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http://dx.doi.org/10.5916/jkosme.2013.37.7.743

Optimal iterative learning control with model uncertainty  

Le, Dang Khanh (Department of Marine Engineering, Mokpo Maritime University)
Nam, Taek-Kun (Division of Marine Engineering, Mokpo Maritime University)
Abstract
In this paper, an approach to deal with model uncertainty using norm-optimal iterative learning control (ILC) is mentioned. Model uncertainty generally degrades the convergence and performance of conventional learning algorithms. To deal with model uncertainty, a worst-case norm-optimal ILC is introduced. The problem is then reformulated as a convex minimization problem, which can be solved efficiently to generate the control signal. The paper also investigates the relationship between the proposed approach and conventional norm-optimal ILC; where it is found that the suggested design method is equivalent to conventional norm-optimal ILC with trial-varying parameters. Finally, simulation results of the presented technique are given.
Keywords
ILC; Optimal control; Model uncertainty; Convex minimization problem; Trial-varying parameters; worst-case norm-optimal ILC;
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1 D. A. Bristow, M. Tharayil, and A. G. Alleyne, "A survey of iterative learning control: a learning based method for high-performance tracking control," IEEE Control Systems Magazine, vol. 26, pp. 96-114, June 2006.   DOI   ScienceOn
2 H.-S. Ahn, Y. Chen, and K. Moore, "Iterative learning control: Brief survey and categorization," Part C: Applications and Reviews, IEEE Transactions on Systems, Man, and Cybernetics, vol. 37, pp. 1099-1121, nov. 2007.
3 T. J. Harte, J. Hatonen, and D. H. Owens, "Discrete-time inverse model-based iterative learning control: stability, monotonicity and robustness," International Journal of Control, vol. 78, no. 8, pp. 577-586, 2005.   DOI   ScienceOn
4 R. W. Longman, "Iterative learning control and repetitive control for engineering practice," International Journal of Control, vol. 73, pp. 930-954, 2000.   DOI   ScienceOn
5 T. Donkers, J. van de Wijdeven, and O. Bosgra, "Robustness against model uncertainties of norm optimal iterative learning control," Proceedings of the American Control Conference, 2008.
6 E. Rogers, J. Lam, K. Galkowski, S. Xu, J. Wood, and D. Owens, "LMI based stability analysis and controller design for a class of 2D discrete linear systems," Proceedings of the 40th IEEE Conference on Decision and Control, vol. 5, pp. 4457-4462, 2001.
7 D. Owens and S. Daley, "Robust gradient iterative learning control: time and frequency domain conditions," International Journal of Modeling, Identification and Control, vol. 4, no. 4, pp. 315-322, 2008.   DOI
8 K. Moore, Y. Chen, and H.-S. Ahn, "Algebraic H1 design of higher-order iterative learning controllers," Proceedings of the IEEE International Symposium on Intelligent Control, pp. 1207-1212, june 2005.
9 D. Bristow and A. Alleyne, "Monotonic convergence of iterative learning control for uncertain systems using a time-varying filter," Automatic Control, IEEE Transactions on, vol. 53, pp. 582-585, march 2008.   DOI   ScienceOn
10 H.-S. Ahn, K. Moore, and Y. Chen, "Monotonic convergent iterative learning controller design based on interval model conversion," IEEE Transactions on Automatic Control, vol. 51, pp. 366-371, Feb. 2006.   DOI   ScienceOn
11 D. H. Nguyen and D. Banjerdpongchai, "A convex optimization approach to robust iterative learning control for linear systems with time-varying parametric uncertainties," Automatica, vol. 47, no. 9, pp. 2039-2043, 2011.   DOI   ScienceOn
12 N. Amann, D. H. Owens, E. Rogers, and A. Wahl, "An H1 approach to linear iterative learning control design," International Journal of Adaptive Control and Signal processing, vol. 10, no. 6, pp. 767-781, 1996.   DOI   ScienceOn
13 D. Roover, "Synthesis of a robust iterative learning controller using an approach," Proceedings of the 35th IEEE Conference on Decision and Control, vol. 3, pp. 3044-3049, dec 1996.
14 K. L. Moore, H.-S. Ahn, and Y. Q. Chen, "Iteration domain optimal iterative learning controller design," International Journal of Robust and Nonlinear Control, vol. 18, no. 10, pp. 1001-1017, 2008.   DOI   ScienceOn
15 J. J. M. van de Wijdeven, M. C. F. Donkers, and O. H. Bosgra, "Iterative learning control for uncertain systems: Non-causal finite time interval robust control design," International Journal of Robust and Nonlinear Control, vol. 21, no. 14, pp. 1645-1666, 2011.   DOI   ScienceOn
16 S. Skogestad and I. Postlethwaite, Multivariable feedback control: analysis and design. John Wiley, 2005.
17 S. Gunnarsson and Mikael Norrlof, "On the design of ILC algorithms using optimization," Automatica, vol. 37, no. 12, pp. 2011-2016, 2001.   DOI   ScienceOn
18 M. Norrlof and S. Gunnarsson, "Time and frequency domain conver-gence properties in iterative learning control," International Journal of Control, vol. 75, no. 14, pp. 1114-1126, 2002.   DOI   ScienceOn
19 K. Barton and A. Alleyne, "A norm optimal approach to time-varying ILC with application to a multi-axis robotic testbed," IEEE Transactions on Control Systems Technology, vol. 19, pp. 166-180, Jan. 2011.   DOI   ScienceOn
20 T. K. Nam and Dang Khanh Le, "A study on the control scheme of vibration isolator with electrical motor", Journal of the Korean Society of Marine Engineering, vol. 36, no. 1, pp. 133-140, 2012.   과학기술학회마을   DOI   ScienceOn
21 S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press, 2004.