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<p>This article deals with the issues of reconstructibility analysis and state estimation for time-delay probabilistic Boolean networks (TDPBNs). Firstly, the concepts of strongly (weakly) reconstructible TDPBN and state separation point are proposed, and a set observer is given for TDPBNs. Meanwhile, the reason why the final state of a weakly reconstructible TDPBN cannot be uniquely determined is analyzed. Secondly, in order to tackle the problem caused by state separation point, a time-delay probabilistic network with pinning control is constructed, where a logical matrix set is designed such that the successor state of state separation point can be uniquely determined. Thirdly, based on the pinning control technique, a strongly reconstructible TDPBN is proposed such that the final state of a weakly reconstructible TDPBN can always uniquely determined. Then, the sufficient condition for transforming the weakly reconstructible TDPBN into a strongly reconstructible one is obtained, and an observer of the weakly reconstructible TDPBN is also provided. Finally, the effectiveness of the proposed method is verified by a biological example.</p>

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Pinning Control-based Reconstructibility Analysis and State Estimation of Time-delay Probabilistic Boolean Networks

  • 期刊论文

  • 发表日期：

    2025年7月14日

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  • Zhi Chen,
  • Junqi Yang,
  • Hao Li

摘要

This article deals with the issues of reconstructibility analysis and state estimation for time-delay probabilistic Boolean networks (TDPBNs). Firstly, the concepts of strongly (weakly) reconstructible TDPBN and state separation point are proposed, and a set observer is given for TDPBNs. Meanwhile, the reason why the final state of a weakly reconstructible TDPBN cannot be uniquely determined is analyzed. Secondly, in order to tackle the problem caused by state separation point, a time-delay probabilistic network with pinning control is constructed, where a logical matrix set is designed such that the successor state of state separation point can be uniquely determined. Thirdly, based on the pinning control technique, a strongly reconstructible TDPBN is proposed such that the final state of a weakly reconstructible TDPBN can always uniquely determined. Then, the sufficient condition for transforming the weakly reconstructible TDPBN into a strongly reconstructible one is obtained, and an observer of the weakly reconstructible TDPBN is also provided. Finally, the effectiveness of the proposed method is verified by a biological example.