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    Area of Science:

    • Control Systems Engineering
    • Systems Theory
    • Information Theory

    Background:

    • Controlling unknown discrete-time linear systems presents challenges.
    • Event-triggering and self-triggering schemes aim to optimize data transmission for control systems.

    Purpose of the Study:

    • To develop and analyze model-based and data-driven control strategies for unknown discrete-time linear systems.
    • To introduce dynamic event-triggering schemes (ETS) and self-triggering schemes (STS) for efficient data transmission.
    • To establish stability conditions and co-design methods for the controller and triggering mechanisms.

    Main Methods:

    • A dynamic event-triggering scheme (ETS) based on periodic sampling and a discrete-time looped-functional approach.
    • Derivation of a model-based stability condition.
    • Development of a data-driven stability criterion using linear matrix inequalities (LMIs) by combining model-based conditions with data-based system representation.
    • Design of a self-triggering scheme (STS) with an algorithm for predicting transmission instants using pre-collected input-state data.

    Main Results:

    • A model-based stability condition for the ETS.
    • A data-driven stability criterion in the form of LMIs, enabling co-design of the ETS matrix and controller.
    • A self-triggering scheme (STS) algorithm that ensures system stability.
    • Demonstration of reduced data transmissions for both ETS and STS through numerical simulations.

    Conclusions:

    • The proposed dynamic event-triggering scheme (ETS) and self-triggering scheme (STS) effectively reduce data transmissions in unknown discrete-time linear systems.
    • The developed co-design methods for the triggering schemes and controllers are practical and ensure system stability.
    • The data-driven approach offers a robust alternative for control system design when system models are uncertain.