Adaptive Prescribed-Time Control of Uncertain Self-Restructuring Nonaffine Nonlinear Systems

For uncertain strict-feedback nonlinear systems with self-restructuring structures and nonaffine dynamics, this article addresses the challenge of achieving exact full state zero-error stabilization within a prescribed finite time. An adaptive prescribed-time control scheme is proposed, which guarantees that all system states converge to zero within the user-specified settling time, irrespective of initial conditions. The controller is designed based on a time-varying scaling state transformation and incorporates the Nussbaum function to handle unknown self-restructuring control gains. The self-restructuring structures are treated as a time-state-dependent lump, which is effectively estimated by freezing both time and system states and then applying an adaptive estimation strategy. Numerical simulations on a piezoelectric-actuated stage and a second-order nonlinear system are conducted to demonstrate the effectiveness of the proposed scheme.