Prescribed‐Time Stabilization of a Class of Nonlinear Systems Based on Fully Actuated System Approach

ABSTRACT This article investigates the prescribed‐time control problem for a class of nonlinear systems with disturbances. Using general backstepping and state scaling techniques to deal with high‐order systems with disturbances may lead to differential explosion and complicate stability analysis. To avoid these problems, this paper proposes a prescribed‐time control scheme based on a fully actuated system (FAS) approach. Transform the nonlinear system into FAS with disturbances, giving the system a more concise structure, and then use a state scaling function to transform the original system state. Using strictly bounded prescribed‐time controllers to achieve asymptotic stability of the new FAS with amplified disturbances, thereby achieving prescribed‐time stability of the original system. Finally, the effectiveness of the algorithm was verified through numerical examples.