Skip to main content
Log in

Nonlinear stable adaptive control based upon Elman networks

  • Published:
Applied Mathematics-A Journal of Chinese Universities Aims and scope Submit manuscript

Abstract

Elman networks’ dynamical modeling capability is discussed in this paper firstly. According to Elman networks’ unique structure, a weight training algorithm is designed and a nonlinear adaptive controller is constructed. Without the PE presumption, neural networks controller’s closed-loop properties are studied and the whole Elman networks’ passivity is demonstrated.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Narendra, K. S., Neural networks for control: Theory and practice, Proceeding of the IEEE, 1996, 84 (10):1385–1406.

    Article  Google Scholar 

  2. Rovithakis, George A., Christodoulou, Manolis A., Adaptive control of unknown plants using dynamical neural networks, IEEE Trans. Systems Man. Cybernet., 1994, 24(3):400–411.

    Article  Google Scholar 

  3. Wang Yaonan, A kind of dynamical recurrent neural networks-based intelligent control, Control and Decision, 1995, 10(6):508–513.

    Google Scholar 

  4. Ku Chao-Chee, Lee, Kwang Y., Diagonal recurrent neural networks for dynamic systems control, IEEE Trans. Neural Networks, 1995, 6(1):144–156.

    Article  Google Scholar 

  5. Elman, J. L., Finding structure in time, Cognitive Science, 1990, 14:179–211.

    Article  Google Scholar 

  6. Pham, D. T., Liu, X., Training of Elman network and dynamic system modelling, Internet J. Systems Sci. 1996, 27(2):221–226.

    Article  MATH  Google Scholar 

  7. Sperduti Alessandro, On the computational power of recurrent neural networks for structures, Neural Networks, 1997, 10(3):395–400.

    Article  Google Scholar 

  8. Wang Deliang, Liu Xiaomei, Ahalt, Stanley C., On temporal generalization of simple recurrent networks, Neural Networks, 1996, 9(7):1099–1118.

    Article  Google Scholar 

  9. Li Xiang, Chen Zengqiang, Yuan Zhuzhi, An extended Elman networks-based nonlinear self-tuning controller, Automical Instrument, 1999, 20(12):17–20.

    Google Scholar 

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

    Article  Google Scholar 

  11. Barron, Andrew R., Universal approximation bounds for superpositions of a sigmoidal function, IEEE Trans. Inform. Theory, 1993, 39(3):930–945.

    Article  MATH  Google Scholar 

  12. Chen Tianping, Chen Hong, Liu Ruey-wen, Approximation capability in \(C\left( {\bar R^n } \right)\) by multilayer feedforward networks and related problems, IEEE Trans. Neural Networks, 1995, 6(1):25–30.

    Article  Google Scholar 

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

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This research was supported by the National 863 Project Foundation (863-511-945-010), Tianjin Natural Science Foundation (983602011) and the Young Teacher Foundation of Ministry of Education.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xiang, L., Zengqiang, C. & Zhuzhi, Y. Nonlinear stable adaptive control based upon Elman networks. Appl. Math. Chin. Univ. 15, 332–340 (2000). https://doi.org/10.1007/s11766-000-0058-8

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11766-000-0058-8

1991 MR Subject Classification

Keywords

Navigation