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Volume 11 Issue 7
Jul.  2024

IEEE/CAA Journal of Automatica Sinica

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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

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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  • 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.

     

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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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    Highlights

    • 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

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