Adaptive Prescribed-Time Stabilization of Uncertain Nonlinear Singularly Perturbed Systems

A class of uncertain singularly perturbed nonlinear systems comprised of a cascade structure of slow and fast subsystems, both in strict-feedback-like forms, is considered. A dynamic output-feedback prescribed-time stabilizing controller is developed to attain regulation of the system state and control input to the origin within a specified (prescribed) time interval irrespective of the initial state. The control design is structured as dynamic scaling-based observer/controller designs for the slow and fast subsystems in combination with a coupling subsystem that can be viewed as dynamically enforcing temporal state evolution over a desired slow manifold. Adaptations are used to address uncertain parameters coupled with unmeasured state variables from both the slow and fast subsystems.