Automation and Remote Control

, Volume 80, Issue 9, pp 1561–1573 | Cite as

Iterative Learning Control Design Based on State Observer

  • J. P. EmelianovaEmail author
  • P. V. PakshinEmail author
Topical Issue


Linear control systems operating in a repetitive mode with a constant period and returning each time to the initial state are considered. The problem is to find a control law that will employ information about the output variable at the current and previous repetitions and also the estimates of state variables from an observer in order to guarantee the convergence of this variable to a reference trajectory under unlimited increasing the repetitions number. This type of control is known as iterative learning control. The problem is solved using the dissipativity of 2D models and the divergent method of vector Lyapunov functions. The final results are expressed in the form of linear matrix inequalities. An example is given.


iterative learning control repetitive processes 2D systems stability dissipativity vector Lyapunov function 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



This work was supported by the Russian Science Foundation, project no. 18-79-00088.


  1. 1.
    Bristow, D.A., Tharayil, M., and Alleyne, A.G., A Survey of Iterative Learning Control, IEEE Control Syst. Magazine, 2006, vol. 23, no. 3, pp. 96–114.Google Scholar
  2. 2.
    Ahn, H.-S., Chen, Y.Q., and Moore, K.L., Iterative Learning Control: Brief Survey and Categorization, IEEE Trans. Syst., Man, Cybernet., Part C: Applications and Reviews, 2007, vol. 37, no. 6, pp. 1099–1121.CrossRefGoogle Scholar
  3. 3.
    Ahn, H.-S., Moore, K.L., and Chen, Y.Q., Iterative Learning Control. Robustness and Monotonic Convergence for Interval Systems, London: Springer-Verlag, 2007.zbMATHGoogle Scholar
  4. 4.
    Arimoto, S., Kawamura, S., and Miyazaki, F., Bettering Operation of Dynamic Systems by Learning: A New Control Theory for Servomechanism or Mechatronic Systems, Proc. 23rd Conf. Decision Control, Las Vegas, 1984, pp. 1064–1069.Google Scholar
  5. 5.
    Arimoto, S., Kawamura, S., and Miyazaki, F., Bettering Operation of Robots by Learning, J. Robot. Syst., 1984, vol. 1, no. 2, pp. 123–140.CrossRefGoogle Scholar
  6. 6.
    Hladowski, L., Galkowski, K., Cai, Z., Rogers, E., Freeman, C., and Lewin, P., Experimentally Supported 2D Systems Based Iterative Learning Control Law Design for Error Convergence and Performance, Control Eng. Pract., 2010, vol. 18, pp. 339–348.CrossRefGoogle Scholar
  7. 7.
    Shen, D. and Wang, Y., Survey on Stochastic Iterative Learning Control, J. Process Control, 2014, vol. 24, pp. 64–77.CrossRefGoogle Scholar
  8. 8.
    Shen, D., A Technical Overview of Recent Progresses on Stochastic Iterative Learning Control, Unmanned Syst., 2018, vol. 6, no. 3, pp. 147–164.CrossRefGoogle Scholar
  9. 9.
    Jayawardhana, R.N. and Ghosh, B.K., Observer Based Iterative Learning Controller Design for MIMO Systems in Discrete Time, Proc. 2018 Ann. Am. Control Conf. (ACC), Milwaukee, 2018, pp. 6402–6408.CrossRefGoogle Scholar
  10. 10.
    Jayawardhana, R.N. and Ghosh, B.K., Kalman Filter Based Iterative Learning Control for Discrete Time MIMO Systems, Proc. 30th Chinese Control and Decision Conf. (2018 CCDC), Shenyang, 2018, pp. 2257–2264.Google Scholar
  11. 11.
    Saab, S.S., A Discrete-Time Stochastic Learning Control Algorithm, IEEE Trans. Autom. Control, 2001, vol. 46, pp. 877–887.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Paszke, W., Rogers, E., and Patan, K., Observer-Based Iterative Learning Control Design in the Repetitive Process Setting, IFAC-PapersOnline, 2017, vol. 50, no. 1, pp. 13390–13395.CrossRefGoogle Scholar
  13. 13.
    Rogers, E., Galkowski, K., and Owens, D.H., Control Systems Theory and Applications for Linear Repetitive Processes, Lect. Notes Control Inform. Sci., vol. 349, Berlin: Springer-Verlag, 2007.zbMATHGoogle Scholar
  14. 14.
    Pakshin, P., Emelianova, J., Emelianov, M., Galkowski, K., and Rogers, E., Dissipivity and Stabilization of Nonlinear Repetitive Processes, Syst. Control Lett., 2016, vol. 91, pp. 14–20.CrossRefzbMATHGoogle Scholar
  15. 15.
    Galkowski, K., Emelianov, M., Pakshin, P., and Rogers, E., Vector Lyapunov Functions for Stability and Stabilization of Differential Repetitive Processes, J. Comput. Syst. Sci. Int., 2016, vol. 55, pp. 503–514.MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Goldsmith, P.B., On the Equivalence of Causal LTI Iterative Learning Control and Feedback Control, Automatica, 2002, vol. 38, no. 4, pp. 703–708.MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Goldsmith, P.B., Author's reply to “On the Equivalence of Causal LTI Iterative Learning Control and Feedback Control,” Automatica, 2004, vol. 40, no. 5, pp. 899–900.MathSciNetCrossRefGoogle Scholar
  18. 18.
    Owens, D.H. and Rogers, E., Comments on “On the Equivalence of Causal LTI Iterative Learning Control and Feedback Control,” Automatica, 2004, vol. 40, no. 5, pp. 895–898.MathSciNetCrossRefGoogle Scholar
  19. 19.
    Willems, J.C., Dissipative Dynamical Systems. Part I: General Theory, Arch. Ration. Mech. Anal., 1972, vol. 45, pp. 321–351.CrossRefzbMATHGoogle Scholar
  20. 20.
    Byrnes, C.I., Isidori, A., and Willems, J.C., Passivity, Feedback Equivalence and the Global Stabilization of Minimun Phase Nonlinear Systems, IEEE Trans. Autom. Control, 1991, vol. 36, pp. 1228–1240.CrossRefzbMATHGoogle Scholar
  21. 21.
    Fradkov, A.L. and Hill, D.J., Exponential Feedback Passivity and Stabilizability of Nonlinear Systems, Automatica, 1998, vol. 34, pp. 697–703.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Arzamas Polytechnic Institute of R.E. Alekseev Nizhny Novgorod State Technical UniversityArzamasRussia

Personalised recommendations