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    This study addresses data loss in Boolean control networks (BCNs) by developing a probabilistic model. It establishes conditions and methods for analyzing and designing state feedback controllers for stabilizing BCNs with missing data.

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    Area of Science:

    • Control Theory
    • Networked Systems
    • Computer Science

    Background:

    • Data loss is a common issue in real-world networks, leading to complex dynamics in Boolean control networks (BCNs).
    • Existing models struggle to represent BCNs with random data loss and unbounded time delays, leaving stabilization results unavailable.
    • The challenge lies in modeling and analyzing these delayed systems effectively.

    Purpose of the Study:

    • To investigate the stabilization of Boolean control networks (BCNs) subject to Bernoulli-distributed missing data.
    • To develop a novel framework for modeling and analyzing BCNs with data loss.
    • To provide methods for designing state feedback controllers for such systems.

    Main Methods:

    • Construction of an augmented probabilistic Boolean control network (PBCN) to model data loss.
    • Development of necessary and sufficient conditions for stabilizability using reachable matrices and state transition probability matrices.
    • Design of algorithms for state feedback stabilizability analysis and controller synthesis.

    Main Results:

    • Proposed a probabilistic model (PBCN) to effectively represent data loss in BCNs.
    • Established concrete conditions for analyzing the stabilizability of BCNs with missing data.
    • Developed a constructive approach for designing state feedback controllers.

    Conclusions:

    • The developed methods and conditions are effective for analyzing and controlling BCNs with random data loss.
    • The proposed framework provides a significant advancement in the study of delayed Boolean control systems.
    • Illustrative examples confirm the practical applicability of the results.