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    Area of Science:

    • Control Systems Engineering
    • Nonlinear System Dynamics
    • Optimization Theory

    Background:

    • Periodic event-triggered control (PETC) is applied to nonlinear systems using quasi-linear parameter-varying (quasi-LPV) representations.
    • Gain-scheduling controllers offer improved performance but face challenges with asynchronous scheduling functions in PETC, leading to conservative results.
    • Existing methods for handling asynchronous functions rely on bounding assumptions that may not hold during closed-loop operation.

    Purpose of the Study:

    • To develop a novel PETC scheme that effectively manages asynchronous scheduling functions in nonlinear systems.
    • To co-design an event-triggering mechanism and a gain-scheduled controller for improved system stabilization.
    • To maximize the region of attraction and minimize data transmissions within the PETC framework.

    Main Methods:

    • Utilizing a looped-functional approach and a nonquadratic Lyapunov function.
    • Deriving linear matrix inequality (LMI)-based conditions for controller and event-trigger design.
    • Formulating a multiobjective optimization problem to balance performance and transmission efficiency.

    Main Results:

    • The proposed PETC scheme successfully addresses the asynchronous scheduling phenomenon.
    • Guaranteed convergence of closed-loop trajectories to the origin from the estimated region of attraction.
    • Demonstrated avoidance of mismatched scheduling function boundedness violations during operation.
    • Validation through two numerical examples showcasing the methodology's effectiveness.

    Conclusions:

    • The novel PETC scheme provides a robust solution for controlling nonlinear systems with asynchronous scheduling.
    • The co-design approach optimizes performance by maximizing the region of attraction and minimizing transmissions.
    • This work advances the field of event-triggered control for complex nonlinear systems.