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

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.