On the convergence of iterative learning control

We derive frequency-domain criteria for the convergence of linear iterative learning control (ILC) on finite-time intervals that are less restrictive than existing ones in the literature. In particular, the former can be used to establish the convergence of ILC in certain cases where the latter are violated. The results cover ILC with non-causal filters and provide insights into the transient behaviors of the algorithm before convergence. We also stipulate some practical rules under which ILC can be applied to a wider range of applications.

[1]  Frank Spitzer,et al.  The Toeplitz Matrices of an Arbitrary Laurent Polynomial. , 1960 .

[2]  J. Ryoo,et al.  Feedback-Based Iterative Learning Control for MIMO LTI Systems , 2008 .

[3]  Z. Zenn Bien,et al.  Decentralized Iterative Learning Control to Large-Scale Industrial Processes for Nonrepetitive Trajectory Tracking , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[4]  Mikael Norrlöf,et al.  Iterative Learning Control : Analysis, Design, and Experiments , 2000 .

[5]  Yongqiang Ye,et al.  Practical Iterative Learning Control with Frequency Domain Design and Sampled Data Implementation , 2014 .

[6]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[7]  J. Kurek,et al.  Iterative learning control synthesis based on 2-D system theory , 1993, IEEE Trans. Autom. Control..

[8]  Albrecht Böttcher,et al.  Spectral properties of banded Toeplitz matrices , 1987 .

[9]  W. Rugh.  Linear System Theory , 1992 .

[10]  L. Vandenberghe,et al.  Interior-Point Algorithms for Semidefinite Programming Problems Derived from the KYP Lemma , 2005 .

[11]  S. Bhattacharyya,et al.  Learning control for robotics , 1989 .

[12]  M. Tomizuka,et al.  Precision Positioning of Wafer Scanners Segmented Iterative Learning Control for Nonrepetitive Disturbances [Applications of Control] , 2007, IEEE Control Systems.

[13]  Kevin L. Moore,et al.  Iterative Learning Control: Brief Survey and Categorization , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[14]  Richard W. Longman,et al.  The Phenomenon of Apparent Convergence Followed by Divergence in Learning and Repetitive Control , 2002, Intell. Autom. Soft Comput..

[15]  E. Rogers,et al.  Iterative Learning Control in Health Care: Electrical Stimulation and Robotic-Assisted Upper-Limb Stroke Rehabilitation , 2012, IEEE Control Systems.

[16]  L. Trefethen,et al.  Eigenvalues and pseudo-eigenvalues of Toeplitz matrices , 1992 .

[17]  Bo Bernhardsson,et al.  Frequency-domain iterative learning control of a marine vibrator , 2016 .

[18]  E. Kreyszig.  Introductory Functional Analysis With Applications , 1978 .

[19]  Svante Gunnarsson,et al.  Time and frequency domain convergence properties in iterative learning control , 2002 .

[20]  Richard W. Longman,et al.  Simple learning control made practical by zero-phase filtering: applications to robotics , 2002 .

[21]  M. V. Bolotnikov,et al.  Time and frequency , 1976 .

[22]  A.G. Alleyne,et al.  A survey of iterative learning control , 2006, IEEE Control Systems.

[23]  Richard W. Longman,et al.  Iterative learning control and repetitive control for engineering practice , 2000 .

[24]  Karl Johan Åström,et al.  Computer-Controlled Systems: Theory and Design , 1984 .

[25]  D. de Roover,et al.  Synthesis of a robust iterative learning controller using an H/sub /spl infin// approach , 1996 .