Adaptive Prescribed-Time Stabilization Control for Fully-Actuated Nonlinear Systems

This paper investigates the adaptive prescribed-time stabilization problem for a class of fully actuated nonlinear systems with unknown parameters. An adaptive controller is developed via the introduction of a regression filter and a coordinate transformation. In contrast to existing prescribed-time stability theorems, a more general stability criterion is established by leveraging properties of parametric Lyapunov equations (PLE). By integrating a prescribed-time adjustment function μ(t) with a novel adaptive law, the proposed control scheme ensures exact convergence of the system states to zero within a user-defined time Tp. Simulation results confirm that the method achieves strict convergence exactly at Tp while ensuring boundedness of all closed-loop signals.