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Set Stabilization of Probabilistic Boolean Networks Using Pinning Control.

Fangfei Li, Lihua Xie

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    This study introduces a pinning controller design for Probabilistic Boolean Networks (PBNs), enabling set stabilization with probability one. The novel algorithm addresses the inherent randomness of PBNs for robust control.

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    Area of Science:

    • Control Theory
    • Computational Biology
    • Network Science

    Background:

    • Probabilistic Boolean Networks (PBNs) are stochastic logical systems where update functions are probabilistically chosen.
    • Controlling PBNs is challenging due to their inherent randomness and non-deterministic Boolean functions.

    Purpose of the Study:

    • To propose a pinning controller design algorithm for achieving set stabilization of any PBN with probability one.
    • To develop a method for selecting pinning nodes and designing controllers for stochastic logical systems.

    Main Methods:

    • An algorithm to modify the transition matrix of a PBN.
    • Selection of pinning nodes based on the modified transition matrix.
    • Solving logical matrix equations to determine pinning controller structure matrices.

    Main Results:

    • A novel algorithm for designing pinning controllers for PBNs is presented.
    • The proposed method guarantees set stabilization for any PBN with probability one.
    • Theoretical results are validated through several illustrative examples.

    Conclusions:

    • The developed pinning controller design algorithm effectively stabilizes Probabilistic Boolean Networks.
    • This approach provides a robust method for controlling complex stochastic logical systems.
    • The findings contribute to the advancement of control strategies for PBNs.