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Adaptive Control for a Class of Nonlinear Time-Delay Systems Using RBF Neural Networks

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Advances in Neural Networks – ISNN 2007 (ISNN 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4491))

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Abstract

In this paper, adaptive neural network control is proposed for a class of strict-feedback nonlinear time-delay systems. Unknown smooth function vectors and unknown time-delay functions are approximated by two neural networks, respectively, such that the requirement on the unknown time-delay functions is relaxed. In addition, the proposed systematic backstepping design method has been proven to be able to guarantee semiglobally uniformly ultimately bounded of closed loop signals, and the output of the system has been proven to converge to a small neighborhood of the desired trajectory. Finally, simulation result is presented to demonstrate the effectiveness of the approach.

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References

  1. Ge, S.S., Hang, C.C., Lee, T.H., Zhang, T.: Stable Adaptive Neural Network Control. Kluwer, Norwell (2002)

    Book  MATH  Google Scholar 

  2. Krstić, M., Kanellakopoulos, I., Kokotović, P.: Nonlinear and Adaptive Control Design. Wiley, New York (1995)

    MATH  Google Scholar 

  3. Polycarpou, M.M., Mears, M.J.: Stable Adaptive Tracking of Uncertain Systems Using Nonlinearly Parametrized On-Line Approximators. International Journal of Control 70(3), 363–384 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  4. Zhang, Y., Peng, P.Y., Jiang, Z.P.: Stable Neural Controller Design for Unknown Nonlinear Systems Using Backstepping. IEEE Transactions on Neural Networks 11, 1347–1359 (2000)

    Article  Google Scholar 

  5. 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 

  6. Ge, S.S., Wang, C.: Direct Adaptive NN Control of a Class of Nonlinear Systems. IEEE Transactions on Neural Networks 13(1), 214–221 (2002)

    Article  Google Scholar 

  7. Li, Y.H., Qiang, S., Zhuang, X.Y., Kaynak, O.: Robust and Adaptive Backstepping Control for Nonlinear Systems Using RBF Neural Networks. IEEE Transactions on Neural Networks 15(3), 693–701 (2004)

    Article  Google Scholar 

  8. Cao, J.D., Ho, D.W.C.: A General Framework for Global Asymptotic Stability Analysis of Delayed Neural Networks Based on LMI Approach. Chaos, Solitons & Fractals 24(5), 1317–1329 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Xu, S.Y., Lam, J.: A New Approach to Exponential Stability Analysis of Neural Networks with Time-varying Delays. Neural Networks 19(1), 76–83 (2006)

    Article  MATH  Google Scholar 

  10. Zeng, Z.G., Wang, J., Liao, X.X.: Global Exponential Stability of Neural Networks with Time-Varying Delays. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 50(10), 1353–1358 (2003)

    Article  Google Scholar 

  11. Chen, W.S., Li, J.M.: Adaptive Neural Network Backstepping Control for Nonlinear Time-Delay Systems (in Chinese). Electric Machines and Control 9(5), 500–503, 511 (2005)

    Google Scholar 

  12. Ge, S.S., Hong, F., Lee, T.H.: Adaptive Neural Network Control of Nonlinear Systems with Unknown Time Delays. IEEE Transactions on Automatic Control 48(11), 2004–2010 (2003)

    Article  MathSciNet  Google Scholar 

  13. Qu, Z.: Robust Control of Nonlinear Uncertain Systems. Wiley, New York (1998)

    MATH  Google Scholar 

  14. Haykin, S.: Neural Networks: A Comprehensive Foundation, 2nd edn. Prentice-Hall, Upper Saddle River (1999)

    MATH  Google Scholar 

  15. Ioannou, P.A., Sun, J.: Robust Adaptive Control. Prentice-Hall, Englewood Cliffs (1995)

    MATH  Google Scholar 

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© 2007 Springer-Verlag Berlin Heidelberg

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Ji, G., Luo, Q. (2007). Adaptive Control for a Class of Nonlinear Time-Delay Systems Using RBF Neural Networks. In: Liu, D., Fei, S., Hou, ZG., Zhang, H., Sun, C. (eds) Advances in Neural Networks – ISNN 2007. ISNN 2007. Lecture Notes in Computer Science, vol 4491. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72383-7_21

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  • DOI: https://doi.org/10.1007/978-3-540-72383-7_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72382-0

  • Online ISBN: 978-3-540-72383-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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