Adaptive predefined-time observer design for generalized strict-feedback second-order systems under perturbations

This article studies the predefined-time observation problem of generalized strict-feedback second-order systems commonly encountered in practice. A nonaffine control input, a matched perturbation, and nonlinear functions satisfying the Hölder growth condition are considered. A class of adaptive predefined-time observers (PTOs) is designed to reconstruct unknown states and lumped perturbations based on a barrier function and specific time-varying functions. Distinct from existing observers for strict-feedback systems, the PTO accomplishes a complete reconstruction in a predefined time with trivial peaking observation errors. Furthermore, the upper bound of the settling time of the PTO is tightly and explicitly predefined by only one design parameter, and is irrelevant to the initial conditions. Hence, tuning procedures for the physically realizable temporal demands become less conservative and more straightforward. Moreover, the adaptive coefficients of the PTO are self-adjusted along with the magnitude of perturbation, efficiently improving the transient performance under wide-range perturbations. Finally, numerical simulations on a robot manipulator system demonstrate the effectiveness of the PTO.