• Dong ShenEmail author
  • Xuefang Li


This chapter provides a rudimentary introduction of iterative learning control (ILC) and its basic formulation for both discrete-time and continuous-time systems, which is followed by a review on recent developments of ILC with iteration-varying trial lengths. At the end of this chapter, the structure/organization of the whole monograph is also presented.


  1. 1.
    Garden M (1967) Learning control of actuators in control systems. US Patent, Appl No 637769Google Scholar
  2. 2.
    Uchiyama M (1978) Formulation of high-speed motion pattern of a mechanical arm by trial. Trans Soc Instrum Control Eng 14(6):706–712CrossRefGoogle Scholar
  3. 3.
    Arimoto S, Kawamura S, Miyazaki F (1984) Bettering operation of robots by learning. J Robotic Syst 1(2):123–140CrossRefGoogle Scholar
  4. 4.
    Bristow DA, Tharayil M, Alleyne AG (2006) A survey of iterative learning control: a learning-based method for high-performance tracking control. IEEE Control Syst Mag 26(3):96–114CrossRefGoogle Scholar
  5. 5.
    Ahn H-S, Chen YQ, Moore KL (2007) Iterative learning control: survey and categorization from 1998 to 2004. IEEE Trans Syst Man Cybern Part C 37(6):1099–1121CrossRefGoogle Scholar
  6. 6.
    Wang Y, Gao F, Doyle FJ III (2009) Survey on iterative learning control, repetitive control and run-to-run control. J Process Control 19(10):1589–1600CrossRefGoogle Scholar
  7. 7.
    Shen D, Wang Y (2014) Survey on stochastic iterative learning control. J Process Control 24(12):64–77CrossRefGoogle Scholar
  8. 8.
    Shen D (2018) Iterative learning control with incomplete information: a survey. IEEE/CAA J Autom Sin 5(5):885–901MathSciNetCrossRefGoogle Scholar
  9. 9.
    Shen D (2018) A technical overview of recent progresses on stochastic iterative learning control. Unmanned Syst 6(3):147–164CrossRefGoogle Scholar
  10. 10.
    Seel T, Schauer T, Raisch J (2011) Iterative learning control for variable pass length systems. In: Proceedings of the 18th IFAC World congress. Milano, Italy, pp 4880–4885, 28 Aug–2 Sept 2011Google Scholar
  11. 11.
    Seel T, Werner C, Schauer T (2016) The adaptive drop foot stimulator - multivariable learning control of foot pitch and roll motion in paretic gait. Med Eng Phys 38(11):1205–1213CrossRefGoogle Scholar
  12. 12.
    Seel T, Werner C, Raisch J, Schauer T (2016) Iterative learning control of a drop foot neuroprosthesis - generating physiological foot motion in paretic gait by automatic feedback control. Control Eng Pract 48:87–97CrossRefGoogle Scholar
  13. 13.
    Longman RW, Mombaur KD (2014) Investigating the use of iterative learning control and repetitive control to implement periodic gaits. Lect Notes Control Inf Sci 340:189–218MathSciNetzbMATHGoogle Scholar
  14. 14.
    Guth M, Seel T, Raisch J (2013) Iterative learning control with variable pass length applied to trajectory tracking on a crane with output constraints. In: Proceedings of the 52nd IEEE conference on decision and control. Florence, Italy, pp 6676–6681Google Scholar
  15. 15.
    Seel T, Schauer T, Raisch J (2017) Monotonic convergence of iterative learning control systems with variable pass length. Int J Control 90(3):393–406MathSciNetCrossRefGoogle Scholar
  16. 16.
    Li X, Xu J-X, Huang D (2014) An iterative learning control approach for linear systems with randomly varying trial lengths. IEEE Trans Autom Control 59(7):1954–1960MathSciNetCrossRefGoogle Scholar
  17. 17.
    Li X, Xu J-X, Huang D (2015) Iterative learning control for nonlinear dynamic systems with randomly varying trial lengths. Int J Adapt Control Signal Process 29(11):1341–1353MathSciNetCrossRefGoogle Scholar
  18. 18.
    Li X, Xu J-X (2015) Lifted system framework for learning control with different trial lengths. Int J Autom Comput 12(3):273–280MathSciNetCrossRefGoogle Scholar
  19. 19.
    Shen D, Zhang W, Wang Y, Chien C-J (2016) On almost sure and mean square convergence of P-type ILC under randomly varying iteration lengths. Automatica 63:359–365MathSciNetCrossRefGoogle Scholar
  20. 20.
    Shen D, Zhang W, Xu J-X (2016) Iterative learning control for discrete nonlinear systems with randomly iteration varying lengths. Syst Control Lett 96:81–87MathSciNetCrossRefGoogle Scholar
  21. 21.
    Li X, Shen D (2017) Two novel iterative learning control schemes for systems with randomly varying trial lengths. Syst Control Lett 107:9–16MathSciNetCrossRefGoogle Scholar
  22. 22.
    Shi J, He X, Zhou D (2016) Iterative learning control for nonlinear stochastic systems with variable pass length. J Frankl Inst 353:4016–4038MathSciNetCrossRefGoogle Scholar
  23. 23.
    Wei Y-S, Li X-D (2017) Varying trail lengths-based iterative learning control for linear discrete-time systems with vector relative degree. Int J Syst Sci 48(10):2146–2156MathSciNetCrossRefGoogle Scholar
  24. 24.
    Liu S, Debbouche A, Wang J (2017) On the iterative learning control for stochastic impulsive differential equations with randomly varying trial lengths. J Comput Appl Math 312:47–57MathSciNetCrossRefGoogle Scholar
  25. 25.
    Liu S, Wang J (2017) Fractional order iterative learning control with randomly varying trial lengths. J Frankl Inst 354:967–992MathSciNetCrossRefGoogle Scholar
  26. 26.
    Meng D, Zhang J (2018) Deterministic convergence for learning control systems over iteration-dependent tracking intervals. IEEE Trans Neural Netw Learn Syst 29(8):3885–3892MathSciNetCrossRefGoogle Scholar
  27. 27.
    Shen D, Xu J-X (2018) Adaptive learning control for nonlinear systems with randomly varying iteration lengths. IEEE Trans Neural Netw Learn Syst.
  28. 28.
    Zeng C, Shen D, Wang J (2018) Adaptive learning tracking for uncertain systems with partial structure information and varying trial lengths. J Frankl Inst 355(15):7027–7055MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.College of Information Science and TechnologyBeijing University of Chemical TechnologyBeijingChina
  2. 2.Department of Electrical and Electronic EngineeringImperial College LondonLondonUK

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