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

Regular Papers Control Theory

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.

Keywords

High-order learning scheme iterative learning control measurement dropout robustness 

References

  1. [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.CrossRefGoogle Scholar
  2. [2]
    Z. Bien and J. X. Xu, “Iterative learning control: analysis, design, integration and applications,” Dordrecht: Kluwer Academic Publishers, 1998CrossRefGoogle Scholar
  3. [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.CrossRefGoogle Scholar
  4. [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.CrossRefGoogle Scholar
  5. [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. [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.MathSciNetCrossRefGoogle Scholar
  7. [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.MathSciNetMATHCrossRefGoogle Scholar
  8. [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.MathSciNetCrossRefGoogle Scholar
  9. [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.MathSciNetCrossRefGoogle Scholar
  10. [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.MathSciNetMATHCrossRefGoogle Scholar
  11. [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.CrossRefGoogle Scholar
  12. [12]
    S. S. Saab, “A discrete-time stochastic learning control algorithm,” IEEE Trans. on Automatic Control, vol. 46, no. 6, pp. 877–887, 2001.MathSciNetMATHCrossRefGoogle Scholar
  13. [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.CrossRefGoogle Scholar
  14. [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.MathSciNetMATHCrossRefGoogle Scholar
  15. [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.CrossRefGoogle Scholar
  16. [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.Google Scholar
  17. [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.CrossRefGoogle Scholar
  18. [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. [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.CrossRefGoogle Scholar
  20. [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.Google Scholar
  21. [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.CrossRefGoogle Scholar
  22. [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.MathSciNetCrossRefGoogle Scholar
  23. [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.CrossRefGoogle Scholar
  24. [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.MathSciNetCrossRefGoogle Scholar
  25. [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.CrossRefGoogle Scholar
  26. [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.Google Scholar
  27. [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.Google Scholar
  28. [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.Google Scholar
  29. [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.CrossRefGoogle Scholar
  30. [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.Google Scholar
  31. [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.Google Scholar
  32. [32]
    M. C. Frank and A. D. Charles, Linear System Theory, Springer-Verlag, 1991.Google Scholar
  33. [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.MathSciNetCrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg  2011

Authors and Affiliations

  1. 1.School of Electrical Engineering & AutomationHenan Polytechnic UniversityJiaozuoChina
  2. 2.Department of Automatic Control, and Advanced Control Systems Laboratory, School of Electronics and Information EngineeringBeijing Jiaotong UniversityBeijingChina

Personalised recommendations