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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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    This study introduces novel finite-time control (FTC) methods for nonlinear systems with time-delays and quantized inputs. New stability concepts and adaptive backstepping techniques ensure system performance.

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    Area of Science:

    • Control Systems Engineering
    • Nonlinear Dynamics
    • Adaptive Control Theory

    Background:

    • Strict-feedback nonlinear systems often exhibit complex dynamics.
    • Time-delays and input quantization introduce significant control challenges.
    • Existing finite-time control (FTC) methods may not address these combined uncertainties.

    Purpose of the Study:

    • To investigate adaptive finite-time control (FTC) for nonlinear systems with simultaneous time-delays and quantized inputs.
    • To introduce novel concepts for performance and stability analysis.
    • To develop a new control strategy overcoming limitations of existing approaches.

    Main Methods:

    • Definition of a preassigned finite-time performance function (PFTF).
    • Introduction of practically preassigned finite-time stability (PPFTS).
    • Application of neural network (NN) control and adaptive backstepping with a modified barrier function.

    Main Results:

    • A novel sufficient condition for FTC is established.
    • The proposed method effectively handles systems with both time-delays and quantized inputs.
    • Simulation results validate the proposed adaptive control scheme.

    Conclusions:

    • The developed FTC strategy offers a new solution for complex nonlinear systems.
    • The introduced PFTF and PPFTS provide enhanced performance and stability guarantees.
    • This work is the first to address FTC under simultaneous time-delay and input quantization.