Prescribed-time control under unknown control gain and mismatched nonparametric uncertainties

This paper explores the prescribed-time stabilization problem of strict-feedback uncertain systems, which is quite challenging when unknown control gain (both amplitude and direction) and mismatched nonparametric uncertainties are involved. This paper is the first to address prescribed-time control of such uncertain systems. To overcome the main obstacles of mismatched nonparametric uncertainties and unknown control gain, we extract some structural information of the uncertain systems and blend Nussbaum function into prescribed-time controller. When designing the controller by backstepping method, we perform descending power time-varying scaling on system states, converting the prescribed-time stabilization problem into boundedness problem of the new variables. Unlike most existing works on prescribed-time stabilization, we make use of the special property of Nussbaum function to guarantee the boundedness of the new variables. It is shown that the settling time is user-assignable a priori regardless of the initial condition. The effectiveness of the proposed method is validated via numerical simulations.