Skip to main content
SpringerLink
Log in

Adaptive output feedback control for nonlinear time-delay systems using neural network

  • Published:
Journal of Control Theory and Applications Aims and scope Submit manuscript

Abstract

This paper extends the adaptive neural network (NN) control approaches to a class of unknown output feedback nonlinear time-delay systems. An adaptive output feedback NN tracking controller is designed by backstepping technique. NNs are used to approximate unknown functions dependent on time delay. Delay-dependent filters are introduced for state estimation. The domination method is used to deal with the smooth time-delay basis functions. The adaptive bounding technique is employed to estimate the upper bound of the NN approximation errors. Based on Lyapunov-Krasovskii functional, the semi-global uniform ultimate boundedness of all the signals in the closed-loop system is proved. The feasibility is investigated by two illustrative simulation examples.

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. K. Funahashi. On the approximate realization of continuous mappings by neural network[J]. Neural Networks, 1989, 2(1): 183–192.

    Article  Google Scholar 

  2. K. S. Narendra, K. Parthasarathy. Identification and control of dynamic systems using neural networks[J]. IEEE Trans. on Neural Networks, 1990, 1(1): 4–27.

    Article  Google Scholar 

  3. F. L. Lewis, A. Yesildirek, K. Liu. Multilayer neural-net robot controller with guaranteed tracking performance[J]. IEEE Trans. on Neural Networks, 1996, 7(5): 388–398.

    Article  Google Scholar 

  4. M. M. Polycarpou, M. J. Mears. Stable adaptive tracking of uncertain systems using nonlinearly parametrized on-linear approximators[J]. Int. J. Control, 1998, 70(3): 363–384.

    Article  MathSciNet  Google Scholar 

  5. S. Ge, J. Wang. Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems[J]. IEEE Trans. on Neural Networks, 2002, 13(6): 1409–1419.

    Article  Google Scholar 

  6. T. Zhang, S. Ge, C. Hang. Stable adaptive control for a class of nonlinear systems using a modified lyapunov function[J]. IEEE Trans. on Automatic Control, 2000, 45(3): 125–132.

    Google Scholar 

  7. S. Ge, Y. Li, T. Lee. Adaptive NN control for a strict-feedback discrete-time nonlinear systems[J]. Automatica, 2003, 39(4): 807–819.

    Article  MathSciNet  Google Scholar 

  8. A. J. Calise, N. Hovakimyan, M. Idan. Adaptive output feedback control of nonlinear systems using neural networks[J]. Automatica, 2001, 37(6): 1201–1211.

    Article  MathSciNet  Google Scholar 

  9. N. Hovakimyan, F. Nardi, A. Calise, et al. Adaptive output feedback control of uncertain nonlinear systems using single-hidden-layer neural network[J]. IEEE Trans. on Neural Networks, 2002, 13(6): 1420–1431.

    Article  Google Scholar 

  10. J. Y. Choi, J. A. Farrell. Adaptive observer backstepping control using neural networks[J]. IEEE Trans. on Neural Networks, 2001, 12(5): 1103–1112.

    Article  Google Scholar 

  11. J. Stov, J. Y. Choi, J. A. Farrell. Adaptive control for output feedback nonlinear systems in the presence of modeling errors[J]. Automatica, 2001, 38(8): 1761–1767.

    Google Scholar 

  12. S. L. Niculescu. Delay Effects on Stability: A Robust Control Approach[M]. London: Springer-Verlag, 2001.

    Google Scholar 

  13. E. T. Jeung, D. C. Oh, H. B. Park. Delay-dependent control for time-delay t-s fuzzy systems using descriptor representation[J]. Int. J. Control, Automation and Systems, 2004, 2(2): 182–188.

    Google Scholar 

  14. W. Chen, Z. Guan, X. Lu. Delay-dependent output feedback guaranteed cost control for uncertain time-delay systems[J]. Automatica, 2004, 40(6): 1263–1268.

    Article  MathSciNet  Google Scholar 

  15. F. Mazenc, S. Mondie, R. Francisco. Global asymptotic stabilization for feedback systems with delay in the input[J]. IEEE Trans. On Automatic Control, 2004, 49(5): 844–850.

    Article  MathSciNet  Google Scholar 

  16. S. G. Foda, M. S. Mahmound. Adaptive stabilization fo delay diffetential systems with unknown bounds[J]. Int. J. Control, 1998, 70(2): 259–275.

    Article  Google Scholar 

  17. Y. Fu, et al. Output feedback stabilization for time-delay nonlinear systems[J]. Acta Automatica Sinica, 2002, 28(5): 802–805.

    MathSciNet  Google Scholar 

  18. W. Chen, J. Li. Adaptive control for a class of output feedback nonlinear time-delay systems[J]. Control Theory & Applications, 2004, 21(5): 844–847.

    Google Scholar 

  19. S. Ge, F. Hong, T. Lee. Adaptive neural network control of nonlinear systems with unknown time-delays[J]. IEEE Trans. on Automatic Control, 2003, 48(11): 2004–2010.

    Article  MathSciNet  Google Scholar 

  20. S. Ge, H. Hong, T. Lee. Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients[J]. IEEE Trans. on Systems, Man, and Cybernetics, Part B, 2004, 34(1): 499–516.

    Article  MathSciNet  Google Scholar 

  21. D. W. C. Ho, J. M. Li, Y. Gang. Adaptive neural control for a class of nonlinear parametric time delay systems[J]. IEEE Trans. on Neural Networks, 2005, 16(3): 625–635.

    Article  Google Scholar 

  22. J. K. Hale, S. M. Lunel. Introduction to Functional Differential Equations[M]. New York: Springer-Verlag, 1993.

    Google Scholar 

  23. M. Krstic, Kanellakopulos, P. V. Kokotovic. Nonlinear and Adaptive Control Design[M]. New York: Wiley, 1995.

    Google Scholar 

  24. W. Li, C. Qian. Add one power integrator: a tool for global stabilization of high-order lower-triangular systems[J]. Systems & Control Letters, 2000, 39(3): 339–351.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Xidian University, Xi’an, Shaanxi, 710071, China

    Weisheng Chen & Junmin Li

Authors
  1. Weisheng Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Junmin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported by the National Natural Science Foundation of China (No. 60374015) and Shaanxi Province Nature Science Foundation (No. 2003A15).

Weisheng CHEN was born in 1977. He received the B.S. degree in Mathematics Department from Qufu Normal University in 2000, and the M.S. degree in Applied Mathematics from Xidian University in 2004. He is currently a Ph.D. candidate and Lecturer in applied mathematics at Xidian University. His research interests include that nonlinear adaptive control and stochastic control with application in industrial processes.

Junmin LI was born in 1965. He received the B.S. and M.S. degrees in Applied Mathematics from Xidian University, Xi’an, China, in 1987 and in 1989, respectively, and the Ph.D. degree in systems engineering from Xi’an Jiaotong University, Xi’an, China. He is currently a professor in applied mathematics at Xidian University. He research interests include adaptive control, iterative learning control and networked control systems.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, W., Li, J. Adaptive output feedback control for nonlinear time-delay systems using neural network. J. Control Theory Appl. 4, 313–320 (2006). https://doi.org/10.1007/s11768-006-5230-0

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11768-006-5230-0

Keywords

Search

Navigation