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Adaptive iterative learning controller with input learning technique for a class of uncertain MIMO nonlinear systems

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Abstract

In this paper, an adaptive iterative learning controller (AILC) with input learning technique is presented for uncertain multi-input multi-output (MIMO) nonlinear systems in the normal form. The proposed AILC learns the internal parameter of the state equation as well as the input gain parameter, and also estimates the desired input using an input learning rule to track the whole history of command trajectory. The features of the proposed control scheme can be briefly summarized as follows: 1) To the best of authors’ knowledge, the AILC with input learning is first developed for uncertain MIMO nonlinear systems in the normal form; 2) The convergence of learning input error is ensured; 3) The input learning rule is simple; therefore, it can be easily implemented in industrial applications. With the proposed AILC scheme, the tracking error and desired input error converge to zero as the repetition of the learning operation increases. Single-link and two-link manipulators are presented as simulation examples to confirm the feasibility and performance of the proposed AILC.

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References

  1. Z. Bien and J.-X. Xu, Iterative Learning Control: Analysis, Design, Integration and Applications, Kluwer Academic, Norwell, MA, 1998.

    Book  Google Scholar 

  2. Y. Chen and C. Wen, “Iterative learning control: convergence, robustness and applications,” Lecture Notes in Control and Information Sciences, Berlin, Germany: Springer-Verlag 1999.

    Google Scholar 

  3. M. Norrlof, “An adaptive iterative learning control algorithm with experiments on an industrial robot,” IEEE Trans. Robot. Autom., vol. 18, no. 2, pp. 245–251, Feb. 2002.

    Article  Google Scholar 

  4. D. Bristow, M. Tharayil, and A. G. Alleyne, “A survey of iterative learning control,” Control Systems, IEEE, vol. 26, no. 3, pp. 96–114, Mar. 2006.

    Article  Google Scholar 

  5. Y. Wang, F. Gao, and F. J. Doyle, “Survey on iterative learning control, repetitive control, and run-to-run control,” Journal of Process Control, vol. 19, no. 10, pp. 1589–1600, Oct. 2009. [click]

    Article  Google Scholar 

  6. S. Arimoto, “Bettering operation of dynamic system by learning: a new control theory for servomechanism or mechatronics system,” IEEE Conf. Decision and Control, pp. 1064–1069, 1984.

    Chapter  Google Scholar 

  7. T. Y. Kuc, K. Nam, and J. S. Lee, “An iterative learning control of robot manipulators,” IEEE Trans. on Robot. Autom., vol. 7, no. 6, pp. 835–841, Jun. 1991.

    Article  Google Scholar 

  8. T. Y. Kuc, J. S. Lee, and K. Nam, “Iterative learning control theory for a class of nonlinear dynamic systems,” Automatica, vol. 28, no. 6, pp. 1215–1221, Jun. 1992.

    Article  MathSciNet  MATH  Google Scholar 

  9. H.-S. Ahn, C.-H. Choi, and K.-B. Kim, “Iterative learning control for a class of nonlinear systems,” Automatica, vol. 29, no. 6, pp. 1575–1578, Jun. 1993.

    Article  MathSciNet  MATH  Google Scholar 

  10. S. S. Saab, “On the P-type learning control,” IEEE Trans. Autom. Control, vol. 39, no. 11, pp. 2298–2302, Nov. 1994.

    Article  MathSciNet  MATH  Google Scholar 

  11. J.-X. Xu and Y. Tan, Linear and Nonlinear Iterative Learning Control, Springer, Berlin, 2003.

    MATH  Google Scholar 

  12. T. Y. Kuc and J. S. Lee, “An adaptive learning control of uncertain robotic systems,” Proc. of IEEE Conf. Decision and Control, pp. 1206–1211, Dec. 1991.

    Google Scholar 

  13. B. H. Park, T. Y. Kuc, and J. S. Lee, “Adaptive learning control of uncertain robotic systems,” Int. J. Control, vol. 65, no. 5, pp. 725–744, May 1996.

    Article  MathSciNet  MATH  Google Scholar 

  14. J. Y. Choi and J. S. Lee, “Adaptive iterative learning control of uncertain robotic systems,” IEE Proc. Control Theory and Applications, vol. 147, no. 2, pp. 217–223, Feb. 2000.

    Article  Google Scholar 

  15. M. French and E. Rogers, “Nonlinear iterative learning by an adaptive Lyapunov technique,” Int. J. Control, vol. 73, no. 10, pp. 840–850, Oct. 2000.

    Article  MathSciNet  MATH  Google Scholar 

  16. J.-X. Xu, “A new periodic adaptive control approach for time-varying parameters with known periodicity,” IEEE Trans. Autom. Control vol. 49, no. 4, pp. 579–583, Apr. 2004.

    Article  MathSciNet  Google Scholar 

  17. A. Tayebi and C.-J. Chien, “An adaptive iterative learning control framework for a class of uncertain nonlinear systems,” Proc. 45th IEEE Conf. Decision Control, San Diego, CA, pp. 5054–5059, Dec. 2006.

    Chapter  Google Scholar 

  18. A. Tayebi and C.-J. Chien, “A unified adaptive iterative learning control framework for uncertain nonlinear systems,” IEEE Trans. Autom. Control, vol. 52, no. 10, pp. 1907–1913, Oct. 2007.

    Article  MathSciNet  Google Scholar 

  19. X. D. Li, T. F. Xiao, and H. X. Zheng, “Adaptive discretetime iterative learning control for non-linear multiple input multiple output systems with iteration-varying initial error and reference trajectory,” IET Control Theory and Applications, vol. 5, no. 9, pp. 1131–1139, Sep. 2011.

    Article  MathSciNet  Google Scholar 

  20. W. Messner, R. Horowitz, W. W. Kao, and M. Boals, “A new adaptive learning rule,” IEEE Trans. Autom. Control, vol. 36, no. 2, pp. 188–197, Feb. 1991.

    Article  MathSciNet  MATH  Google Scholar 

  21. D. Del Vecchio, R. Marino, and P. Tomei, “An adaptive learning control for feedback linearizable systems,” Proc. Amer. Control Conf., Ariington, VA, pp. 2817–2821, Jun. 2001.

    Google Scholar 

  22. S. Liuzzo, R. Marino, and P. Tomei, “Adaptive learning control of nonlinear systems by output error feedback,” IEEE Trans. Autom. Control, vol. 52, no. 7, pp. 1232–1248, Jul. 2007.

    Article  MathSciNet  MATH  Google Scholar 

  23. R. Marino, P. Tomei, and C. M. Verrelli, “Learning control for nonlinear systems in output feedback form,” Systems and Control Letters, vol. 61, no. 12, pp. 1242–1247, Dec. 2012.

    Article  MathSciNet  MATH  Google Scholar 

  24. J.-X. Xu and R. Yan, “On repetitive learning control for periodic tracking tasks,” IEEE Trans. Autom. Control, vol. 51, no. 11, pp. 1842–1848, Nov. 2006.

    Article  MathSciNet  Google Scholar 

  25. R. Marino and P. Tomei, “An iterative learning control for a class of partially feedback linearizable systems,” IEEE Trans. Autom. Control, vol. 54, no. 8, pp. 1991–1996, Aug. 2009.

    Article  MathSciNet  Google Scholar 

  26. X. Liu, Z. Hou, B. Yao, H. Su, and M. Sun, “Output feedback adaptive robust learning control of a class of nonlinear systems with periodic disturbances,” Proc. 18th IEEE Conf. IFAC World Congress, Milano, Italy, pp. 4874–4879, Sep. 2011.

    Google Scholar 

  27. S. Bifaretti, P. Tomei, and C. M. Verrelli, “Establishing improved convergence and robustness properties for the repetitive learning control,” Applied Mathematics and Computation, vol. 218, no. 22, pp. 11311–11322, Jul. 2012. [click]

    Article  MathSciNet  MATH  Google Scholar 

  28. Y. Su and J. Huang, “Stability of a class of linear switching systems with applications to two consensus problems,” IEEE Trans. Autom. Control, vol. 57, no. 6, pp. 1420–1430, Jun. 2012.

    Article  MathSciNet  Google Scholar 

  29. P. A. Ioannou and J. Sun, Robust Adaptive Control, Prentice-Hall, Englewood Cliffs, NJ, 1996.

    MATH  Google Scholar 

  30. H. G. Dotsch, H. T. Smakman, P. M. Van den Hof, and M. Steinbuch, “Adaptive repetitive control of a compact disc mechanism,” Proc. of the 34th IEEE Conf. on Decision and Control, pp. 1720–1725, Dec. 1995.

    Google Scholar 

  31. T. C. Tsao and J. Bentsman, “Rejection of unknown periodic load disturbances in continuous steel casting process using learning repetitive control approach,” IEEE Transactions on Control Systems Technology, vol. 4, no. 3, pp. 259–265, May 1996.

    Article  Google Scholar 

  32. M. Steinbuch, “Repetitive control for systems with uncertain period-time,” Automatica, vol. 38, no. 12, pp. 2103–2109, Dec. 2002. [click]

    Article  MathSciNet  MATH  Google Scholar 

  33. T. Li, R. Li, and J. Li, “Decentralized adaptive neural control of nonlinear systems with unknown time delays,” Nonlinear Dyn. vol. 67, no. 3, pp. 2017–2026, Feb. 2012. [click]

    Article  MathSciNet  MATH  Google Scholar 

  34. D. Gao, Z. Sun, and B. Xu, “Fuzzy adaptive control for pure-feedback system via time scale separation,” International Journal of Control, Automation and Systems, vol. 11, no. 1, pp. 147–158, Jan. 2013. [click]

    Article  Google Scholar 

  35. Y. Q. Fan, Y. H. Wang, Y. Zhang, and Q. R. Wang, “Adaptive fuzzy control with compressors and limiters for a class of uncertain nonlinear systems,” International Journal of Control, Automation and Systems, vol. 11, no. 3, pp. 624–629, Jun. 2013. [click]

    Article  Google Scholar 

  36. Z. Li, T. Li, and G. Feng, “Adaptive neural control for a class of stochastic nonlinear timedelay systems with unknown dead zone using dynamic surface technique,” International Journal of Robust and Nonlinear Control, vol. 26, no. 4, Mar. 2015.

    Google Scholar 

  37. J. Li and H. Yue, “Adaptive fuzzy backstepping dynamic surface control for a class of MIMO nonlinear systems with input delays and state timevarying delays,” International Journal of Adaptive Control and Signal Processing vol. 29, no. 5, pp. 614–638, May 2015. [click]

    Article  MathSciNet  MATH  Google Scholar 

  38. B. Miao and T. Li, “A novel neural network-based adaptive control for a class of uncertain nonlinear systems in strictfeedback form,” Nonlinear Dyn., vol. 79, no. 2, pp. 1005–1013, Jan. 2015. [click]

    Article  MathSciNet  Google Scholar 

  39. J. Craig, P. Hsu, and S. Sastry, “Adaptive control of mechanical manipulators,” Proc. of IEEE Conf. on Robotics and Automation, San Francisco, CA, pp. 190–195, 1986.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Creative IT Engineering, POSTECH, Pohang, Kyungbuk, Korea

    Minsung Kim & Jin S. Lee

  2. School of Electrical and Computer Engineering, Sung Kyun Kwan University, Suwon, Kyunggi, Korea

    Tae-Yong Kuc

  3. Department of Electrical Engineering, POSTECH, Pohang, Kyungbuk, Korea

    Hyosin Kim

Authors
  1. Minsung Kim
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  2. Tae-Yong Kuc
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  3. Hyosin Kim
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  4. Jin S. Lee
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Corresponding author

Correspondence to Minsung Kim.

Additional information

Recommended by Associate Editor Sing Kiong Nguang under the direction of Editor Ju Hyun Park. This research was partially supported by the MSIP (Ministry of Science, ICT and Future Planning), Korea, under the “ICT Consilience Creative Program” (IITP-R0346-16-1007) supervised by the IITP (Institute for Information & communications Technology Promotion) and in part by a grant (#S0417-16-1004) from Regional Software Convergence Products Commercialization Project funded by MSIP and NIPA (National IT Industry Promotion Agency).

Minsung Kim was born in Ulsan, Korea, in 1986. He received the B.S. degree in electrical engineering from Pohang University of Science and Technology (POSTECH), Pohang, Korea, in 2004, and the Ph.D. degree in electrical engineering from POSTECH, Pohang, Korea, in 2013. Since 2013, he has been with Future IT Research Laboratory, POSTECH, Pohang, Korea, where he is currently a Research Professor. Since 2016, he has also worked as Research Scholar at Virginia Tech’s Future Energy Electronics Center, Blacksburg, VA. His current research interests include renewable energy system, power conversion circuit design, nonlinear system analysis, and controller design for industrial process.

Tae-Yong Kuc received the B.S. degree in Control and Instrumentation Engineering from Seoul National University, Korea in 1988 and the M.S. and Ph.D. degrees from Pohang University of Science and Technology, Korea in 1990 and 1993, respectively. From April to August 1993, he worked as Chief Research Engineer at Precision Machinery Institute of Samsung Aerospace Company and from September 1993 to February 1995 as Senior Lecturer in the Department of Electrical Engineering, Mokpo National University, Korea. Since March 1995, he has been with the College of Information and Communication Engineering at Sung Kyun Kwan University, Suwon, Korea. His research interests include intelligent robotics, adaptive and learning control, and intelligent sensor-data processing and fusion.

Hyosin Kim received the B.S degree in electrical engineering from Pohang University of Science and Technology (POSTECH), Pohang, Korea, in 2008, where he is currently pursuing the Ph.D. degree in electrical engineering. His research interests include nonlinear system analysis, intelligent control theory, and controller design of power system.

Jin S. Lee received the B.S. degree in electronics engineering from Seoul National University, Seoul, Korea, in 1975, the M.S. degree in electrical engineering and computer science from the University of California, Berkeley, in 1980, and the Ph.D. degree in system science from the University of California, Los Angeles, in 1984. From 1984 to 1985, he worked as a Member of the Technical Staff at AT&T Bell Laboratories, Holmdel, NJ, and, from 1985 to 1989, as a Senior Member of the Engineering Staff at GE Advanced Technology Laboratories, Mt. Laurel, NJ. Since 1989, he has been a Professor at Pohang University of Science and Technology (POSTECH), Pohang, Korea. From 2000 to 2003, he has served as the Dean of Research Affairs at POSTECH. From 2007 to 2012, he also have served as the Dean of Academic Affairs at POSTECH. He is currently the Head of Creative IT Engineering Department and the Director of Future IT Innovation Laboratory at POSTECH. His research interests include nonlinear systems and control, robotics, and intelligent control.

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Kim, M., Kuc, TY., Kim, H. et al. Adaptive iterative learning controller with input learning technique for a class of uncertain MIMO nonlinear systems. Int. J. Control Autom. Syst. 15, 315–328 (2017). https://doi.org/10.1007/s12555-016-0049-z

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  • DOI: https://doi.org/10.1007/s12555-016-0049-z

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