A prescribed-time convergence criterion with application to adaptive control for parametric strict-feedback systems

This study proposes a prescribed-time stability (PTS) criterion that dispenses with the requirement for the Lyapunov function to be present on the right-hand side of its derivative inequality. Different from the existing PTS criteria in literature, Barbalat's lemma is used in the prescribed-time convergence analysis. By application of this criterion, we develop an adaptive prescribed-time control algorithm tailored for a class of strict-feedback systems subject to parametric and dynamic uncertainties. It is established that, under the proposed prescribed-time control scheme, the system states reach the origin within the prescribed time irrespective of the initial conditions. The proposed control scheme is verified through the prescribed-time set-point tracking control of a pendulum system with unknown parameters.