Skip to main content
SpringerLink
Log in

Repetitive learning control of nonlinear systems over finite intervals

  • Research Papers
  • Published:
Science in China Series F: Information Sciences Aims and scope Submit manuscript

Abstract

Iterative learning control requires initial repositioning, while the time functions to be learned should be of periodicity in repetitive control. However, there are cases in practice where the time-varying unknowns are not periodic but repetitive, and repetitive learning control is applicable with avoidance of initial repositioning. In this paper, repetitive learning control designs are presented for a broader class of nonlinear systems over finite intervals. The Freeman formula is modified and used for stabilization of the nominal nonlinear time-varying system undertaken. The global stability of the learning system and asymptotic convergence of the tracking error are established through analysis of both partially and fully saturated learning algorithms, respectively. The repetitive learning control method is theoretically shown to be effective in dealing with time-varying parametric uncertainties.

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.

Similar content being viewed by others

References

  1. Moore J R. Combination open cycle closed-cycle systems. Proc Instit Radio Eng, 1951, 39: 1421–1432

    Google Scholar 

  2. Brockett R W. Poles, zeros, and feedback: state space interpretation. IEEE Trans Automat Cntrol, 1965, 10: 129–135

    Article  Google Scholar 

  3. Arimoto S, Kawamura S, Miyazaki F. Bettering operation of robotics by learning. J Robot Syst, 1984, 1: 123–140

    Article  Google Scholar 

  4. Heinzinger G, Fenwick D, Paden B, et al. Robust learning control. In: Proceedings of the 28th IEEE Conference on Decision and Control, Tempa, Florida, USA, 1989. 2640–2645

  5. Arimoto S, Naniwa T, Suzuki H. Robustness of P-type learning control with a forgetting factor for robotic motions. In: Proceedings of the 29th IEEE Conference on Decision and Control, Honolulu, Hawaii, USA, 1990. 436–440

  6. Wang D W. On D-type and P-type ILC designs and anticipatory approach. Int J Control, 2000, 73: 890–901

    Article  MATH  Google Scholar 

  7. Sun M X, Huang B. Iterative Learning Control (in Chinese). Beijing: National Defence Press, 1999

    Google Scholar 

  8. Chen P N, Qin H S, Ye X D. P-type iterative learning control of nonlinear systems with uncertainties. In: Proceedings of the 15th International Conference on Systems Science, Wroclaw, Poland, 2004. 79–86

  9. Lee H S, Bien Z. Study on robustness of iterative learning control with non-zero initial error. Int J Control, 1996, 64: 345–359

    Article  MATH  MathSciNet  Google Scholar 

  10. Porter B, Mohamed S S. Iterative learning control of partially irregular multivariable plants with initial impulsive action. Int J Syst Sci, 1991, 22: 447–454

    Article  MATH  MathSciNet  Google Scholar 

  11. Sun M X, Wang D W. Iterative learning control with initial rectifying action. Automatica. 2002, 38: 1177–1182

    Article  MATH  Google Scholar 

  12. Saab S S. A discrete-time stochastic learning control algorithm. IEEE Trans Automat Control, 2001, 46: 877–887

    Article  MATH  MathSciNet  Google Scholar 

  13. Chen H F. Almost sure convergence of iterative learning control for stochastic systems. Sci China Ser F-Inf Sci, 2003, 46: 67–79

    Article  MATH  Google Scholar 

  14. Park K H. An averaged operator-based PD-type iterative learning control for variable initial state error. IEEE Trans Automa Control, 2005, 50: 865–869

    Article  Google Scholar 

  15. Park B H, Kuc T Y. Adaptive learning control of uncertain robotic systems. Int J Control, 1996, 65: 725–744

    Article  MATH  MathSciNet  Google Scholar 

  16. Xu J X, Tan Y. A composite energy function-based learning control approach for non-linear systems with time-varying parametric uncertainties. IEEE Trans Automat Control, 2002, 47: 1940–1945

    Article  MathSciNet  Google Scholar 

  17. French M, Rogers E. Nonlinear iterative learning by an adaptive Lyapunov technique. Int J Control, 2000, 73: 840–850

    Article  MATH  MathSciNet  Google Scholar 

  18. Choi J Y, Lee J S. Adaptive iterative learning control of uncertain robotic systems. IEE Proc D, 2000, 147: 217–223

    Google Scholar 

  19. Ham C, Qu Z, Kaloust J H. A new framework of learning control for a class of nonlinear systems. In: Proceeding of 1995 IEEE American Control Conference, Seattle, Washington, 1995. 3024–3028

  20. Chien C J, Hsu C T, Yao C Y. Fuzzy system-based adaptive iterative learning control for nonlinear plants with initial state errors. IEEE Trans Fuzzy Syst, 2004, 12: 724–732

    Article  Google Scholar 

  21. Xu J X, Yan R. On initial conditions in iterative learning control. IEEE Trans Automat Control, 2005, 50: 1349–1354

    Article  MathSciNet  Google Scholar 

  22. Xu J X, Tan Y, Lee T H. Iterative learning control design based on composite energy function with input saturation. Automatica, 2004, 40: 1371–1377

    Article  MATH  MathSciNet  Google Scholar 

  23. Inoue T, Nakano M, Kubo T, et al. High accuracy control of a proton synchrotron magnet power supply. In: Proceedings of the 8th IFAC World Congress, Kyoto, 1981. 216–221

  24. Hara S, Yamamoto Y, Omata T, et al. Repetitive control system: A new type servo system for periodic exogenous signals. IEEE Trans Automat Control, 1988, 33: 659–668

    Article  MATH  MathSciNet  Google Scholar 

  25. Tomizuka M, Tsao T C, Chew K K. Analysis and synthesis of discrete-time repetitive controllers. ASME J Dynam Syst, Measure Control, 1989, 111: 353–358

    Article  MATH  Google Scholar 

  26. Sadegh N, Horowitz R, Kao W W, et al. A unified approach to design of adaptive and repetitive controllers for robotic manipulators. ASME J Dynam Syst Measure Control, 1990, 112: 618–629

    Article  Google Scholar 

  27. Messner W, Horowitz R, Kao W W, et al. A new adaptive learning law. IEEE Trans Automat Control, 1991, 36: 188–197

    Article  MATH  MathSciNet  Google Scholar 

  28. Xu J X, Yan R. On repetitive learning control for periodic tracking tasks. IEEE Trans Automat Control, 2006, 51: 1842–1848

    Article  MathSciNet  Google Scholar 

  29. Sun M X, Ge S S. Adaptive repetitive control for a class of nonlinearly parametrzed systems. IEEE Trans Automat Control, 2006, 51: 1684–1688

    Article  MathSciNet  Google Scholar 

  30. Sun M X, Ge S S, Mareels I M Y. Adaptive repetitive learning control of robotic manipulators without the requirement for initial repositioning. IEEE Trans Robot, 2006, 22: 563–568

    Article  Google Scholar 

  31. Xu J X, Qu Z. Robust iterative learning control for a class of nonlinear systems. Automatica, 1998, 34: 983–988

    Article  MATH  MathSciNet  Google Scholar 

  32. Sun M X, Cheng Y, Huang B. Higher-order iterative learning control of nonlinear time-varying systems (in Chinese). Acta Automat Sin, 1994, 20: 360–365

    Google Scholar 

  33. Sun M X, Ge S S. Adaptive repetitive learning control of servo mechanisms. In: Proceedings of the 5th World Congress on Intelligent Control and Automation, Hangzhou, 2004. 1212–1216

  34. Sun M X, He X, Chen B. Repetitive learning control for time-varying robotic systems: a hybrid learning scheme. Acta Automat Sin, 2007, 33: 1189–1195

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Information Engineering, Zhejiang University of Technology, Hangzhou, 310014, China

    MingXuan Sun

  2. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, 639794, Singapore

    DanWei Wang

  3. Department of Mathematics, China Institute of Metrology, Hangzhou, 310018, China

    PengNian Chen

Authors
  1. MingXuan Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. DanWei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. PengNian Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to MingXuan Sun.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sun, M., Wang, D. & Chen, P. Repetitive learning control of nonlinear systems over finite intervals. Sci. China Ser. F-Inf. Sci. 53, 115–128 (2010). https://doi.org/10.1007/s11432-010-0018-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-010-0018-8

Keywords

Search

Navigation