An optimal filter for updated input of iterative learning controllers with multiplicative and additive noises

Abstract

Multiplicative and additive noises, arising from both sensor-to-controller and controller-to-actuator channels, affect the convergence performance of wireless networked iterative learning control (ILC) systems. In order to guarantee the convergence performance of such ILC systems, this paper designs an input filter at the actuator side for estimating the controller updated input. Specifically, a P-type learning controller is considered firstly, and then a mathematical model is developed to describe the transmission processes of both measured output data and updated input data with the effect of those noises. On the basis of state augmentation, these two data transmission processes are further combined with the controller learning process to build a filtering model. Finally, according to this filtering model and the orthogonality projection theory, the optimal input filter in the sense of linear minimum variance is designed in front of actuators. The convergence performance of the filtering error covariance matrix is analysed theoretically. Furthermore, because the input filter is designed only with the controller learning process and the two data transmission processes, the convergence performance of any system with the considered controller can be improved by driving with the filtered input. Finally, numerical results are given to illustrate the effectiveness of the proposed method.

Keywords:

• Iterative learning controller
• multiplicative noise
• additive noise
• input filter

Acknowledgments

The authors wish to express their gratitude for all the reviewer insightful comments and suggestions to improve this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are available from the corresponding author (LS) upon reasonable request.

Additional information

Funding

The authors sincerely appreciate the support of the National Natural Science Foundation of China [Nos 61771432, 61302118, 61973104, U1604151, 61901418 and 61671011].

Notes on contributors

Lixun Huang

Lixun Huang received Ph.D. in Communication and Information System from Shanghai University, China in 2013. He has been with Zhengzhou University of Light Industry as a lecturer since Jul. 2013. His interest is in iterative learning control and networked control systems.

Lijun Sun

Lijun Sun received the BS degree from Xidian University, China, in 1989, the MS degree from HeFei University of Technology, China, in 2001, and the PhD degree from the Northwestern Polytechnical University, China, in 2005. Now, she is currently a professor in School of Electrical Engineering, Henan University of Technology, Zhengzhou, China. Her research interests include artificial intelligent, wireless sensor network, computational intelligence, signal processing and robot application.

Tao Wang

Tao Wang received Ph.D. from Universite Catholique de Louvain (UCL), Belgium in 2012, and from Zhejiang University, China, in 2006, respectively. He has been with Shanghai University as a Professor since Feb. 2013. His current interest is in the signal processing and control techniques for wireless systems. He was an associate editor for EURASIP Journal on Wireless Communications and Networking.

Qiuwen Zhang

Qiuwen Zhang received his Ph.D. degree in communication and information systems from Shanghai University, Shanghai, China, in 2012. Since 2012, he has been with the faculty of the College of Computer and Communication Engineering, Zhengzhou University of Light Industry, where he is currently an Associate Professor. He has published over 30 technical papers in the field of pattern recognition and image processing. His major research interests include signal processing, machine learning, pattern recognition, video codec optimization, and multimedia communication.

Weihua Liu

Weihua Liu received the M.S. degree in Applied Mathematics from Zhengzhou University, Zhengzhou, China, in 2014 and the Ph.D. degree in communication and information system from University of Chinese Academy of Sciences, Beijing, China, in 2018, respectively. He is currently a Lecturer with the School on Computer and Communication Engineering, Zhengzhou University of Light Industry, China. His research interests include information theory and wireless communication.

Zhe Zhang

Zhe Zhang received the B.E. degree in electronic and information engineering from The First Aviation Academy of Chinese Air Force, Xinyang, China, in 2009, and the Ph.D. degree in information and communication engineering from Zhengzhou University, Zhengzhou, in 2017. She is currently a lecturer with the School on Computer and Communication Engineering, Zhengzhou University of Light Industry, Zhengzhou, China. Her research interests include radio resource management and signal processing for wireless communications.