Off-line fault detection of logical control networks

Abstract

This paper investigates the off-line fault detectability of logical control networks (LCNs) by the method of semi-tensor product. Firstly, two concepts of off-line fault detectability, that is, weak off-line fault detectability and strong off-line detectability, are presented. Secondly, based on a recursive algorithm, the verification matrix for off-line fault detection is proposed to verify the off-line detectability of LCNs. Thirdly, necessary and sufficient conditions are presented to analyse the off-line fault detectability of LCNs. Finally, two illustrative examples show the effectiveness of the obtained new results.

Keywords:

• Logical control network
• off-line fault detection
• semi-tensor product of matrices

Disclosure statement

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

Additional information

Funding

The research was supported by the National Natural Science Foundation of China under grants 62073202 and 61903237, and the Young Experts of Taishan Scholar Project under grant tsqn201909076.

Notes on contributors

Wenhui Dou

Wenhui Dou, received the MS degree from the School of Mathematics and Statistics, Shandong Normal University in 2021. She is currentlypursuing the PhD degree at the School of Electrical and Information Engineering, Jiangsu University. Her research interests include finite automata, logical networks, etc.

Guodong Zhao

Guodong Zhao, received the MS Degree in control theory from Qufu Normal University in 2013, and the PhD Degree at the School of Control Science and Engineering, Shandong University in 2017. Since Jul. 2017, he has been with the School of Mathematics and Statistics, Shandong Normal University, China, where he is currently a lecturer. His research interests include the method of semi-tensor product of matrices, networked evolutionary games, cyber-physical system, game theory etc.

Haitao Li

Haitao Li, received the PhD degree at the School of Control Science and Engineering, Shandong University in 2014. Since Dec. 2014, he has been with the School of Mathematics and Statistics, Shandong Normal University, China, where he is currently a professor. From Jan. 2014 to Jan. 2015, he worked as a Research Fellow in Nanyang Technological University, Singapore. His research interests include logical dynamic systems, networked evolutionary games, etc. He received the Distinguished Young Scholars of Shandong Province in 2016, the “Guan Zhaozhi Award'' in 2012, and the ”Best Student Paper Award'' at the 10th World Congress on Intelligent Control and Automation.

Qi Chen

Qi Chen, received the BS degree from the School of Mathematics and Statistics, Shandong Normal University, Jinan, China. She is currently pursuing the master degree at the School of Mathematics and Statistics, Shandong Normal University. Her research interests include logical dynamic systems, fuzzy control, etc.