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    Area of Science:

    • Control Theory
    • Optimization
    • Nonlinear Systems

    Background:

    • Distributed optimization is crucial for multiagent systems (MASs).
    • Prescribed-time control offers finite-time convergence guarantees.
    • Existing methods often lack robustness or adaptability for high-order nonlinear MASs.

    Purpose of the Study:

    • To address the distributed prescribed-time convex optimization (DPTCO) problem for high-order nonlinear MASs.
    • To develop a unified cascade design framework for DPTCO.
    • To establish criteria for prescribed-time stabilization and ensure signal boundedness.

    Main Methods:

    • A cascade design framework separating trajectory generation and tracking control.
    • Transformation of DPTCO into a prescribed-time stabilization problem.
    • Utilizing changing Lyapunov functions and time-varying state transformations.
    • Employing sliding-mode variables and time-varying gains for robustness.
    • Applying backstepping and descending power transformations for adaptive control.

    Main Results:

    • Criteria for prescribed-time stabilization are established.
    • Boundedness of internal signals in closed-loop MASs is proven.
    • The framework successfully handles robust DPTCO with disturbances.
    • Adaptive DPTCO with parameter uncertainty is solved for strict-feedback MASs.

    Conclusions:

    • The proposed cascade framework effectively solves the DPTCO problem for high-order nonlinear MASs.
    • The method provides robust and adaptive solutions under disturbances and parameter uncertainty.
    • Numerical examples validate the theoretical findings and the framework's efficacy.