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Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
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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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Linear time-invariant Systems01:23

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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
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In control systems, test signals are essential for evaluating performance under various conditions. The ramp function is effective for systems undergoing gradual changes, while the step function is suitable for assessing systems facing sudden disturbances. For systems subjected to shock inputs, the impulse function is the most appropriate test signal.
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Self-Triggered Prescribed-Time Impulsive Control for Nonlinear Systems.

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    Summary
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    This study introduces self-triggered impulsive control (STIC) for nonlinear systems, ensuring stability within a set time. The novel approach uses a designable control strength and a non-Zeno self-triggering mechanism for guaranteed performance.

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    Area of Science:

    • Control Systems Engineering
    • Nonlinear Dynamics
    • Applied Mathematics

    Background:

    • Impulsive control strategies are crucial for stabilizing nonlinear systems.
    • Existing methods often lack precise time-bound stability guarantees.
    • Prescribed-time stability (PTS) offers enhanced control over system convergence time.

    Purpose of the Study:

    • To design a novel self-triggered impulsive control (STIC) scheme for achieving prescribed-time stability (PTS) in nonlinear systems.
    • To develop a method for determining impulsive control strength and interval using a prescribed-time convergent function.
    • To implement STIC under a non-Zeno self-triggering mechanism (STM) with bounded execution times.

    Main Methods:

    • A prescribed-time convergent function is utilized to calculate impulsive control strength and interval.
    • A non-Zeno self-triggering mechanism (STM) is employed, ensuring bounded execution times.
    • A comparison system establishes triggering times for the impulsive control.
    • The upper bound of the impulsive interval influences both control strength and STM.

    Main Results:

    • The proposed STIC scheme guarantees prescribed-time stability for the closed-loop system.
    • Impulsive control strengths decrease as the system approaches the prescribed time.
    • The STM ensures bounded execution times, avoiding Zeno behavior.
    • The method was successfully applied to achieve prescribed-time synchronization of reaction-diffusion neural networks (RDNNs).

    Conclusions:

    • The developed STIC scheme effectively achieves PTS for nonlinear systems.
    • The integration of STM with designable impulsive strength offers a robust control solution.
    • The findings are validated through application to RDNNs and numerical simulations, demonstrating practical applicability.