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The prescribed-time stabilization problem for a general class of nonlinearsystems with unknown input gain and appended dynamics (with unmeasured state)is addressed. Unlike the asymptotic stabilization problem, the prescribed-timestabilization objective requires convergence of the state to the origin in afinite time that can be arbitrarily picked (i.e., prescribed) by the controlsystem designer irrespective of the initial condition of the system. The classof systems considered is allowed to have general nonlinear uncertain termsthroughout the system dynamics as well as uncertain appended dynamics (thateffectively generate a time-varying non-vanishing disturbance signal input intothe nominal system). The control design is based on a time scaletransformation, dynamic high-gain scaling, and adaptation dynamics withtemporal forcing terms.

Prescribed-Time Regulation of Nonlinear Uncertain Systems with Unknown Input Gain and Appended Dynamics