Skip to main content
SpringerLink
Log in

Stability of first and high order iterative learning control with data dropouts

  • Regular Papers
  • Control Theory
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper presents a stability analysis of the iterative learning control (ILC) problem for discrete-time systems when the plants are subject to output measurement data dropouts. It is assumed that data dropout occurs during the data transfers from the plant to the ILC controller, resulting in what is called intermittent ILC. Using the super-vector approach for ILC, the expectation of output error is used to develop conditions for stability of the first order ILC and high order ILC processes. Through the theoretical analysis, it is shown that the convergence of the intermittent ILC is guaranteed although some measurements are missing. The analysis is also supported by numerical 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. S. Arimoto, S. Kawamura, and F. Miyazaki, “Bettering operation of robots by learning,” J. of Robotic Systems, vol. 1, no. 2, pp. 123–140, 1984.

    Article  Google Scholar 

  2. Z. Bien and J. X. Xu, “Iterative learning control: analysis, design, integration and applications,” Dordrecht: Kluwer Academic Publishers, 1998

    Book  Google Scholar 

  3. H. S. Ahn, Y. Chen, and K. L. Moore, “Iterative learning control: brief survey and categorization,” IEEE Trans. on Systems, Man, and Cybernetics-Part C: Applications and Reviews, vol. 37, no. 6, pp. 1099–1121, 2007.

    Article  Google Scholar 

  4. W. S. Chen and L. Zhang, “Adaptive iterative learning control for nonlinearly parameterized systems with unknown time-varying delays,” International Journal of Control, Automation, and Systems, vol. 8, no. 2, pp. 177–186, 2010.

    Article  Google Scholar 

  5. T. Y. Doh and J. R. Ryoo, “Feedback-based iterative learning control for MIMO LTI systems,” International Journal of Control, Automation, and Systems, vol. 6, no. 2, pp. 269–277, 2008.

    Google Scholar 

  6. A. Tayebi and M. B. Zaremba, “Robust iterative learning control design is straightforward for uncertain LTI systems satisfying the robust performance condition,” IEEE Trans. on Automatic Control, vol. 48, no. 1, pp. 101–106, 2003.

    Article  MathSciNet  Google Scholar 

  7. H. S. Ahn, K. L. Moore, and Y. Chen, “Stability analysis of discrete-time iterative learning control systems with interval uncertainty,” Automatica, vol. 43, no. 5, pp. 892–902, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  8. C. K. Yin, J. X. Xu, and Z. S. Hou, “A high-order internal model based iterative learning control scheme for nonlinear systems with time-iterationvarying parameters,” IEEE Trans. on Automatic Control, vol. 55, no. 11, pp. 2665–2670, 2010.

    Article  MathSciNet  Google Scholar 

  9. R. H. Chi, Z. S. Hou, and J. X. Xu, “A discretetime adaptive ILC for systems with iterationvarying trajectory and random initial condition,” Automatica, vol. 44, no. 8, pp. 2207–2213, 2008.

    Article  MathSciNet  Google Scholar 

  10. Y. Q Chen, C. Wen, Z. Gong, and M. Sun, “An iterative learning controller with initial state learning,” IEEE Trans. on Automatic Control, vol. 44, no. 2, pp. 371–376, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  11. M. X. Sun and D. W. Wang, “Initial shift issues on discrete-time iterative learning control with system relative degree,” IEEE Trans. on Automatic Control, vol. 48, no. 1, pp. 144–148, 2003.

    Article  Google Scholar 

  12. S. S. Saab, “A discrete-time stochastic learning control algorithm,” IEEE Trans. on Automatic Control, vol. 46, no. 6, pp. 877–887, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  13. M. Norrlof and S. Gunnarsson, “Disturbance aspects of iterative learning control,” Engineering Applications of Artificial Intelligence, vol. 14, no. 1, pp. 87–94, 2001.

    Article  Google Scholar 

  14. M. Butcher, A. Karimi, and R. Longchamp, “A statistical analysis of certain iterative learning control algorithms,” International Journal of Control, vol. 81, no. 1, pp. 156–166, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  15. M. X. Sun and D. W. Wang, “Iterative learning control design for uncertain dynamic systems with delayed states,” Dynamics and Control, vol. 10, no. 4, pp. 341–357, 2001.

    Article  Google Scholar 

  16. W. S. Chen and Z. Q. Zhang, “Nonlinear adaptive learning control for unknown time-varying parameters and unknown time-varying delays,” Asian Journal of Control, in press.

  17. J. P. Hespanha, P. Naghshtabrizi, and Y. G. Xu, “A survey of recent results in networked control systems,” Proc. of the IEEE, vol. 95, no. 1, pp. 138–162, 2007.

    Article  Google Scholar 

  18. W. Zhang, M. S. Branicky, and S. M. Phillips, “Stability of networked control systems,” IEEE Control Systems magazine, vol. 21, no. 1, pp. 85–99, 2001.

    Google Scholar 

  19. Y. L. Wang and G. H. Yang, “Robust H ∞ model reference tracking control for networked control systems with communication constraints,” International Journal of Control, Automation and Systems, vol. 7, no. 6, pp. 992–1000, 2009.

    Article  Google Scholar 

  20. M. Yu, L. Wang, T. G. Chu, and G. M. Xie, “Stabilization of networked control systems with data packet dropout and network delays via switching system approach,” Proe. of the 43rd IEEE Conference on Decision and Control, pp. 14–17, 2004.

  21. T. G. Jia, Y. G. Niu, and X. Wang, “H ∞ control for networked systems with data packet dropout,” International Journal of Control, Automation and Systems, vol. 8, no. 2, pp. 198–203, 2010.

    Article  Google Scholar 

  22. P. Seiler and R. Sengupta, “An H ∞ approach to networked control,” IEEE Trans. on Automatic Control, vol. 50, no. 3, pp. 356–364, 2005.

    Article  MathSciNet  Google Scholar 

  23. F. W. Yang, W. Wang, Y. G. Niu, and Y. M. Li, “Observer-based H ∞ control for networked systems with consecutive packet delays and losses,” International Journal of Control, Automation and Systems, vol. 8, no. 4, pp. 769–775, 2010.

    Article  Google Scholar 

  24. Q. Ling and M. D. Lemmon, “Power spectral analysis of networked control systems with data dropouts,” IEEE Trans. on Automatic Control, vol. 49, no. 6, pp. 955–960, 2004.

    Article  MathSciNet  Google Scholar 

  25. X. L. Zhao, S. M. Fei, and C. Y. Sun, “Impulsive controller design for singular networked control systems with packet dropouts,” International Journal of Control, Automation and Systems, vol. 7, no. 6, pp. 1020–1025, 2009.

    Article  Google Scholar 

  26. H.-S. Ahn, Y. Chen, and K. L. Moore, “Intermittent iterative learning control,” Proc. of the IEEE Int. Symposium on Intelligent Control, Germany, pp. 832–837, 2006.

  27. H. S. Ahn, Y. Q. Chen, and K. L. Moore, “Discrete-time intermittent iterative learning control with independent data dropouts,” Proc. of 17th IFAC world congress, Korea, pp. 12442–12447, 2008.

  28. C. P. Liu, J. X. Xu, and J. Wu, “Iterative learning control for network systems with communication delay or data dropout,” Proe. of the 48th IEEE Conference on Decision and Control, China, pp. 4858–4863, 2009.

  29. X. H. Bu and Z. S. Hou, “Stability of iterative learning control with data dropouts via asynchronous dynamical system,” International Journal of Automation and Computing, vol. 8, no. 1, pp. 29–36, 2011.

    Article  Google Scholar 

  30. K. L. Moore, Y. Chen, and H. S. Ahn, “Iterative learning control: a tutorial and big picture view,” Proc. of 45th IEEE Conference on Decision and Control, pp. 2352–2357, 2006.

  31. K. L. Moore, “An observation about monotonic convergence in discrete-time, P-type iterative learning control,” Proc. of IEEE International Symposium on ISIC’01, MX, USA. 2001.

  32. M. C. Frank and A. D. Charles, Linear System Theory, Springer-Verlag, 1991.

  33. M. Norrlof and S. Gunnarsson, “Time and frequency domain convergence properties in iterative learning control,” International Journal of Control, vol. 75, no. 14, pp. 1114–1126, 2002.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electrical Engineering & Automation, Henan Polytechnic University, Jiaozuo, China

    Xuhui Bu & Fashan Yu

  2. Department of Automatic Control, and Advanced Control Systems Laboratory, School of Electronics and Information Engineering, Beijing Jiaotong University, Beijing, China

    Zhongsheng Hou

Authors
  1. Xuhui Bu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhongsheng Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fashan Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xuhui Bu.

Additional information

Recommended by Editorial Board member Euntai Kim under the direction of Editor Young Il Lee. This work was supported by State Key Program (No.60834001) of National Natural Science Foundation of China and Program for Science & Technology Innovation Talents of Henan Province (No.104200510021).

Xuhui Bu received his Bachelor’s and Master’s degree in Automation Control from Henan Polytechnic University, JiaoZuo, China, in 2004 and 2007, respectively, and his Ph.D. degree in Control Thoery and Application from Beijing Jiaotong University, Beijing, China, in 2011. He is currently an Associate Professor in Henan Polytechnic University, JiaoZuo, China. His research is mainly related to data-driven control, iterative learning control, traffic control, etc.

Zhongsheng Hou received his Bachelor’s and Master’s degrees in Applied Mathematics from Jilin University of Technology, Changchun, China, in 1983 and 1988, respectively, and his Ph.D. degree in Control Theory from Northeastern University, Shenyang, China, in 1994. From 1988 to 1992, he was a Lecturer with the Department of Applied Mathematics, Shenyang Polytechnic University. He was a Postdoctoral Fellow with the Harbin Institute of Technology, Harbin, China, from 1995 to 1997 and a Visiting Scholar with Yale University, New Haven, CT, from 2002 to 2003. In 1997, he joined the Beijing Jiaotong University, Beijing, China, and is currently a Full Professor with the Department of Automatic Control. His research interests lie in the fields of the model free adaptive control, learning control, and intelligent transportation systems. He is the author of the monograph Nonparametric Model and its Adaptive Control Theory (Science Press of China) and the holder of the patent invention Model Free Control Technique Chinese Patent (ZL 94 112504. 1) issued in 2000.

Fashan Yu received his B.S. degree in Automation from Henan Polytechnic University, Jiaozuo, China, in 1977. He is currently a Professor and Dean of School of Electrical Engineering & Automation in Henan Polytechnic University. In 2006, he was appointed as the Director of National Electrical & Electronic Experiment Center, and a member of teaching guide committee on Automation organized by the Ministry of Education. His current research interests include industrial process control, PLC control, computer simulation, AC-DC speed control system, etc. He is author and co-author of numerous papers and of several books in the field of Control Theory and Control Engineering.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bu, X., Hou, Z. & Yu, F. Stability of first and high order iterative learning control with data dropouts. Int. J. Control Autom. Syst. 9, 843–849 (2011). https://doi.org/10.1007/s12555-011-0504-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-011-0504-9

Keywords

Search

Navigation