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Asynchronous Controllability of Non-Homogeneous Markov Switch Generalized Asynchronous Boolean Control Networks With

Hao Zhang, Xianghui Su, Shihua Fu

    IEEE Transactions on Computational Biology and Bioinformatics
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    This study establishes asynchronous controllability for non-homogeneous Markov switch generalized asynchronous Boolean control networks (NMHGABCNs). The research uses the semi-tensor product to derive criteria for controlling these complex networks with random switching signals.

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    Area of Science:

    • Control Theory
    • Network Science
    • Computational Biology

    Background:

    • Boolean control networks (BCNs) are crucial for modeling biological systems.
    • Generalized asynchronous BCNs (GABCNs) offer more realistic modeling capabilities.
    • Non-homogeneous Markov switch dynamics introduce complexity in network behavior.

    Purpose of the Study:

    • To investigate the asynchronous controllability of non-homogeneous Markov switch generalized asynchronous Boolean control networks (NMHGABCNs).
    • To develop criteria for controlling NMHGABCNs under random switching signals.
    • To ensure network behavior aligns with a non-homogeneous Markov process.

    Main Methods:

    • Utilizing the semi-tensor product (STP) to derive algebraic forms of NMHGABCNs.
    • Employing the discrepancy between Markov chain mode and control mode for controllability.
    • Deriving sufficient and necessary criteria for asynchronous controllability.

    Main Results:

    • Established criteria for the asynchronous controllability of NMHGABCNs.
    • Demonstrated the effectiveness of the derived criteria through theoretical analysis.
    • Validated the controllability approach with two illustrative examples.

    Conclusions:

    • The study provides a robust framework for analyzing and achieving asynchronous controllability in complex biological networks.
    • The developed criteria offer practical tools for designing and manipulating NMHGABCNs.
    • The findings contribute to a deeper understanding of control mechanisms in dynamic systems.