Predefined-Time Adaptive Command Filter Control for Nonstrict-Feedback Nonlinear Systems with Input Delay and Unmodeled Dynamics

This work addresses the tracking control problem of nonstrict-feedback nonlinear systems affected by unmodeled dynamics and input delays, which significantly complicate controller design and degrade system performance. To overcome these challenges, a predefined-time adaptive control framework is developed. A command-filtered backstepping scheme is employed to reduce computational complexity, while an error compensation mechanism is introduced to counteract the inaccuracies caused by command filtering. The unknown nonlinear dynamics are approximated using radial basis function-based estimators, and a dynamic auxiliary signal is designed to mitigate the effects of unmodeled dynamics. Input delays are handled by integrating Padé approximation with an intermediate compensating variable. The proposed control strategy guarantees uniform boundedness of all closed-loop signals and ensures that the tracking error converges to a small neighborhood of the desired trajectory within a predefined time. Simulation results and comparative studies are provided to demonstrate the effectiveness and advantages of the proposed method.