Prescribed‐Time Control via Dynamic‐High‐Gain Output Feedback

Abstract

In this article, we propose a new strategy for prescribed‐time stabilization of uncertain nonlinear systems via continuous adaptive output feedback. Notably, the systems allow non‐parameterized unknown nonlinearities and particularly permit unknown control directions for the first time. The two ingredients lead to the stabilization rather intractable and appeal to new methods and analysis routes. Following a conversion idea, we transform the system in finite‐time horizon into a new system with strong time‐variants in infinite‐time horizon. Integrated with a capable dynamic high gain and an unbounded time‐varying gain, a new concise observer which owns control‐free and tractable error dynamics is worked out for the new system. We particularly exploit a new set of time‐varying scalings, to devise a weakly time‐varying entire system whose boundedness amounts to the wanted prescribed‐time convergence. From the entire system, the adaptive controller design is conducted. The high gain, which is endowed with tailored dynamics, is integrated with (sufficiently smooth) pseudosign and pseudo‐dead‐zone functions to largely simplify the design and analysis.