Adaptive output-feedback stabilization in prescribed time for nonlinear systems with unknown parameters coupled with unmeasured states

The prescribed-time output-feedback stabilization (ie, regulation of the state and control input to zero within a “prescribed” time picked by the control designer irrespective of the initial state) of a general class of uncertain nonlinear strict-feedback-like systems is considered. Unlike prior results, the class of systems considered in this article allows crossproducts of unknown parameters (without any required magnitude bounds on unknown parameters) and unmeasured state variables in uncertain state-dependent nonlinear functions throughout the system dynamics. We show that prescribed-time output-feedback stabilization (ie, both prescribed-time state estimation and prescribed-time regulation) is achieved through a novel output-feedback control design involving specially designed dynamics of an adaptation state variable and a high-gain scaling parameter in combination with a temporal transformation and a dual high-gain scaling based observer and controller design. While standard dynamic adaptation techniques cannot be applied due to crossproducts of unknown parameters and unmeasured states, we show that instead, the dynamics of the high-gain scaling parameter and adaptation parameter can be designed with temporal forcing terms to ensure that unknown parameters in system dynamics are dominated by a particular fractional power of the high-gain scaling parameter and the adaptation parameter after a subinterval (of unknown length) of the prescribed time interval. We show that the control law can be designed such that the system state and input are regulated to zero in the remaining subinterval of the prescribed time interval.