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    This study introduces a new adaptive distributed observer for cooperative bipartite containment control in linear multiagent systems. The method ensures follower outputs converge to convex hulls defined by leaders without needing exosystem matrices.

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    Area of Science:

    • Control Theory
    • Systems Engineering
    • Networked Systems

    Background:

    • Investigating cooperative bipartite containment control for linear multiagent systems.
    • Addressing challenges where exosystem matrices are unavailable to followers.
    • Utilizing structurally balanced communication graphs among agents.

    Purpose of the Study:

    • To develop a novel distributed adaptive observer for cooperative bipartite containment control.
    • To design an output-feedback control protocol to achieve bipartite containment.
    • To present a general verification method for the observer's validity, removing the need for M-matrix definitions.

    Main Methods:

    • Designing a novel distributed error term for follower output convergence.
    • Implementing an adaptive distributed observer.
    • Developing an output-feedback control protocol.
    • Employing a new verification method for observer validity.

    Main Results:

    • Follower outputs converge to the convex hull and symmetric convex hull spanned by leaders.
    • The proposed adaptive distributed observer is validated without relying on M-matrix properties.
    • The control protocol effectively solves the bipartite containment control problem.

    Conclusions:

    • The developed adaptive distributed observer and output-feedback control protocol successfully address the cooperative bipartite containment control problem for linear multiagent systems.
    • The novel verification method simplifies the analysis and applicability of distributed observers.
    • Numerical simulations confirm the theoretical results and the effectiveness of the proposed approach.