Skip to main content
SpringerLink
Log in

Observer-based adaptive iterative learning control for nonlinear systems with time-varying delays

  • Published:
International Journal of Automation and Computing Aims and scope Submit manuscript

Abstract

An observer-based adaptive iterative learning control (AILC) scheme is developed for a class of nonlinear systems with unknown time-varying parameters and unknown time-varying delays. The linear matrix inequality (LMI) method is employed to design the nonlinear observer. The designed controller contains a proportional-integral-derivative (PID) feedback term in time domain. The learning law of unknown constant parameter is differential-difference-type, and the learning law of unknown time-varying parameter is difference-type. It is assumed that the unknown delay-dependent uncertainty is nonlinearly parameterized. By constructing a Lyapunov-Krasovskii-like composite energy function (CEF), we prove the boundedness of all closed-loop signals and the convergence of tracking error. A simulation example is provided to illustrate the effectiveness of the control algorithm proposed in this paper.

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. L. Moor. Iterative Learning Control for Deterministic Systems, Advances in Industrial Control Series, London, UK: Springer-Verlag, 1993.

    Google Scholar 

  2. D. H. Owens, M. Tomas-Rodriguez, J. J. Hatonen. Limiting behaviour in parameter optimal iterative learning control. International Journal of Automation and Computing, vol.3, no. 3, pp. 222–228, 2006.

    Article  Google Scholar 

  3. H. F. Chen, H. T. Fang. Output tracking for nonlinear stochastic systems by iterative learning control. IEEE Transactions on Automatic Control, vol. 49, no. 4, pp. 583–588, 2004.

    Article  MathSciNet  Google Scholar 

  4. D. H. Owens. Universal iterative learning control using adaptive high gain feedback. International Journal of Adaptive Control and Signal Processing, vol. 7, no. 5, pp. 383–388, 2007.

    Article  MathSciNet  Google Scholar 

  5. T. Y. Kuc, W. G. Han. An adaptive PID learning control of robot manipulators. Automatica, vol. 36, no. 5, pp. 717–725, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  6. B. H. Park, T. Y. Kuc, J. S. Li. Adaptive learning control of uncertain robotic systems. International Journal of Control, vol. 65, no. 5, pp. 725–744, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  7. W. G. Seo, B. H. Park, J. S. Li. Intelligent learning control for a class of nonlinear dynamic systems. IEE Proceedings: Control Theory and Application, vol. 146, no. 2, pp. 165–170, 2000.

    Article  Google Scholar 

  8. J. Y. Choi, J. S. Lee. Adaptive iterative learning control of uncertain robotic systems. IEE Proceedings: Control Theory and Application, vol. 147, no. 2, pp. 217–223, 2000.

    Article  Google Scholar 

  9. M. French, E. Rogers. Non-linear iterative learning by an adaptive Lypunov technique. International Journal of Control, vol. 73, no. 10, pp. 840–850, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  10. A. Tayebi. Adaptive iterative learning control for robot manipulators. Automatica, vol. 40, no. 7, pp. 1195–1203, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  11. Y. C. Wang, C. J. Chien, C. C. Teng. Direct adaptive iterative learning control of nonlinear systems using an output-recurrent fuzzy neural network. IEEE Transactions on Systems, Man, and Cybernetics — Part B, vol. 34, no. 3, pp. 1348–1359, 2004.

    Article  Google Scholar 

  12. J. X. Xu, B. Viswanathan. Adaptive robust iterative learning control with dead zone scheme. Automatica, vol. 36, no. 1, pp. 91–99, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  13. J. X. Xu, Y. Tian. A composite energy function-based learning control approach for nonlinear systems with time-varying parametric uncertainties. IEEE Transactions on Automatic Control, vol. 47, no. 11, pp. 1940–1945, 2002.

    Article  Google Scholar 

  14. J. X. Xu, J. Xu. On iterative learning from different tracking tasks in the presence of time-varying uncertainties. IEEE Transactions on Systems, Man, and Cybernetics — Part B, vol. 34, no. 1, pp. 589–597, 2004.

    Article  Google Scholar 

  15. J. X. Xu, R. Yan. On initial conditions in iterative learning control. IEEE Transactions on Automatic Control, vol. 50, no. 9, pp. 1349–1354, 2005.

    Article  MathSciNet  Google Scholar 

  16. J. X. Xu, Y. Tan. Linear and Nonlinear Iteration Learning Control, Lecture Notes in Control and Information Sciences, Springer, 2003.

  17. S. Hara, Y. Yamamoto, T. Omata, M. Nakano. Repetitive control system: A new type servo system for periodic exogenous signals. IEEE Transactions on Automatic Control, vol. 33, no. 7, pp. 659–668, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  18. X. D. Li, T. W. S. Chow, J. K. L. Ho, H. Z. Tan. Repetitive learning control of nonlinear continuous-time systems using quasi-sliding mode. IEEE Transactions on Control System Technology, vol. 15, no. 2, pp. 369–374, 2007.

    Article  Google Scholar 

  19. W. E. Dixon, E. Zergeroglu, D. M. Dawsan, B. T. Costic. Repetitive learning control: A Lyapunov-based approach. IEEE Transactions on Systems, Man, and Cybernetics — Part B: Cybernetics, vol. 32, no. 4, pp. 538–545, 2002.

    Article  Google Scholar 

  20. M. Sun, S. S. Ge, I. M. Y. Mareels. Adaptive repetitive learning control of robotic manipulators without the requirement for initial repositioning. IEEE Transactions on Robotics, vol. 22, no. 3, pp. 563–568, 2006.

    Article  Google Scholar 

  21. J. X. Xu, R. Yan. On repetitive learning control for periodic tracking tasks. IEEE Transactions on Automatic Control, vol. 51, no. 11, pp. 1842–1848, 2006.

    Article  MathSciNet  Google Scholar 

  22. Z. H. Qu, J. X. Xu. Model based learning control and their comparisons using Lyapunov direct method. Asian Journal of Control, vol. 4, no. 1, pp. 99–110, 2002.

    Article  Google Scholar 

  23. Y. P. Tian, X. Yu. Robust learning control for a class of nonlinear systems with periodic and aperiodic uncertainties. Automatica, vol. 39, no. 11, pp. 1957–1966, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  24. A. Tayebi. Analysis of two particular iterative learning control schemes in frequency and time domains. Automatica, vol. 43, no. 9, pp. 1565–1572, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  25. S. Liuzzo, R. Marino, P. Tomei. Adaptive learning control of linear systems by output error feedback. Automatica, vol. 43, no. 4, pp. 669–676, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  26. S. Liuzzo, R. Marino, P. Tomei. Adaptive learning control of nonlinear systems by output error feedback. IEEE Transactions on Automatic Control, vol. 52, no. 7, pp. 1232–1248, 2007.

    Article  MathSciNet  Google Scholar 

  27. R. W. Longman. Iterative learning control and repetitive control for engineer practice. International Journal of Control, vol. 73, no. 10, pp. 930–954, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  28. J. X. Xu. A new periodic adaptive control approach for time-varying parameters with known periodicity. IEEE Transactions on Automatic Control, vol. 49, no. 4, pp. 579–583, 2004.

    Article  Google Scholar 

  29. J. X. Xu, J. Xu. Observer based learning control for a class of nonlinear systems with time-varying parametric uncertainties. IEEE Transactions on Automatic Control, vol. 49, no. 2, pp. 275–281, 2004.

    Article  Google Scholar 

  30. K. H. Park, Z. Bien, D. H. Hwang. Design of an iterative learning controller for a class of linear dynamic systems with time delay. IEE Proceedings: Control Theory and Applications, vol. 145, no. 6, pp. 507–512, 1998.

    Article  Google Scholar 

  31. X. D. Li, T. W. S. Chow, J. K. L. Ho. 2-D system theory based iterative learning control for linear continuous systems with time delays. IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 52, no. 7, pp. 1421–1430, 2005.

    Article  MathSciNet  Google Scholar 

  32. H. Wu. Design of iterative learning controllers for linear discrete systems with multiple time delays. IEEJ Transactions on Electronics, Information and Systems, vol. 126, no. 9, pp. 1138–1143, 2006.

    Article  Google Scholar 

  33. S. L. Niculescu. Delay Effects on Stability: A Robust Control Approach, Lecture Notes in Control and Information Sciences, Springer-Verlag, 2001.

  34. Y. S. Fu, Z. H. Tian, S. J. Shi. Output feedback stabilization for a class of stochastic time-delay nonlinear systems. IEEE Transactions on Automatic Control, vol. 50, no. 6, 847–851, 2005.

    Article  MathSciNet  Google Scholar 

  35. C. C. Hua, X. P Guan, P. Shi. Robust backstepping control for a class of time delay systems. IEEE Transactions on Automatic Control, vol. 50, no. 6, pp. 894–899, 2005.

    Article  MathSciNet  Google Scholar 

  36. X. H. Jiao, T. L. Shen. Adaptive feedback control of nonlinear time-delay systems: The Lasalle-Razumikhin-based approach. IEEE Transactions on Automatic Control, vol. 50, no. 11, pp. 1909–1913, 2005.

    Article  MathSciNet  Google Scholar 

  37. F. Hong, S. S. Ge, T. H. Lee. Practical adaptive neural control of nonlinear systems with unknown time delay. IEEE Transactions on Systems, Man, and Cyberhetics — Part B, vol. 35, no. 4, pp. 849–854, 2005.

    Article  Google Scholar 

  38. D. W. C. Ho, J. M. Li, Y. G. Niu. Adaptive neural control for a class of nonlinearly parametric time-delay systems. IEEE Transactions on Neural Networks, vol. 16, no. 3, pp. 625–635, 2005.

    Article  Google Scholar 

  39. W. S. Chen, J. M. Li. Adaptive output feedback control for nonlinear time-delay systems using neural networks. Journal of Control Theory and Application, vol. 4, no. 4, pp. 313–320, 2006.

    Article  MATH  Google Scholar 

  40. W. S. Chen, J. M. Li. Adaptive output-feedback regulation for nonlinear delayed systems using neural network. International Journal of Automation and Computing, vol.5, no. 1, pp. 103–108, 2008.

    Article  Google Scholar 

  41. W. S. Chen, Y. L. Wang, J. M. Li. Adaptive learning control for nonlinear parameterized systems with periodically time-varying delays. Acta Automatica Sinica, vol. 34, no. 12, pp. 1556–1560, 2008. (in Chinese)

    Article  MathSciNet  Google Scholar 

  42. W. S. Chen. Novel Adaptive learning control of linear systems with completely unknown time delays. International Journal of Automation and Computing, vol. 6, no. 2, pp. 177–185, 2009.

    Article  Google Scholar 

  43. S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory, Philadelphia PA, USA: SIAM, 1994.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Wei-Sheng Chen, Rui-Hong Li & Jing Li

Authors
  1. Wei-Sheng Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rui-Hong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jing Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wei-Sheng Chen.

Additional information

This work was supported by National Natural Science Foundation of China (No. 60804021, No. 60702063).

Wei-Sheng Chen received the B. Sc. degree in 2000 from the Department of Mathematics of Qufu Normal University, Qufu, PRC, and the M. Sc. and Ph.D. degrees from the Department of Applied Mathematics of Xidian University, Xi’an, PRC in 2004 and 2007, respectively. From 2008 to 2009, he was a visiting scholar in the Automation School at Southeast University, Nanjing, PRC. Since 2009, he has been a post doctoral candidate in the School of Electronic Engineering, Xidian University, and is currently an associate professor in the Department of Applied Mathematics, Xidian University.

His research interests include adaptive control, learning control, neural network control, backstepping control for uncertain nonlinear systems such as time-delay or stochastic nonlinear systems.

Rui-Hong Li received the B. Sc. degree in 2003 from the Department of Applied Mathematics of Xidian University, Xi’an, PRC, and the M. Sc. and Ph.D. degrees from the Department of Applied Mathematics of Northwestern Polytechnical University in 2006 and 2009, respectively. She is currently a lecture in the Department of Applied Mathematics, Xidian University.

Her research interests include chaos control and synchronization, random dynamic systems, and complex network.

Jing Li received the B. Sc. degree in 2001 from the Department of Mathematics of Henan University, Kaifeng, PRC, and M. Sc. degree from the Department of Applied Mathematics of Xidian University, Xi’an, PRC in 2004. She is currently a Ph.D. candidate in the Department of Applied Mathematics, Xidian University.

Her research interests include neural network control and adaptive backstepping control.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, WS., Li, RH. & Li, J. Observer-based adaptive iterative learning control for nonlinear systems with time-varying delays. Int. J. Autom. Comput. 7, 438–446 (2010). https://doi.org/10.1007/s11633-010-0525-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11633-010-0525-5

Keywords

Search

Navigation