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Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
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    Area of Science:

    • Control Systems Engineering
    • Fuzzy Logic Systems
    • Network Security

    Background:

    • Two-dimensional (2-D) fuzzy systems are crucial in complex control applications.
    • Limited communication channels and network attacks pose significant challenges to system stability and performance.
    • Existing control strategies often struggle with resource constraints and security vulnerabilities.

    Purpose of the Study:

    • To develop an attack-compensated control strategy for 2-D fuzzy systems under communication constraints.
    • To introduce a novel event-triggered stochastic protocol (ETSP) for efficient communication resource management.
    • To design a robust compensation mechanism against false data injection in control signals.

    Main Methods:

    • Modeling 2-D fuzzy systems using the Roesser framework.
    • Designing an event-triggered stochastic protocol (ETSP) with nonhomogeneous sojourn probabilities.
    • Developing a sojourn-probability-based predictor for attack compensation.
    • Establishing stability conditions using Lyapunov theory.
    • Optimizing controller design with the particle swarm optimization (PSO) algorithm.

    Main Results:

    • The proposed ETSP effectively reduces communication load by randomly selecting controller nodes.
    • The sojourn-probability-based predictor successfully compensates for false data injection.
    • Sufficient conditions for mean-square asymptotic stability and guaranteed performance were derived.
    • PSO algorithm enhanced controller design, improving system robustness.

    Conclusions:

    • The developed attack-compensated control strategy is effective for 2-D fuzzy systems with limited communication.
    • The ETSP offers a resource-efficient and secure communication solution.
    • The study validates the proposed method's effectiveness and applicability through simulations.