Analysis of Linear Iterative Learning Control Schemes - A 2D Systems/Repetitive Processes Approach

  • D. H. Owens
  • N. Amann
  • E. Rogers
  • M. French


This paper first develops results on the stability and convergence properties of a general class of iterative learning control schemes using, in the main, theory first developed for the branch of 2D linear systems known as linear repetitive processes. A general learning law that uses information from the current and a finite number of previous trials is considered and the results, in the form of fundamental limitations on the benefits of using this law, are interpreted in terms of basic systems theoretic concepts such as the relative degree and minimum phase characteristics of the example under consideration. Following this, previously reported powerful 2D predictive and adaptive control algorithms are reviewed. Finally, new iterative adaptive learning control laws which solve iterative learning control algorithms under weak assumptions are developed.

repetitive processes iterative learning adaptive control 


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  1. 1.
    S. Arimoto, S. Kawamura, and F. Miyazaki, “Bettering Operations of Robots by Learning,” Journal of Robotic Systems, vol. 1, 1984, pp. 123-140.Google Scholar
  2. 2.
    K. L. Moore, Iterative Learning Control for Deterministic Systems, Advances in Industrial Control Series, London U. K.: Springer-Verlag, 1983.Google Scholar
  3. 3.
    K. L. Moore and J-X Xu (Eds), Special Issue of The International Journal of Control, 2000.Google Scholar
  4. 4.
    Dedicated Web Server for Iterative Learning Control, URL Scholar
  5. 5.
    E. Rogers and D. H. Owens, Stability Analysis for Linear Repetitive Processes, Lecture Notes in Control and Information Series, vol 175, Berlin: Springer-Verlag, 1992.Google Scholar
  6. 6.
    F. Padieu and R. Su, “An H1 Approach to Learning Control Systems,” International Journal of Adaptive Control and Signal Processing, vol. 4, 1990, pp. 465-474.Google Scholar
  7. 7.
    N. Amann, Optimal Algorithms for Iterative Learning Control, PhD Thesis, University of Exeter, U.K., 1996.Google Scholar
  8. 8.
    D. H. Owens, Feedback and Multivariable Systems, London: Peter Peregrinus, 1978.Google Scholar
  9. 9.
    D. H. Owens and D. Neuffer, “Theoretical and Computational Studies and Iterative Learning Control,” Report No. 92/02, School of Engineering and Computer Science, University of Exeter, U. K., 1992.Google Scholar
  10. 10.
    D. H. Owens, A. Wahl, and N. Amann, “Studies in Optimization Based Iterative Learning Control,” Report No. 93/09, School of Engineering and Computer Science, University of Exeter, U. K., 1993.Google Scholar
  11. 11.
    D. J. Clements and B. D. O. Anderson, Singular Optimal Control: The Linear Quadratic Problem, Berlin: Springer-Verlag, 1978.Google Scholar
  12. 12.
    J. C. Willems, A. Kitapci, and L. M. Silverman, “Singular Optimal Control: A Geometric Approach,” SIAM Journal on Control and Optimization, vol. 24, 1986, pp. 323-327.Google Scholar
  13. 13.
    K. Furuta and M. Yamakita, “The Design of a Learning Control System for Multivariable Systems,” In Proceedings of the IEEE International Symposium on Intelligent Control, 1987, pp. 371-376.Google Scholar
  14. 14.
    N. Amann, D. H. Owens and E. Rogers, “Iterative Learning Control Using Optimal Feedback and Feedforward Actions,” International Journal of Control, vol. 65, no. 2, 1996, pp. 277-293.Google Scholar
  15. 15.
    D. W. Marquardt, “An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” Journal of the Society of Industrial and Applied Mathematics, vol. 11, 1963, pp. 431-441.Google Scholar
  16. 16.
    B. D. O. Anderson and J. B. Moore, Optimal Control-Linear Optimal Control, Englewood Cliffs, N. J.: Prentice-Hall, 1989.Google Scholar
  17. 17.
    D. G. Luenberger, Optimization by Vector Space Methods, New York: John Wiley, 1969.Google Scholar
  18. 18.
    B. A. Francis, “The Optimal Linear-Quadratic Time-Invariant Regulator with Cheap Control,” IEEE Transactions on Automatic Control, vol. AC-24, no. 4, 1979, pp. 616-621.Google Scholar
  19. 19.
    H. Kwakernaak and R. Sivan, “The Maximally Achievable Accuracy of Linear Optimal Regulators and Linear Optimal Filters,” IEEE Transactions on Automatic Control, vol. AC-17, no. 1, pp. 79-86.Google Scholar
  20. 20.
    G. Curtelin, B. Caron, and H. Saari, “A Specific Repetitive Control Algorithm for Continuous and Digital Systems: Study and Applications,” In IEE International Conference Control 94, pp. 634-639.Google Scholar
  21. 21.
    C. A. Gari?a, D. M. Prett, and M. Morari, “Model Predictive Control: Theory and Practice-A Survey,” Automatica, vol. 25, 1989, pp 335-348.Google Scholar
  22. 22.
    D. W. Clarke, C. Mohtadi, and P. S. Tuffs, “Generalized Predictive Control,” Automatica, vol. 23, 1987, pp. 137-160.Google Scholar
  23. 23.
    N. Amann, D. H. Owens, and E. Rogers. “Predictive Optimal Iterative Learning Control,” International Journal of Control, vol. 69, no. 2, 1998, pp. 203-226.Google Scholar
  24. 24.
    L. M. Silverman, “Inversion of Multivariable Linear Systems,” IEEE Transactions on Automatic Control, vol. AC 14, 1969, pp. 270-276.Google Scholar
  25. 25.
    T. Kato, Perturbation Theory for Linear Operators, 2nd edition, Berlin: Springer-Verlag.Google Scholar
  26. 26.
    R. E. Skelton, Dynamic Systems Control, New York: Wiley, 1988.Google Scholar
  27. 27.
    A. Ilchmann, “Non-identifier Based Control of Dynamical Systems-A Survey,” IMA Journal of Mathematical Control and Information, vol. 8, 1991, pp. 321-366.Google Scholar
  28. 28.
    G. S. Munde, Adaptive Iterative Learning Control, PhD Thesis, University of Exeter, UK, 1998.Google Scholar
  29. 29.
    B. D. O. Anderson, “A Systems Theoretical Criterion for Positive Real Systems,” SIAM Journal on Control and Optimization, vol. 5, no. 2, 1967, pp. 171-182.Google Scholar
  30. 30.
    D. H. Owens, D. Pratzel-Volters, and A. Ilchmann, “Positive Real Structures and High Gain Adaptive Stabilization,” IMA Journal of Mathematical Control and Information, vol. 4, 1987, pp. 167-181.Google Scholar
  31. 31.
    M. Kristic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and Adaptive Control Design, New York: Wiley, 1995.Google Scholar
  32. 32.
    N. Amann, D. H. Owens, and E. Rogers, “Iterative Learning Control for Discrete-Time Systems with Exponential Rate of Convergence,” Proceedings of The Institution of Electrical Engineers, vol. 143, no. 2, 1996, pp. 217-224.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • D. H. Owens
    • 1
  • N. Amann
    • 2
  • E. Rogers
    • 3
  • M. French
    • 3
  1. 1.Department of Automatic Control and Systems EngineeringUniversity of SheffieldSheffieldUK
  2. 2.Daimlerchrysler, BerlinGermany
  3. 3.Department of Electronics and Computer ScienceUniversity of SouthamptonSouthamptonUK

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