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    Area of Science:

    • Control Theory
    • Nonlinear Systems
    • Optimization

    Background:

    • Addressing H∞ control challenges in continuous-time nonlinear systems with asymmetric input constraints.
    • Existing methods often struggle with disturbance attenuation levels and Zeno behavior in event-driven control.
    • The need for robust control strategies that guarantee system stability under complex conditions.

    Purpose of the Study:

    • To develop an event-driven H∞ control strategy for continuous-time nonlinear systems with asymmetric input constraints.
    • To introduce a novel event-triggering condition that prevents Zeno behavior without strict parameter tuning.
    • To ensure the uniform ultimate boundedness of closed-loop system signals.

    Main Methods:

    • Conversion of the H∞ control problem into a two-person zero-sum game with a discounted nonquadratic cost function.
    • Formulation of the event-driven Hamilton-Jacobi-Isaacs equation (HJIE).
    • Development of a Zeno-behavior-excluding event-triggering condition with a non-negative threshold.
    • Application of adaptive critic learning with a single critic network to solve the HJIE.
    • Utilizing historical and instantaneous state data for parameter tuning.
    • Lyapunov approach for stability analysis.

    Main Results:

    • A novel event-triggering condition is presented, effectively excluding Zeno behavior.
    • The triggering condition allows for a non-negative threshold without needing to pre-select disturbance attenuation levels.
    • Adaptive critic learning successfully solves the event-driven HJIE and tunes parameters.
    • The Lyapunov approach confirms the uniform ultimate boundedness of all closed-loop system signals.
    • Simulations demonstrate the effectiveness of the proposed event-driven H∞ control strategy.

    Conclusions:

    • The developed event-driven H∞ control strategy effectively manages nonlinear systems with asymmetric input constraints.
    • The novel event-triggering mechanism enhances control robustness and simplifies design.
    • The adaptive critic learning approach provides an efficient method for solving the complex HJIE.
    • The guaranteed uniform ultimate boundedness validates the stability and reliability of the proposed control method.