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    Area of Science:

    • Control Systems Engineering
    • Nonlinear System Dynamics
    • Computational Intelligence

    Background:

    • Event-triggered control (ETC) reduces system resource usage compared to time-triggered control.
    • Designing ETC for nonlinear systems while ensuring stability and performance is challenging.
    • Existing ETC methods often lack direct links to optimal control principles like the Hamilton-Jacobi-Bellman (HJB) equation.

    Purpose of the Study:

    • To develop a novel event-triggered optimal control (ETOC) method for continuous-time nonlinear systems.
    • To design an event-triggering condition directly based on the HJB equation solution.
    • To provide formal performance guarantees and ensure practical implementation via adaptive dynamic programming (ADP).

    Main Methods:

    • Derivation of a new event-triggering condition linked to the HJB equation.
    • Formal proof of performance bounds (upper bound) and interexecution time lower bound.
    • Development of an adaptive dynamic programming (ADP) approach using a critic neural network (NN) to approximate the HJB value function.

    Main Results:

    • The proposed ETOC method guarantees a predetermined upper bound on performance.
    • A lower bound on the interexecution time is proven, ensuring practical feasibility.
    • The ADP-based ETOC ensures semiglobal uniform ultimate boundedness for system states and NN weight errors.

    Conclusions:

    • The novel event-triggering condition effectively integrates optimal control with event-based execution for nonlinear systems.
    • The ADP implementation provides a practical and stable solution for ETOC.
    • Simulation results validate the effectiveness and performance of the proposed ADP-based ETOC method.