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Adaptive ILC for tracking non-repetitive reference trajectory of 2-D FMM under random boundary condition

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  • Control Theory and Applications
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Abstract

Almost all of the existing research achievements in Iterative Learning Control (ILC) hitherto have been focused on One-Dimensional (1-D) dynamical systems. Few ILC researches are related to Two-Dimensional Fornasini Marchesina Model (2-D FMM). In this paper, an adaptive ILC approach is proposed for 2-D FMM system with non-repetitive reference trajectory under random boundary condition. The proposed adaptive ILC algorithm learns the coefficient matrices of the system and updates the control input iteratively. As the times of iteration goes to infinity, the ILC tracking error outside the boundary tends to zero and all system signals keep bounded in the whole ILC process. Illustrative examples are provided to verify the validity of the proposed adaptive ILC algorithm.

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Authors and Affiliations

  1. School of Data and Computer Science, Sun Yat-sen University, Guangzhou, China

    Qing-Yuan Xu, Xiao-Dong Li & Mang-Mang Lv

Authors
  1. Qing-Yuan Xu
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  2. Xiao-Dong Li
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  3. Mang-Mang Lv
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Corresponding author

Correspondence to Xiao-Dong Li.

Additional information

Recommended by Associate Editor Sung Jin Yoo under the direction of Editor Ju Hyun Park. This work was supported in part by the National Natural Science Foundation of China under Grants U1135005 and 61573385.

Qing-Yuan Xu received the B.S. degree from the School of Information and Electrical Engineering, China University of Mining and Technology, Xuzhou, China, in 2004, the M. Phil. degree from the Sun Yat-sen University, Guangzhou, China, in 2008, At present, she is pursuing her Ph.D. degree from the School of Data and Computer Science, Sun Yat-sen University, Guangzhou, China. Her research interests include iterative learning control and adaptive tracking control.

Xiao-Dong Li received the B.S. degree from the Department of Mathematics, Shaanxi Normal University, Xian, China, in 1987, the M.Phil. degree from the Nanjing University of Science and Technology, Nanjing, China, in 1990, and the Ph.D. degree from the City University of Hong Kong, Hong Kong, in 2007. He is currently a Professor in the School of Data and Computer Science, Sun Yat-sen University, Guangzhou, China. His research interests include 2-D system theory, iterative learning control, and artificial intelligence.

Mang-Mang Lv received the B.S. degree from the Sun Yat-sen University, Guangzhou, China, in 2010. At present, he is pursuing his M.Phil. degree from the School of Data and Computer Science, Sun Yat-sen University, Guangzhou, China. His research interests include 2-D system theory and iterative learning control.

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Xu, QY., Li, XD. & Lv, MM. Adaptive ILC for tracking non-repetitive reference trajectory of 2-D FMM under random boundary condition. Int. J. Control Autom. Syst. 14, 478–485 (2016). https://doi.org/10.1007/s12555-015-0005-3

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  • DOI: https://doi.org/10.1007/s12555-015-0005-3

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