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Iterative learning control for two-dimensional linear discrete systems with Fornasini-Marchesini model

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  • Control Theory and Applications
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Abstract

Almost all existing iterative learning control (ILC) algorithms have focused on one-dimensional (1-D) dynamical systems, and seldom were designed for multidimensional systems. In this article, a two-gain ILC law is presented to deal with the ILC issue of two-dimensional (2-D) linear discrete systems described by the first Fornasini-Marchesini model (FMMI). Convergence and robustness of the proposed ILC law under two different cases of boundary conditions are discussed, respectively. A super-vector technique is used to transfer the ILC process of 2-D FMMI into a 2-D Roessor model such that sufficient convergence/robustness conditions of the proposed ILC law are derived. An illustrative example is given to validate the effectiveness of the proposed ILC approach.

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Authors and Affiliations

  1. School of Data and Computer Science, Sun Yat-sen University, Key Lab of Machine Intelligence and Advanced Computing, Ministry of Education, Guangzhou, 510006, China

    Kai Wan & Xiao-Dong Li

Authors
  1. Kai Wan
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  2. Xiao-Dong Li
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Corresponding author

Correspondence to Xiao-Dong Li.

Additional information

Recommended by Associate Editor M. Chadli under the direction of Editor Jessie (Ju H.) Park. This work is supported in part by the National Natural Science Foundation of China under Grants 61573385 and U1135005.

Kai Wan received his B. S. degree from the School of Mechanical Engineering and Materials, Jiujiang University, Jiangxi, China, in 2011, his M.Phil. degree from the Tianjin Polytechnic University, Tianjin, China, in 2014. At present, he is pursuing a Ph.D. degree from the School of Data and Computer Science, Sun Yat-sen University, Guangzhou, China. His research interests include two-dimensional system theory and iterative learning control.

Xiao-Dong Li received his B.S. degree from the Department of Mathematics, Shaanxi Normal University, Xian, China, in 1987, an M.Phil. degree from the Nanjing University of Science and Technology, Nanjing, China, in 1990, and a 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 two-dimensional system theory, iterative learning control, and artificial intelligence.

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Wan, K., Li, XD. Iterative learning control for two-dimensional linear discrete systems with Fornasini-Marchesini model. Int. J. Control Autom. Syst. 15, 1710–1719 (2017). https://doi.org/10.1007/s12555-016-0075-x

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  • DOI: https://doi.org/10.1007/s12555-016-0075-x

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