“Prescribed-time” stabilization addresses the problem of regulating the state to the origin in a fixed (prescribed) time irrespective of the initial state. While prior results on prescribed-time stabilization considered specific classes of systems such as a chain of integrators with uncertainties matched with the control input (i.e., normal form), we address here a general class of nonlinear systems in a generalized strict-feedback-like structure with state-dependent nonlinear uncertainties throughout the system dynamics. The proposed control design is based on our dynamic high gain scaling technique along with a novel temporal transformation and form of the scaling dynamics with temporal forcing terms. We show that the proposed control design achieves prescribed-time stabilization for the considered general class of uncertain nonlinear systems.

“规定时间”稳定化解决了在固定（规定）时间内将状态调节到原点的问题，而与初始状态无关。虽然先前在规定时间稳定下的结果考虑了特定类别的系统，例如不确定性与控制输入（即正规形式）相匹配的积分器链，但在此我们以广义的严格反馈式解决一般类别的非线性系统在整个系统动力学中具有状态相关的非线性不确定性的结构。所提出的控制设计基于我们的动态高增益缩放技术以及一种新颖的时间变换和带有时间强制项的缩放动力学形式。我们表明，对于不确定的非线性系统的一般类别，所提出的控制设计实现了规定的时间稳定。