Self-Triggered Set Stabilization of Boolean Control Networks and Its Applications

Rong Zhao; Jun-e Feng; Dawei Zhang

doi:10.1109/JAS.2023.124050

Volume 11 Issue 7

Jul. 2024

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2024 > 11(7): 1631-1642

R. Zhao, J.-e Feng, and D. Zhang, “Self-triggered set stabilization of Boolean control networks and its applications,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 7, pp. 1631–1642, Jul. 2024. doi: 10.1109/JAS.2023.124050

Citation:

R. Zhao, J.-e Feng, and D. Zhang, “Self-triggered set stabilization of Boolean control networks and its applications,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 7, pp. 1631–1642, Jul. 2024. doi: 10.1109/JAS.2023.124050

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Self-Triggered Set Stabilization of Boolean Control Networks and Its Applications

doi: 10.1109/JAS.2023.124050

Funds: This work was supported by the National Natural Science Foundation of China (62273201, 62173209, 72134004, 62303170) and the Research Fund for the Taishan Scholar Project of Shandong Province of China (TSTP20221103)

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Author Bio:
Rong Zhao received the B.S. degree in mathematics and applied mathematics from the School of Mathematics and Statistics, Shandong Normal University in 2020. She is currently a Ph.D. candidate in operational research and cybernetics at the School of Mathematics, Shandong University. Her research interests include control theory and application, logical networks, singular systems, game theory

Jun-e Feng received the B.S. degree in mathematics from Liaocheng Normal University (now Liaocheng University) in 1994, and the M.S. and Ph.D. degrees in mathematics from the School of Mathematics, Shandong University in 1997 and 2003, respectively. She was a Visiting Scholar at Massachusetts Institute of Technology, USA, from 2006 to 2007, and a Visiting Scholar at the University of Hong Kong, China, in 2008, 2009, and 2013. She is currently a Professor and Doctoral Supervisor the at School of Mathematics, Shandong University. Her research interests include singular systems, Boolean networks, and robust control. She serves as a Reviewer of American Mathematical Review, a Member of the “Cyber-Physical System Control and Decision Professional Committee” of the Chinese Society of Automation, and the Editorial Board Member of IEEE Control Systems Society. She has authored or coauthored more than 100 SCI papers and more than 50 EI papers

Dawei Zhang received the B.S. degree in information and computing science and the M.Sc. degree in pattern recognition and intelligent systems from Shanxi University in 2005 and 2008, respectively, and the Ph.D. degree in computer science from Central Queensland University, Australia in 2012. From Jan. 2013 to Dec. 2018, he worked in the School of Mathematical Sciences, Shanxi University. From Feb. 2017 to Feb. 2018, he was a Post-Doctoral Research Fellow with the School of Software and Electrical Engineering, Swinburne University of Technology, Australia. He is currently a Professor with the School of Mathematics, Shandong University. His research interests include networked intelligent control, vehicle control and state estimation
Corresponding author: Jun-e Feng, e-mail: fengjune@sdu.edu.cn
¹ The induced subgraph \begin{document}$ {\cal{G}}|_{{\cal{M}}} $\end{document} is the subgraph of \begin{document}$ {\cal{G}} $\end{document}, which has \begin{document}$ {\cal{M}} $\end{document} as its set of vertices and contains all the edges of \begin{document}$ {\cal{G}} $\end{document} that have both endpoints in \begin{document}$ {\cal{M}} $\end{document}.
² Tarjan’s algorithm is a linear-time algorithm proposed by Tarjan [37] to solve the SCCs of a directed graph.
Received Date: 2023-09-02
Revised Date: 2023-10-10
Accepted Date: 2023-10-14

Available Online: 2024-04-23

Abstract

Abstract

Set stabilization is one of the essential problems in engineering systems, and self-triggered control (STC) can save the storage space for interactive information, and can be successfully applied in networked control systems with limited communication resources. In this study, the set stabilization problem and STC design of Boolean control networks are investigated via the semi-tensor product technique. On the one hand, the largest control invariant subset is calculated in terms of the strongly connected components of the state transition graph, by which a graph-theoretical condition for set stabilization is derived. On the other hand, a characteristic function is exploited to determine the triggering mechanism and feasible controls. Based on this, the minimum-time and minimum-triggering open-loop, state-feedback and output-feedback STCs for set stabilization are designed, respectively. As classic applications of self-triggered set stabilization, self-triggered synchronization, self-triggered output tracking and self-triggered output regulation are discussed as well. Additionally, several practical examples are given to illustrate the effectiveness of theoretical results.
- Boolean control networks (BCNs),
- output regulation,
- self-triggered control,
- semi-tensor product of matrices,
- set stabilization,
- synchronization

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¹ The induced subgraph $ {\cal{G}}|_{{\cal{M}}} $ is the subgraph of $ {\cal{G}} $, which has $ {\cal{M}} $ as its set of vertices and contains all the edges of $ {\cal{G}} $ that have both endpoints in $ {\cal{M}} $.
² Tarjan’s algorithm is a linear-time algorithm proposed by Tarjan [37] to solve the SCCs of a directed graph.

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Graphical criteria with lower computational complexity for the set stabilization are provided
Minimum-time and minimum-triggering self-triggered set stabilizers are designed
As applications, self-triggered synchronization and output tracking/regulation are discussed

Self-Triggered Set Stabilization of Boolean Control Networks and Its Applications

doi: 10.1109/JAS.2023.124050

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