  28. Sun, G., Wang, D., Li, T.S., Peng, Z.H., Wang, H.: Single neural network approximation based adaptive control for a class of uncertain strict-feedback nonlinear systems. Nonlinear Dyn. 72, 175–184 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  29. Sun, G., Wang, D., Peng, Z.H.: Adaptive control based on single neural network approximation for non-linear pure-feedback systems. IET Control Theory Appl. 6, 2387–2396 (2012)

    Article  MathSciNet  Google Scholar 

  30. Zhang, H.M., Zhang, G.S.: Adaptive backstepping sliding mode control for nonlinear systems with input saturation. Trans. Tianjin Univ. 18, 46–51 (2012)

    Article  Google Scholar 

  31. Farrell, J.A., Polycarpou, M., Sharma, M., Dong, W.J.: Command filtered backstepping. IEEE Trans. Autom. Control 54, 1391–1395 (2009)

    Article  MathSciNet  Google Scholar 

  32. Na, J.: Adaptive prescribed performance control of nonlinear systems with unknown dead zone. Int. J. Adapt. Control Signal Process. 27, 426–446 (2013)

  33. Do, K.D., Pan, J.: Global robust adaptive path following of underactuated ships. Automatica 42, 1713–1722 (2006)

  34. Li, Z.J., Yang, C.G., Ding, N., Bogdan, S., Ge, T.: Robust adaptive motion control for underwater remotely operated vehicles with velocity constraints. Int. J. Control Autom. Syst. 10, 421–429 (2012)

  35. Li, T.S., Feng, G., Wang, D.: Neural-network-based simple adaptive control of uncertain MIMO nonlinear systems. IET Control Theory Appl. 4, 1543–1557 (2010)

    Article  MathSciNet  Google Scholar 

  36. Yang, Y.S., Ren, J.S.: Adaptive fuzzy robust tracking controller design via small gain approach and its application. IEEE Trans. Fuzzy Syst. 11, 783–795 (2003)

    Article  Google Scholar 

  37. Yang, Y.S., Feng, G., Ren, J.S.: A combined backstepping and small gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems. IEEE Trans. Syst. Man Cybern. A Syst. Humans 34, 406–420 (2004)

    Article  Google Scholar 

  38. Wang, H.Q., Chen, B., Lin, C.: Direct adaptive neural control for strict-feedback stochastic nonlinear systems. Nonlinear Dyn. 67, 2703–2718 (2012)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China (Nos. 51179019, 61374114, 61001090), the Natural Science Foundation of Liaoning Province (No. 20102012), the Program for Liaoning Excellent Talents in University (LNET) (Grant No. LR 2012016), the Applied Basic Research Program of Ministry of Transport of P. R. China (Nos. 2011-329-225-390 and 2013-329-225-270), and the National Fundamental Research 973 Program of China under Grant 2011CB302801, the Macau Science and Technology Development Foundation under Grant 008/2010/A1, and Multiyear Research Grants.

Author information

Authors and Affiliations

  1. Navigation College, Dalian Maritime University, Dalian, 116026, China

    Baobin Miao & Tieshan Li

Authors
  1. Baobin Miao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tieshan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Baobin Miao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Miao, B., Li, T. A novel neural network-based adaptive control for a class of uncertain nonlinear systems in strict-feedback form. Nonlinear Dyn 79, 1005–1013 (2015). https://doi.org/10.1007/s11071-014-1717-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-014-1717-2

Keywords

Search

Navigation