Prescribed-time tracking for strict-feedback nonlinear systems with saturation and disturbances: an adaptive boundary approach

This paper investigates prescribed-time tracking for a class of strict-feedback nonlinear systems subject to input saturation and external disturbances. An improved adaptive prescribed-time control scheme is developed to guarantee that the tracking error evolves within adjustable prescribed-time performance bounds. An adaptive prescribed-time performance function is constructed by introducing a saturation-related auxiliary dynamics, such that the admissible error region can be enlarged adaptively under saturation and gradually returns to the nominal boundary when the saturation is relieved and the control burden decreases. To further suppress excessive control peaks caused by disturbances and saturation, a half-width adjustment mechanism is introduced by incorporating a control burden-related lower-bound term into the boundary design. By combining smooth saturation decomposition, neural-network approximation, and state-feedback design, a control law is developed for uncertain nonlinear systems. Stability analysis establishes the semiglobal uniform ultimate boundedness of all closed-loop signals and guarantees that the tracking error remains within the prescribed flexible performance bounds. Simulation results demonstrate the effectiveness of the proposed method and improved adaptation capability under stronger saturation.