Prescribed-Time Control for a Class of Underactuated Systems: A High-Order Fully Actuated System Approach
针对不确定连杆型欠驱动机械系统，结合全驱动系统理论与奇异摄动，设计自适应预设时间控制器，通过分解动力学、引入新型预设时间增益和自适应律，实现预设时间收敛，并在桥式起重机实验中验证有效性。
For uncertain link-type underactuated mechanical systems (LUMSs), existing fully actuated system (FAS)-based approaches are often difficult to apply because the required structural conditions are not satisfied. This article develops an adaptive prescribed-time controller for a class of LUMSs by combining FAS theory with singular perturbation (SP). First, the underactuated dynamics are decomposed into slow and fast subsystems, and the reduced slow subsystem is transformed into a lower-order FAS without approximating the key nonlinear terms. Second, a novel prescribed-time gain (NPTG) is incorporated to improve the early transient response while alleviating the sharp-braking effect and reducing the risk of actuator saturation associated with conventional prescribed-time gains. In addition, a prescribed-time adaptive law is introduced without requiring a priori disturbance bounds. Lyapunov analysis establishes prescribed-time convergence of the reduced slow subsystem, while standard SP arguments justify practical regulation of the full-order closed-loop system. Experiments on an overhead crane verify the effectiveness and robustness of the proposed method.