Stabilisation of multi-agent systems over finite fields based on high-order fully actuated system approaches

Abstract

In this paper, the controllability of multi-agent systems over finite fields is studied based on the high-order fully actuated (HOFA) system approaches. The concept of HOFA systems over finite fields is introduced. Necessary and sufficient conditions for the controllability of linear systems over finite fields are established. It is proved that a leader–follower multi-agent system over finite fields is controllable if and only if it can be transformed into an HOFA system. Then the stabilisation control protocol is proposed based on the full-actuation property, and the upper bound of settling time for the system can be determined. The uncontrollable leader–follower multi-agent system over finite fields can be transformed into a controllable subsystem and an autonomous subsystem via structural decomposition, the conditions for the system to be stabilisable are provided. Finally, an illustrative example is shown to verify the validity of the main results of this paper.

Keywords:

• Multi-agent systems
• finite fields
• HOFA system approaches
• controllability
• stabilisation

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 62188101 and 62273201], the Research Fund for the Taishan Scholar Project of Shandong Province of China [grant number 20221103].

Notes on contributors

Yunsi Yang

Yunsi Yang received the B.S. degree in applied mathematics from Hunan University, Changsha, China, in 2019. He is currently pursuing the Ph.D. degree in control science and engineering, Shandong University, Jinan, China. His current research interests include high-order fully actuated system approaches, multi-agent systems, and finite-field networks.

Jun-e Feng

Jun-e Feng received the B.S. degree in mathematics education from Liaocheng University, Liaocheng, China, in 1994, the M.S. degree in mathematics and the Ph.D. degree in control theory and its applications from Shandong University, Jinan, China, in 1997 and 2003, respectively. She is currently a Professor with the School of Mathematics, Shandong University. From 2006 to 2007, she was a visiting scholar with MIT, Cambridge, MA, USA, and in 2008, 2009, and 2013, a visiting scholar with the University of Hong Kong, Hong Kong, China. Her current research interests include fuzzy systems, Boolean networks, and robust control.

Lei Jia

Lei Jia received the Ph.D. degree in industrial automation from Zhejiang University, Hangzhou, China, in 1993. He was with the Department of Mechanical and Electrical Engineering, Shandong University of Light Industry, Jinan, China, from 1982 to 1999. He is currently a Professor with the School of Control Science and Engineering, Shandong University, Jinan. His main research interests include new detection technology and application.