Iterative learning control

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title: "Iterative learning control" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["control-theory"] topic_path: "general/control-theory" source: "https://en.wikipedia.org/wiki/Iterative_learning_control" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

Iterative Learning Control (ILC) is an open-loop control approach of tracking control for systems that work in a repetitive mode.{{Cite journal |author1=S.Arimoto, S. Kawamura |author2=F. Miyazaki | title = Bettering operation of robots by learning | journal = Journal of Robotic Systems | year = 1984 | volume = 1 | issue = 2 | pages = 123–140 | doi = 10.1002/rob.4620010203

Repetition allows the system to sequentially improve tracking accuracy, in effect learning the required input needed to track the reference as closely as possible. The learning process uses information from previous repetitions to improve the control signal, ultimately enabling a suitable control action to be found iteratively. The internal model principle yields conditions under which perfect tracking can be achieved but the design of the control algorithm still leaves many decisions to be made to suit the application. A typical, simple control law is of the form:

:u_{p+1}=u_p +K * e_p

where u_p is the input to the system during the pth repetition, e_p is the tracking error during the pth repetition and K is a design parameter representing operations on e_p.{{Cite book | last = Moore | first = K.L. | year = 1993 | title = Iterative Learning Control for Deterministic Systems | publisher = Springer-Verlag | location = London | isbn = 0-387-19707-9 |author1=Owens D.H. |author2=Feng K. | title = Parameter optimization in iterative learning control | journal = International Journal of Control | date = 20 July 2003 | volume = 76 | issue = 11 | pages = 1059–1069 | doi = 10.1080/0020717031000121410 |s2cid=120288506 }}

In many cases a low-pass filter is added to the input to improve performance. The control law then takes the form

u_{p+1}=Q(u_p +K * e_p)

where Q is a low-pass filtering matrix. This removes high-frequency disturbances which may otherwise be amplified during the learning process.{{Cite magazine | author1 = Bristow, D. A. |author2=Tharayil, M. |author3=Alleyne, A. G.|authorlink3=Andrew G. Alleyne | title = A Survey of Iterative Learning Control A learning-based method for high-performance tracking control |magazine=IEEE Control Systems Magazine | year = 2006 | volume = 26 | pages =96–114

References

  • {{Cite journal |author1=S.Arimoto, S. Kawamura |author2=F. Miyazaki | title = Bettering operation of robots by learning | journal = Journal of Robotic Systems | year = 1984 | volume = 1 | issue = 2 | pages = 123–140 | doi = 10.1002/rob.4620010203
  • {{Cite book | last = Moore | first = K.L. | year = 1993 | title = Iterative Learning Control for Deterministic Systems | publisher = Springer-Verlag | location = London | isbn = 0-387-19707-9
  • {{Cite book |author1=Jian Xin Xu |author2=Ying Tan. | year = 2003 | title = Linear and Nonlinear Iterative Learning Control |url=https://archive.org/details/linearnonlineari00xuji |url-access=limited | publisher = Springer-Verlag | page = 177 | isbn = 3-540-40173-3 |author1-link=Jian Xin Xu }}
  • {{Cite magazine | author1 = Bristow, D. A. |author2=Tharayil, M. |author3=Alleyne, A. G.|authorlink3=Andrew G. Alleyne | title = A Survey of Iterative Learning Control A learning-based method for high-performance tracking control |magazine=IEEE Control Systems Magazine | year = 2006 | volume = 26 | pages =96–114
  • {{Cite journal |author1=Owens D.H. |author2=Feng K. | title = Parameter optimization in iterative learning control | journal = International Journal of Control | date = 20 July 2003 | volume = 76 | issue = 11 | pages = 1059–1069 | doi = 10.1080/0020717031000121410 |s2cid=120288506 }}
  • {{Cite journal |author1=Owens D.H. |author2=Hätönen J. | title = Iterative learning control — An optimization paradigm | journal = Annual Reviews in Control | year = 2005 | volume = 29 | issue = 1 | pages = 57–70 | doi = 10.1016/j.arcontrol.2005.01.003
  • {{Cite journal |author1=Daley S. |author2=Owens D.H. | title = Iterative Learning Control – Monotonicity and Optimization | journal = International Journal of Applied Mathematics and Computer Science | year = 2008 | volume = 18 | issue = 3 | pages = 179–293 | doi = 10.2478/v10006-008-0026-7 | doi-access = free | url = http://zbc.uz.zgora.pl/Content/78717/AMCS_2008_18_3_3.pdf
  • {{Cite journal |author1=Wang Y. |author2=Gao F. |author3=Doyle III, F.J. | title = Survey on iterative learning control, repetitive control, and run-to-run control | journal = Journal of Process Control | year = 2009 | volume = 19 | issue = 10 | pages = 1589–1600 | doi = 10.1016/j.jprocont.2009.09.006

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control-theory