Adaptive prescribed-time stabilization for uncertain unmeasured-state-dependent systems

This paper proposes an adaptive output-feedback scheme for prescribed-time stabilization of uncertain unmeasured-state-dependent systems. Notably, the systems admit nonlinearities with unknown arbitrary function-of-output growth rate and for the first time allow state-dependent disturbances. The two ingredients lead to the stabilization rather intractable and appeal to new methods and analysis routes. We propose a dynamic-high-gain prescribed-time filter-based observer which owns control-free and tractable error dynamics. This novel and concise observer makes controller design and performance analysis possible. By devising a new set of time-varying scalings, an entire system is obtained whose boundedness amounts to the wanted prescribed-time convergence. From the entire system, the adaptive controller is designed. The dynamics of high gains are endowed with multiple components. It is by the tailored components that the boundedness of the high gains is ensured, getting rid of the noticeable theoretical flaw that the high gains are unbounded in the literature.