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    This study presents adaptive tracking control for nonlinear systems with state constraints and input delay. The proposed method ensures system stability and accurate tracking despite these challenges.

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    Area of Science:

    • Control Theory
    • Nonlinear Systems
    • Adaptive Control

    Background:

    • Strict-feedback nonlinear systems often face challenges with state constraints and input delays.
    • Existing control strategies may struggle to simultaneously address both full state constraints and input time-lags.

    Purpose of the Study:

    • To develop an adaptive tracking control strategy for nonlinear systems with strict-feedback, state constraints, and input delay.
    • To ensure that system states remain within bounds and tracking errors converge to a small region.

    Main Methods:

    • Utilizing barrier Lyapunov functions to handle state constraints.
    • Employing backstepping design combined with Pade approximation and an intermediate variable to manage input delay.
    • Leveraging neural networks for estimating unknown nonlinear functions.

    Main Results:

    • The closed-loop system signals are proven to be semiglobal uniformly ultimately bounded.
    • Tracking errors are shown to converge to a compact set around the origin.
    • System states are guaranteed to remain within predefined bounded intervals.

    Conclusions:

    • The proposed adaptive control strategy effectively handles state constraints and input delay in strict-feedback nonlinear systems.
    • Simulation results validate the performance and robustness of the developed control approach.
    • This work contributes a viable solution for complex control problems in nonlinear dynamics.