A class of non-contractive, trial-dependent update rules for iterative learning control

In this paper, a family of trial-dependent update laws is studied and contrasted with a class of fixed update laws. In particular, it is investigated whether the principle of equivalent feedback extends to trial-dependent update laws. It turns out that this is not the case. Nonetheless, it is shown that a well-known performance bound arising in feedback control architectures, Bode's sensitivity integral, also applies here.

[1]  Renjeng Su,et al.  An H∞ approach to learning control systems , 1990 .

[2]  Mo Jamshidi,et al.  A learning control scheme with gain estimator , 1991, Proceedings of the 1991 IEEE International Symposium on Intelligent Control.

[3]  G. Meinsma,et al.  On the use of noncausal LTI operators in iterative learning control , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[4]  Peter B. Goldsmith.  On the equivalence of causal LTI iterative learning control and feedback control , 2002, Autom..

[5]  Jian-Xin Xu,et al.  Iterative Learning Control , 1998 .

[6]  D. Owens,et al.  Error convergence in an adaptive iterative learning controller , 2000 .

[7]  W. Burnside.  Theory of Functions , 1899, Nature.

[8]  Eric W. Weisstein,et al.  Eric Weisstein''s World of Mathematics , 1999, WWW 1999.

[9]  D. Owens.  Universal iterative learning control using adaptive high-gain feedback , 1993 .

[10]  Kevin L. Moore,et al.  Iterative Learning Control: An Expository Overview , 1999 .

[11]  Tom Kavli.  Frequency domain synthesis of trajectory learning controllers for robot manipulators , 1992, J. Field Robotics.

[12]  Zeungnam Bien,et al.  Iterative learning control: analysis, design, integration and applications , 1998 .

[13]  Gjerrit Meinsma,et al.  On equivalence classes in iterative learning control , 2003, Proceedings of the 2003 American Control Conference, 2003..

[14]  Y. Cho,et al.  Fixed Point Theory and Applications , 2000 .

[15]  Okko H. Bosgra,et al.  Synthesis of robust multivariable iterative learning controllers with application to a wafer stage motion system , 2000 .

[16]  E. Rogers,et al.  An H∞ approach to linear iterative learning control design , 1996 .

[17]  P. Goldsmith.  The fallacy of causal iterative learning control , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[18]  Michael J. Grimble,et al.  Iterative Learning Control for Deterministic Systems , 1992 .