Observability of Periodically Switched Boolean Control Networks

JIANG Chunfeng, WANG Biao, FU Shihua, ZHAO Jianli, SUN Min

系统科学与复杂性(英文) ›› 2023, Vol. 36 ›› Issue (3) : 985-1001.

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系统科学与复杂性(英文) ›› 2023, Vol. 36 ›› Issue (3) : 985-1001. DOI: 10.1007/s11424-023-1162-8

Observability of Periodically Switched Boolean Control Networks

    JIANG Chunfeng1, WANG Biao2, FU Shihua3, ZHAO Jianli3, SUN Min4
作者信息 +

Observability of Periodically Switched Boolean Control Networks

    JIANG Chunfeng1, WANG Biao2, FU Shihua3, ZHAO Jianli3, SUN Min4
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文章历史 +

摘要

In this paper, observability is studied for periodically switched Boolean control networks (PSBCNs), which are managed with periodic switching signal and consist of some Boolean control networks. Firstly, via semi-tensor product of matrices, PSBCNs are expressed as algebraic forms. Secondly, a parallel system is constructed by combining two same PSBCNs, based on which, the observability problem of the original PSBCN can be transformed into the set reachability problem of this parallel system. Then, two necessary and sufficient conditions are obtained to detect reachability of parallel systems and observability of PSBCNs. In addition, the proposed conditions are extended to the case of state constraints. Finally, a practical example and a numerical example are provided to illustrate the results.

Abstract

In this paper, observability is studied for periodically switched Boolean control networks (PSBCNs), which are managed with periodic switching signal and consist of some Boolean control networks. Firstly, via semi-tensor product of matrices, PSBCNs are expressed as algebraic forms. Secondly, a parallel system is constructed by combining two same PSBCNs, based on which, the observability problem of the original PSBCN can be transformed into the set reachability problem of this parallel system. Then, two necessary and sufficient conditions are obtained to detect reachability of parallel systems and observability of PSBCNs. In addition, the proposed conditions are extended to the case of state constraints. Finally, a practical example and a numerical example are provided to illustrate the results.

关键词

Boolean control networks / observability / periodically switched systems / semi-tensor product / state constraints

Key words

Boolean control networks / observability / periodically switched systems / semi-tensor product / state constraints

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JIANG Chunfeng , WANG Biao , FU Shihua , ZHAO Jianli , SUN Min. Observability of Periodically Switched Boolean Control Networks. 系统科学与复杂性(英文), 2023, 36(3): 985-1001 https://doi.org/10.1007/s11424-023-1162-8
JIANG Chunfeng , WANG Biao , FU Shihua , ZHAO Jianli , SUN Min. Observability of Periodically Switched Boolean Control Networks. Journal of Systems Science and Complexity, 2023, 36(3): 985-1001 https://doi.org/10.1007/s11424-023-1162-8

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基金

This research was supported by the National Natural Science Foundation of China under Grant Nos. 12101366, 62103176 and 72134004, and the Natural Science Foundation of Shandong Province under Grant Nos. ZR2020QF117 and ZR2019BF023.
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