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Disturbance Decoupling of Singular Boolean Control Networks.

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    This study designs controllers for singular Boolean control networks to solve the disturbance decoupling problem. The methods ensure controller invariance even with function perturbations in these complex control systems.

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    Area of Science:

    • Control Theory
    • Networked Systems
    • Discrete Mathematics

    Background:

    • Singular Boolean Control Networks (SBCNs) present unique challenges in control design.
    • The Disturbance Decoupling Problem (DDP) is crucial for robust system performance.
    • Existing methods may not fully address the complexities of SBCNs.

    Purpose of the Study:

    • To develop effective controller design strategies for SBCNs.
    • To solve the Disturbance Decoupling Problem (DDP) in SBCNs.
    • To ensure controller invariance under function perturbations.

    Main Methods:

    • Utilizing the semi-tensor product (STP) of matrices to transform SBCNs.
    • Applying the Implicit Function Theorem for network conversion.
    • Employing redundant variable separation for controller synthesis.

    Main Results:

    • Successfully designed state feedback and output feedback controllers for SBCNs.
    • Established sufficient conditions for controller invariance against function perturbations.
    • Demonstrated the effectiveness of the proposed methods through illustrative examples.

    Conclusions:

    • The proposed controller design methodology effectively solves the DDP for SBCNs.
    • The developed controllers exhibit robustness to function perturbations.
    • The findings offer a significant advancement in the control of singular Boolean networks.