Abstract
This paper presents an initial rectifying learning method for trajectory tracking of linear time-invariant systems with rank-defective Markov parameters. The initial shift problem is addressed through introduction of the initial rectifying action. The role of the rectifying action is examined in case of systems with row and column rank-defective Markov parameters, respectively. Sufficient conditions for convergence of the proposed learning algorithms are derived, by which the learning gains can be chosen. It is shown that the output trajectory converges to the desired one with a smooth transition. The merging of the transition to the desired trajectory occurs at a pre-specified time instant.
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Arimoto, S.: Learning control theory for robotic motion. International Journal of Adaptive control and Signal Processing 4, 543–564 (1990)
Sugie, T., Ono, T.: An iterative learning control law for dynamical systems. Automatica 27, 729–732 (1991)
Ahn, H.-S., Choi, C.-H., Kim, K.-B.: Iterative learning control for a class of nonlinear systems. Automatica 29, 1575–1578 (1993)
Porter, B., Mohamed, S.S.: Iterative learning control of partially irregular multivariable plants with initial state shifting. International Journal of Systems Science 22, 229–235 (1991)
Heinzinger, G., Fenwick, D., Paden, B., Miyazaki, F.: Robust learning control. In: Proceedings of the 28th IEEE Conference on Decision and Control, Tempa FL, pp. 436–440 (1989)
Lee, H.-S., Bien, Z.: Study on robustness of iterative learning control with non-zero initial error. International Journal of Control 64, 345–359 (1996)
Porter, B., Mohamed, S.S.: Iterative learning control of partially irregular multivariable plants with initial impulsive action. International Journal of Systems Science 22, 447–454 (1991)
Sun, M., Huang, B.: Iterative Learning Control. National Defence Industrial Press, Beijing (1999)
Sun, M., Wang, D.: Initial condition issues on iterative learning control for nonlinear systems with time delay. International Journal of Systems Science 32, 1365–1375 (2001)
Sun, M., Wang, D.: Iterative learning control with initial rectifying action. Automatica 38, 1177–1182 (2002)
Ortega, J.M., Rheinboldt, W.C.: Iterative solution of nonlinear equations in several variables. Academic Press, New York (1970)
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© 2008 Springer-Verlag Berlin Heidelberg
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Sun, M. (2008). On Initial Rectifying Learning for Linear Time-Invariant Systems with Rank-Defective Markov Parameters. In: Huang, DS., Wunsch, D.C., Levine, D.S., Jo, KH. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Theoretical and Methodological Issues. ICIC 2008. Lecture Notes in Computer Science, vol 5226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87442-3_91
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DOI: https://doi.org/10.1007/978-3-540-87442-3_91
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87440-9
Online ISBN: 978-3-540-87442-3
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