Adaptive prescribed-time tracking control for nonlinear systems with actuator saturation under arbitrary initial errors

This paper tackles the adaptive prescribed-time tracking control problem for strict-feedback nonlinear systems subject to completely unknown dynamics and actuator saturation. A fundamental limitation of conventional prescribed performance control (PPC) is its reliance on the restrictive assumption that the initial tracking error must already satisfy predefined performance bounds. To overcome this limitation, we propose a novel composite error transformation that converts the original constrained error dynamics into an unconstrained form, thereby completely decoupling the control design from initial conditions. This transformation is integrated into an adaptive backstepping framework, which utilises radial basis function (RBF) neural networks for online approximation of unknown system nonlinearities and an asymmetric smooth model based on the Gaussian error function to explicitly handle actuator saturation. The proposed scheme guarantees that the tracking error enters the prescribed performance bounds by a prescribed entry time and converges to zero within a preset settling time. Rigorous stability analysis proves that all closed-loop signals are uniformly ultimately bounded, with both transient and steady-state performance specifications being strictly met. Simulation results validate the effectiveness and robustness of the proposed controller under various challenging conditions, including significant initial errors, system uncertainties, and actuator saturation.