Repetitive learning control of nonlinear systems over finite intervals

Science in China, Series F: Information Sciences

Volumn 53, Issue 1, 2010, Pages 115-128

  Sun, MingXuan ^a   Wang, DanWei ^b   Chen, PengNian ^c  

^a ZHEJIANG UNIVERSITY OF TECHNOLOGY   (China)

^b NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^c CHINA JILIANG UNIVERSITY   (China)

Author keywords

Convergence; Initial condition problem; Iterative learning control; Nonlinear systems; Repetitive control; Repetitive learning control

Indexed keywords

EID: 76149108797     PISSN: 10092757     EISSN: 18622836     Source Type: Journal    
DOI: 10.1007/s11432-010-0018-8     Document Type: Article

References (34)

1. Moore J R. Combination open cycle closed-cycle systems. Proc Instit Radio Eng, 1951, 39: 1421-1432.
2. Brockett R W. Poles, zeros, and feedback: state space interpretation. IEEE Trans Automat Cntrol, 1965, 10: 129-135.
3. Arimoto S, Kawamura S, Miyazaki F. Bettering operation of robotics by learning. J Robot Syst, 1984, 1: 123-140.
4. Heinzinger G, Fenwick D, Paden B, et al. Robust learning control. In: Proceedings of the 28th IEEE Conference on Decision and Control, Tempa, Florida, USA, 1989. 2640-2645.
5. Arimoto S, Naniwa T, Suzuki H. Robustness of P-type learning control with a forgetting factor for robotic motions. In: Proceedings of the 29th IEEE Conference on Decision and Control, Honolulu, Hawaii, USA, 1990. 436-440.
6. Wang D W. On D-type and P-type ILC designs and anticipatory approach. Int J Control, 2000, 73: 890-901.
7. Sun M X, Huang B. Iterative Learning Control (in Chinese). Beijing: National Defence Press, 1999.
8. Chen P N, Qin H S, Ye X D. P-type iterative learning control of nonlinear systems with uncertainties. In: Proceedings of the 15th International Conference on Systems Science, Wroclaw, Poland, 2004. 79-86.
9. Lee H S, Bien Z. Study on robustness of iterative learning control with non-zero initial error. Int J Control, 1996, 64: 345-359.
10. Porter B, Mohamed S S. Iterative learning control of partially irregular multivariable plants with initial impulsive action. Int J Syst Sci, 1991, 22: 447-454.
11. Sun M X, Wang D W. Iterative learning control with initial rectifying action. Automatica. 2002, 38: 1177-1182.
12. Saab S S. A discrete-time stochastic learning control algorithm. IEEE Trans Automat Control, 2001, 46: 877-887.
13. Chen H F. Almost sure convergence of iterative learning control for stochastic systems. Sci China Ser F-Inf Sci, 2003, 46: 67-79.
14. Park K H. An averaged operator-based PD-type iterative learning control for variable initial state error. IEEE Trans Automa Control, 2005, 50: 865-869.
15. Park B H, Kuc T Y. Adaptive learning control of uncertain robotic systems. Int J Control, 1996, 65: 725-744.
16. Xu J X, Tan Y. A composite energy function-based learning control approach for non-linear systems with time-varying parametric uncertainties. IEEE Trans Automat Control, 2002, 47: 1940-1945.
17. French M, Rogers E. Nonlinear iterative learning by an adaptive Lyapunov technique. Int J Control, 2000, 73: 840-850.
18. Choi J Y, Lee J S. Adaptive iterative learning control of uncertain robotic systems. IEE Proc D, 2000, 147: 217-223.
19. Ham C, Qu Z, Kaloust J H. A new framework of learning control for a class of nonlinear systems. In: Proceeding of 1995 IEEE American Control Conference, Seattle, Washington, 1995. 3024-3028.
20. Chien C J, Hsu C T, Yao C Y. Fuzzy system-based adaptive iterative learning control for nonlinear plants with initial state errors. IEEE Trans Fuzzy Syst, 2004, 12: 724-732.
21. Xu J X, Yan R. On initial conditions in iterative learning control. IEEE Trans Automat Control, 2005, 50: 1349-1354.
22. Xu J X, Tan Y, Lee T H. Iterative learning control design based on composite energy function with input saturation. Automatica, 2004, 40: 1371-1377.
23. Inoue T, Nakano M, Kubo T, et al. High accuracy control of a proton synchrotron magnet power supply. In: Proceedings of the 8th IFAC World Congress, Kyoto, 1981. 216-221.
24. Hara S, Yamamoto Y, Omata T, et al. Repetitive control system: A new type servo system for periodic exogenous signals. IEEE Trans Automat Control, 1988, 33: 659-668.
25. Tomizuka M, Tsao T C, Chew K K. Analysis and synthesis of discrete-time repetitive controllers. ASME J Dynam Syst, Measure Control, 1989, 111: 353-358.
26. Sadegh N, Horowitz R, Kao W W, et al. A unified approach to design of adaptive and repetitive controllers for robotic manipulators. ASME J Dynam Syst Measure Control, 1990, 112: 618-629.
27. Messner W, Horowitz R, Kao W W, et al. A new adaptive learning law. IEEE Trans Automat Control, 1991, 36: 188-197.
28. Xu J X, Yan R. On repetitive learning control for periodic tracking tasks. IEEE Trans Automat Control, 2006, 51: 1842-1848.
29. Sun M X, Ge S S. Adaptive repetitive control for a class of nonlinearly parametrzed systems. IEEE Trans Automat Control, 2006, 51: 1684-1688.
30. Sun M X, Ge S S, Mareels I M Y. Adaptive repetitive learning control of robotic manipulators without the requirement for initial repositioning. IEEE Trans Robot, 2006, 22: 563-568.
31. Xu J X, Qu Z. Robust iterative learning control for a class of nonlinear systems. Automatica, 1998, 34: 983-988.
32. Sun M X, Cheng Y, Huang B. Higher-order iterative learning control of nonlinear time-varying systems (in Chinese). Acta Automat Sin, 1994, 20: 360-365.
33. Sun M X, Ge S S. Adaptive repetitive learning control of servo mechanisms. In: Proceedings of the 5th World Congress on Intelligent Control and Automation, Hangzhou, 2004. 1212-1216.
34. Sun M X, He X, Chen B. Repetitive learning control for time-varying robotic systems: a hybrid learning scheme. Acta Automat Sin, 2007, 33: 1189-1195.