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    Area of Science:

    • Control Systems Engineering
    • Artificial Intelligence
    • Robotics

    Background:

    • Multiagent systems (MASs) require robust control strategies for complex tasks.
    • Human-in-the-loop (HiTL) systems enhance adaptability but introduce control challenges.
    • Actuator faults can degrade system performance and stability in MASs.

    Purpose of the Study:

    • To develop an optimal fixed-time tracking control scheme for HiTL MASs.
    • To address actuator faults within the control framework.
    • To ensure bounded system signals and efficient tracking in finite time.

    Main Methods:

    • An HiTL optimal control protocol based on simplified optimal control.
    • Embedding synchronization error and leader input into the cost function.
    • A novel reinforcement learning (RL) algorithm with exponential terms for fixed-time convergence.

    Main Results:

    • The proposed control scheme achieves optimal tracking control under HiTL supervision.
    • The RL algorithm ensures fixed-time convergence of system signals.
    • Actuator fault compensation is integrated, maintaining system performance.
    • All closed-loop system signals are proven to be bounded within a fixed time.

    Conclusions:

    • The developed optimal fixed-time tracking control is effective for HiTL MASs with actuator faults.
    • The reinforcement learning approach enhances convergence speed and energy efficiency.
    • The control scheme guarantees robust and bounded system behavior in finite time.