Robust adaptive prescribed-time stabilization via output feedback for uncertain nonlinear strict-feedback-like systems

While control design objectives are formulated most commonly in terms of asymptotic behavior (as time goes to infinity) of signals in the closed-loop system, the recently developed notion of “prescribed-time” stabilization considers closed-loop signal behavior over a fixed (prescribed) time interval and addresses the problem of regulating the state to the origin in the prescribed time irrespective of the initial state. While prior results on prescribed-time stabilization considered a chain of integrators with uncertainties matched with the control input (i.e., normal form), we consider here a general class of nonlinear strict-feedback-like systems with state-dependent uncertainties allowed throughout the system dynamics including uncertain parameters (without requirement of any known bounds on the uncertain parameters). Furthermore, we address the output-feedback problem and show that a dynamic observer and controller can be designed based on our dual dynamic high gain scaling based design methodology along with a novel temporal transformation and form of the scaling dynamics with temporal forcing terms to achieve both state estimation and regulation in the prescribed time.