Adaptive Neural Network Control for a Class of Stochastic Nonlinear Strict-Feedback Systems

  • Zifu Li
  • Tieshan Li
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9377)


An adaptive neural network control approach is proposed for a class of stochastic nonlinear strict-feedback systems with unknown nonlinear function in this paper. Only one NN (neural network) approximator is used to tackle unknown nonlinear functions at the last step and only one actual control law and one adaptive law are contained in the designed controller. This approach simplifies the controller design and alleviates the computational burden. The Lyapunov Stability analysis given in this paper shows that the control law can guarantee the solution of the closed-loop system uniformly ultimate boundedness (UUB) in probability. The simulation example is given to illustrate the effectiveness of the proposed approach.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Krstić, M., Kanellakopulos, I., Kocotovic, P.V.: Nonlinear and Adaptive Control Design. Wiley, New York (1995)Google Scholar
  2. 2.
    Ge, S.S., Huang, C.C., Lee, T., Zhang, T.: Stable Adaptive Neural Network Control. Kluwer, Boston (2002)CrossRefGoogle Scholar
  3. 3.
    Hua, C., Guan, X., Shi, P.: Robust backstepping control for a class of time delayed systems. IEEE Trans. Automat. Control 50(6), 894–899 (2005)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Florchinger, P.: Lyapunov-like techniques for stochastic stability. SIAM J. Contr. Optim. 33, 1151–1169 (1995)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Deng, H., Kristić, M.: Stochastic nonlinear stabilization, Part I: a backstepping design. Syst. Control Lett. 32(3), 143–150 (1997)CrossRefGoogle Scholar
  6. 6.
    Zhou, J., Meng, J.E., Zurada, J.M.: Adaptive neural network control of uncertain nonlinear systems with nonsmooth actuator nonlinearities. Neurocomputing 70, 1062–1070 (2007)CrossRefGoogle Scholar
  7. 7.
    Cheng, L., Hou, Z.G., Tan, M.: Adaptive neural network tracking control for manipulators with uncertain kinematics, dynamics and actuator model. Automatica 45(10), 2312–2318 (2009)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Cheng, L., Hou, Z.G., Tan, M., Zhang, W.J.: Tracking control of a closed-chain five-bar robot with two degrees of freedom by integration of approximation-based approach and mechanical design. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 42(5), 1470–1479 (2012)CrossRefGoogle Scholar
  9. 9.
    Chen, W.S., Jiao, L.C., Li, J., Li, R.H.: Adaptive NN Backstepping Output-Feedback Control for Stochastic Nonlinear Strict-Feedback Systems with Time-Varying Delays. IEEE Trans. Syst., Man, Cybern. B 40(3), 939–950 (2010)CrossRefGoogle Scholar
  10. 10.
    Li, J., Chen, W.S., Li, J.M., Fang, Y.Q.: Adaptive NN output-feedback stabilization for a class of stochastic nonlinear strict-feedback systems. ISA Transactions 48, 468–475 (2009)CrossRefGoogle Scholar
  11. 11.
    Wang, H.Q., Chen, B., Lin, C.: Direct adaptive neural control for strict-feedback stochastic nonlinear systems. Nonlinear Dyn. 67, 2703–2718 (2012)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Yang, Y.S., Ren, J.S.: Adaptive fuzzy robust tracking controller design via small gain approach and its application. IEEE Trans. Fuzzy Syst. 11(6), 783–795 (2003)CrossRefGoogle Scholar
  13. 13.
    Li, T.S., Li, R.H., Wang, D.: Adaptive neural control of nonlinear MIMO systems with unknown time delays. Neurocomputing 78, 83–88 (2012)CrossRefGoogle Scholar
  14. 14.
    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)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Wang, Y.C., Zhang, H.G., Wang, Y.Z.: Fuzzy adaptive control of stochastic nonlinear systems with unknown virtual control gain function. Acta Autom. Sin. 32(2), 170–178 (2006)MathSciNetGoogle Scholar
  16. 16.
    Psillakis, H.E., Alexandridis, A.T.: NN-based adaptive tracking control of uncertain nonlinear systems disturbed by unknown covariance noise. IEEE Transactions on Neural Networks 18(6), 1830–1835 (2007)CrossRefGoogle Scholar
  17. 17.
    Kurdila, A.J., Narcowich, F.J., Ward, J.D.: Persistency of excitation in identification using radial basis function approximants. SIAM Journal on Control and Optimization 33(2), 625–642 (1995)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

<SimplePara><Emphasis Type="Bold">Open Access</Emphasis> This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 2.5 International License (, which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. </SimplePara> <SimplePara>The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.</SimplePara>

Authors and Affiliations

  • Zifu Li
    • 1
    • 2
  • Tieshan Li
    • 1
  1. 1.Navigation CollegeDalian Maritime UniversityDalianChina
  2. 2.Navigation CollegeJimei UniversityXiamenChina

Personalised recommendations