Journal of Systems Science and Complexity

, Volume 32, Issue 2, pp 577–587 | Cite as

Closed-Loop Iterative Learning Control for Discrete Singular Systems with Fixed Initial Shift

  • Panpan Gu
  • Senping TianEmail author
  • Qian Liu


This paper deals with the problem of iterative learning control for a class of discrete singular systems with fixed initial shift. According to the characteristics of the discrete singular systems, a closed-loop learning algorithm is proposed and the corresponding state limiting trajectory is presented. It is shown that the algorithm can guarantee that the system state converges uniformly to the state limiting trajectory on the whole time interval. Then the initial rectifying strategy is introduced to the discrete singular systems for eliminating the effect of the fixed initial shift. Under the action of the initial rectifying strategy, the system state can converge to the desired state trajectory within the pre-specified finite time interval no matter what value the fixed initial shift takes. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.


Closed-loop learning algorithm discrete singular systems fixed initial shift iterative learning control 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Bien Z and Xu J X, Iterative Learning Control: Analysis, Design, Integration and Applications, Kluwer Academic Publishers, Dordrecht, 1998.CrossRefGoogle Scholar
  2. [2]
    Xu J X and Tan Y, Linear and Nonlinear Iterative Learning Control, Springer-Verlag, Berlin, 2003.zbMATHGoogle Scholar
  3. [3]
    Arimoto S, Kawamura S, and Miyazaki F, Bettering operation of robots by learning, Journal of Robotic Systems, 1984, 1(2): 123–140.CrossRefGoogle Scholar
  4. [4]
    Ahn H S, Chen Y Q, and Moore K L, Iterative learning control: Brief survey and categorization, IEEE Transactions on Systems Man and Cybernetics-Part C: Applications and Reviews, 2007, 37(6): 1099–1121.CrossRefGoogle Scholar
  5. [5]
    Bu X H, Yu F S, Hou Z S, et al., Iterative learning control for a class of nonlinear systems with random packet losses, Nonlinear Analysis: Real World Applications, 2013, 14(1): 567–580.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    Hou Z S, Chi R H, and Gao H J, An overview of dynamic-linearization-based data-driven control and applications, IEEE Transactions on Industrial Electronics, 2017, 64(5): 4076–4090.CrossRefGoogle Scholar
  7. [7]
    Chi R H, Hou Z S, Jin S T, et al., An improved data-driven point-to-point ILC using additional on-line control inputs with experimental verification, IEEE Transactions on Systems Man and Cybernetics: Systems, 2017, DOI: 10.1109/TSMC.2017.2693397.Google Scholar
  8. [8]
    Sun M, Ge S S, and Mareels I M Y, Adaptive repetitive learning control of robotic manipulators without the requirement for initial repositioning, IEEE Transactions on Robotics, 2006, 22(3): 563–568.CrossRefGoogle Scholar
  9. [9]
    Chen Y Q, Moore K L, Yu J, et al., Iterative learning control and repetitive control in hard disk drive industry–A tutorial, International Journal of Adaptive Control and Signal Processing, 2008, 22(4): 325–343.CrossRefzbMATHGoogle Scholar
  10. [10]
    Sun H Q, Hou Z S, and Li D, Coordinated iterative learning control schemes for train trajectory tracking with overspeed protection, IEEE Transactions on Automation Science and Engineering, 2013, 10(2): 323–333.CrossRefGoogle Scholar
  11. [11]
    Porter B and Mohamed S S, Iterative learning control of partially irregular multivariable palnts with initial impulsive action, International Journal of Systems Science, 1991, 22(3): 447–454.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    Lee H S and Bien Z, Study on robustness of iterative learning control with non-zero initial error, International Journal of Control, 1996, 64(3): 345–359.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    Park K H, Bien Z, and Hwang D H, A study on the robustness of a PID-type iterative learning controller against initial state error, International Journal of Systems Science, 1999, 30(1): 49–59.CrossRefzbMATHGoogle Scholar
  14. [14]
    Sun M X and Wang D W, Iterative learning control with initial rectifying action, Automatica, 2002, 38(7): 1177–1182.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    Sun M X and Wang D W, Initial shift issues on discrete-time iterative learning control with system relative degree, IEEE Transactions on Automatic Control, 2003, 48(1): 144–148.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    Sun M X, Bi H B, Zhou G L, et al., Feedback-aided PD-type iterative learning control: Initial condition problem and rectifying strategies, Acta Automatica Sinica, 2015, 41(1): 157–164 (in Chinese).zbMATHGoogle Scholar
  17. [17]
    Meng D Y, Jia Y M, and Du J P, Robust ILC with iteration-varying initial state shifts: A 2D approach, International Journal of Systems Science, 2015, 46(1): 1–17.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    Wei Y S and Li X D, Robust higher-order ILC for non-linear discrete-time systems with varying trail lengths and random initial state shifts, IET Control Theory and Applications, 2017, 11(15): 2440–2447.MathSciNetCrossRefGoogle Scholar
  19. [19]
    Dai L Y, Singular Control Systems, Springer-Verlag, New York, 1989.CrossRefzbMATHGoogle Scholar
  20. [20]
    Duan G R, Analysis and Design of Descriptor Linear Systems, Springer-Verlag, New York, 2010.CrossRefzbMATHGoogle Scholar
  21. [21]
    Xu S Y and Lam J, Robust Control and Filtering of Singular Systems, Springer-Verlag, New York, 2006.zbMATHGoogle Scholar
  22. [22]
    Wu L G, Shi P, and Gao H J, State estimation and sliding mode control of Markovian jump singular systems, IEEE Transactions on Automatic Control, 2010, 55(5): 1213–1219.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    Zheng G and Bejarano F J, Observer design for linear singular time-delay systems, Automatica, 2017, 80(6): 1–9.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    Xu Q Y, Zhang Y J, He W L, et al., Event-triggered networked H∞ control of discrete-time nonlinear singular systems, Applied Mathematics and Computation, 2017, 298: 368–382.MathSciNetCrossRefGoogle Scholar
  25. [25]
    Piao F X and Zhang Q L, Iterative learning control for linear singular systems, Control and Decision, 2007, 22(3): 349–356 (in Chinese).Google Scholar
  26. [26]
    Piao F X, Zhang Q L, and Wang Z F, Iterative learning control for a class of singular systems, Acta Automatica Sinica, 2007, 33(6): 658–659 (in Chinese).Google Scholar
  27. [27]
    Tian S P and Zhou X J, State tracking algorithm for a class of singular ILC systems, Journal of Systems Science and Mathematical Sciences, 2012, 32(6): 731–738 (in Chinese).MathSciNetzbMATHGoogle Scholar
  28. [28]
    Gu P P, Fu Q, and Wu J R, State tracking algorithm for linear singular iterative learning control systems with fixed initial shift, Mathematica Applicata, 2017, 30(1): 8–15 (in Chinese).MathSciNetzbMATHGoogle Scholar
  29. [29]
    Tian S P, Liu Q, Dai X S, et al., A PD-type iterative learning control algorithm for singular discrete systems, Advances in Difference Equations, 2016, 2016: 321.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Editorial Office of JSSC & Springer-Verlag GmbH Germany 2019

Authors and Affiliations

  1. 1.School of Automation Science and EngineeringSouth China University of TechnologyGuangzhouChina

Personalised recommendations