Abstract
Many applications can be described by the wave equation, as a kind of important second order partial differential equations. This paper suggests applying PD-type iterative learning control (ILC) scheme with initial state learning (ISL) to a class of linear one-dimensional wave equation. A sufficient condition is given to insure the convergence of the tracking errors. Finally, a numerical simulation is presented to illustrate the efficiency of the proposed method.
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Recommended by Associate Editor Guangdeng Zong under the direction of Editor Guang-Hong Yang. This work is partly financial supported by the High-tech Research and Development Program of China (2014AA041802).
Meryem Hamidaoui received her Bachelor’s degree and Master’s degree in Applied Mathematics from the Department of Mathematics, University of Abou Bekr Belkaid, Tlemcen, Algeria, in 2014 and 2016, respectively. At present, she is pursuing a Ph.D. degree from Institute of Advanced Control Technology, Dalian University of Technology, Dalian, P.R. China. Her research interests include control of partial differential equation and iterative learning control.
Cheng Shao is a Professor and Head of Institute of Advanced Control Technology, Dalian University of Technology, Dalian, P. R. China and a Dean of Liaoning Province Key Laboratory of Advanced Control System for Industrial Equipment. He received his Ph.D. degree and Master degree in Control Science and Engineering at Northeastern University, P. R. China, in 1992 and 1986, respectively, and his Bachelor degree in Mathematics at Liaoning University, P. R. China in 1982. His research interests include control theory in intelligent manufacturing, advanced process control, robust adaptive control, intelligent measurement and control.
Samia Haouassi received her Bachelor degree and Master degree in Computer vision and Image processing from the Department of Software Technologies and Information Systems, Abdelhamid Mehri University of Constantine 2, Constantine, Algeria, in 2012 and 2014, respectively. At present, she is pursuing a Ph.D. degree from the School of Computer Science, Dalian University of Technology, Dalian, P.R. China. Her research interests include image processing, computer vision and deep learning.
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Hamidaoui, M., Shao, C. & Haouassi, S. A PD-type Iterative Learning Control Algorithm for One-dimension Linear Wave Equation. Int. J. Control Autom. Syst. 18, 1045–1052 (2020). https://doi.org/10.1007/s12555-019-0094-5
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DOI: https://doi.org/10.1007/s12555-019-0094-5