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Minimal observability of Boolean networks

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Abstract

In this study, the minimum observability of Boolean networks (BNs) is investigated by using the semi-tensor product (STP) of matrices. First, a new system based on the considered BN is obtained to analyze states pair dynamic trajectories, from which a necessary and sufficient condition for the observability of BNs is determined. Second, adding a new observer improves the observability without affecting the observable states. Thus, an algorithm is presented to design an observer for an unobservable BN. In addition, a necessary condition is obtained to determine the minimum number of nodes required to be directly measurable. Further, an algorithm to address the minimal observability is presented. Finally, examples are provided to demonstrate the effectiveness of the obtained results.

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Acknowledgements

This work was supported in part by Natural Science Foundation of Zhejiang Province of China (Grant Nos. LR20F030001, LY22F030005, LD19A010001) and National Natural Science Foundation of China (Grant Nos. 62173308, 61903339). The authors would like to thank the anonymous reviewers who helped improve the quality of this article. The authors also would like to thank Huachao LIU for his valuable suggestions on designing minimal observability of BNs.

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua, 321004, China

    Yang Liu & Jie Zhong

  2. Department of Mathematics, City University of Hong Kong, Hong Kong, 999077, China

    Daniel W. C. Ho

  3. School of Information Science and Engineering, Central South University, Changsha, 410083, China

    Weihua Gui

Authors
  1. Yang Liu
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  2. Jie Zhong
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  3. Daniel W. C. Ho
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  4. Weihua Gui
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Correspondence to Yang Liu.

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Liu, Y., Zhong, J., Ho, D.W.C. et al. Minimal observability of Boolean networks. Sci. China Inf. Sci. 65, 152203 (2022). https://doi.org/10.1007/s11432-021-3365-2

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  • DOI: https://doi.org/10.1007/s11432-021-3365-2

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