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    This study introduces hierarchical containment control (HCC) for mirrored collaboration, enabling bipartite cluster consensus in symmetric convex hulls. A novel HCC protocol with a layer-signal compensator achieves simultaneous consensus, overcoming limitations of existing control methods.

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    Area of Science:

    • Control Theory
    • Robotics
    • Distributed Systems

    Background:

    • Existing cluster consensus methods often require in-degree balance, limiting applications.
    • Cooperative output regulation frameworks struggle with complex mirrored collaboration scenarios.
    • Flexible mirrored collaboration in symmetric convex hulls presents unique control challenges.

    Purpose of the Study:

    • To develop a novel hierarchical containment control (HCC) protocol for flexible mirrored collaboration.
    • To enable bipartite cluster consensus behavior in two symmetric convex hulls.
    • To overcome limitations of existing control protocols and cooperative output regulation.

    Main Methods:

    • Generation of a layer-signed digraph incorporating antagonistic interaction.
    • Extension of cooperative output regulation to address hierarchical mirrored collaborative errors.
    • Design of a layer-signal compensator for leader state estimation and convergence guarantee.

    Main Results:

    • The proposed HCC protocol achieves bipartite cluster consensus in symmetric convex hulls.
    • Antagonistic interaction in the assistant-layer relaxes the in-degree balance assumption.
    • The layer-signal compensator ensures convergence of collaborative behaviors.

    Conclusions:

    • The novel HCC protocol effectively facilitates flexible mirrored collaboration.
    • The approach enables simultaneous bipartite cluster consensus in symmetric formations.
    • Numerical simulations validate the theoretical findings and protocol effectiveness.