zbMATH — the first resource for mathematics

Varying-order iterative learning control against perturbed initial conditions. (English) Zbl 1202.93053
Summary: A homing mechanism is required for repositioning as a system performs tasks repeatedly. By examining the effect of poor repositioning on the tracking performance of iterative learning control, this paper develops a varying-order learning approach for the performance improvement. Through varying-order learning, the resultant system output trajectory is ensured to follow a given trajectory with a lowered error bound, in comparison with the conventional fixed-order method. A discrete-time initial rectifying action is introduced in the formed varying-order learning algorithm, and a sufficient condition for convergence is derived. An implementable scheme is presented based on the proposed approach, and illustrated by numerical results of two examples of robotic manipulators.

93C10 Nonlinear systems in control theory
93C55 Discrete-time control/observation systems
93C85 Automated systems (robots, etc.) in control theory
68T05 Learning and adaptive systems in artificial intelligence
Full Text: DOI
[1] Arimoto, S.; Kawamura, S.; Miyazaki, F., Bettering operation of robots by learning, Journal of robotic systems, 1, 2, 123-140, (1984)
[2] Arimoto, S., Learning control theory for robotic motion, International journal of adaptive control and signal processing, 4, 543-564, (1990) · Zbl 0738.93052
[3] G. Heinzinger, D. Fenwick, B. Paden, F. Miyazaki, Robust learning control, in: Proceedings of the 28th IEEE Conference on Decision and Control, Tempa, FL, USA, December 1989, pp. 436-440.
[4] S. Arimoto, T. Naniwa, H. Suzuki, Selective learning with a forgetting factor for robotic motion control, in: Proceedings of the 1991 IEEE International Conference on Robotics and Automation, Sacramento, CA, USA, 1991, pp. 728-733.
[5] Bien, Z.; Huh, K.M., Higher-order iterative learning control algorithm, IEE proceedings—control theory and applications, 136, 3, 105-112, (1989) · Zbl 0731.93047
[6] Wang, D.; Soh, Y.C.; Cheah, C.C., Robust motion and force control of constrained manipulators by learning, Automatica, 31, 2, 257-262, (1995) · Zbl 0825.93478
[7] Saab, S.S.; Vogt, W.G.; Mickle, M.H., Learning control algorithms for tracking “slowly” varying trajectories, IEEE transactions on systems, man, and cybernetics—part B: cybernetics, 27, 4, 657-670, (1997)
[8] Saab, S.S., Optimal selection of the forgetting matrix into an iterative learning control algorithm, IEEE transactions on automatic control, 50, 12, 2039-2043, (2005) · Zbl 1365.93558
[9] Chien, C.J., A discrete iterative learning control for a class of nonlinear time-varying systems, IEEE transactions on automatic control, 43, 5, 748-752, (1998) · Zbl 0917.93040
[10] Sun, M.; Wang, D., Analysis of nonlinear discrete-time systems with higher-order iterative learning control, Dynamics and control, 11, 1, 81-96, (2001) · Zbl 0999.93037
[11] Hwang, D.-H.; Bien, Z.; Oh, S.-R., Iterative learning control method for discrete-time dynamic systems, IEE proceedings—control theory and applications, 138, 2, 139-144, (1991) · Zbl 0738.93019
[12] Jang, T.-J.; Ahn, H.-S.; Choi, C.-H., Iterative learning control for discrete-time nonlinear systems, International journal of systems science, 25, 7, 1179-1189, (1994) · Zbl 0800.93760
[13] Xu, J.-X., Analysis of iterative learning control for a class of nonlinear discrete-time systems, Automatica, 33, 10, 1905-1907, (1997) · Zbl 0885.93031
[14] Wang, D., Convergence and robustness of discrete time nonlinear systems with iterative learning control, Automatica, 32, 11, 1445-1448, (1998) · Zbl 0961.93029
[15] Saab, S.S., Robustness and convergence rate of a discrete-time learning control algorithm for a class of nonlinear systems, International journal on robust and nonlinear control, 9, 559-571, (1999) · Zbl 0966.93072
[16] Lee, H.-S.; Bien, Z., Study on robustness of iterative learning control with non-zero initial error, International journal of control, 64, 3, 345-359, (1996) · Zbl 0850.93275
[17] S. Arminto, S. Kawamura, F. Miyazaki, Bettering operation of dynamic systems by learning: a new control theory for servomechanism or mechatronics systems, in: Proceedings of the 28th IEEE Conference on Decision and Control, Las Vegas, NV, USA, 1984, pp. 1064-1069.
[18] Park, K.-H.; Bien, Z., A generalized iterative learning controller against initial state error, International journal of control, 73, 10, 871-881, (2000) · Zbl 1006.93601
[19] Choi, C.-H.; Jeong, G.-M., Perfect tracking for maximum-phase nonlinear systems by iterative learning control, International journal of systems science, 32, 9, 1177-1183, (2001) · Zbl 1009.93031
[20] Hillenbrand, S.; Pandit, M., An iterative learning controller with reduced sampling rate for plants with variations of initial states, International journal of control, 73, 10, 882-889, (2000) · Zbl 1006.93597
[21] Sun, M.; Wang, D., Iterative learning control with initial rectifying action, Automatica, 38, 7, 1177-1182, (2002) · Zbl 1002.93508
[22] Sun, M.; Wang, D., Initial shift issues on discrete-time iterative learning control with system relative degree, IEEE transactions on automatic control, 48, 1, 144-148, (2003) · Zbl 1364.93890
[23] Nijmeijer, H.; van der Schaft, A.J., Nonlinear dynamical control systems, (1990), Springer-Verlag New York · Zbl 0701.93001
[24] Horn, R.A.; Johnson, C.R., Matrix analysis, (1985), Cambridge University Press Cambridge · Zbl 0576.15001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.