Global adaptive prescribed-time stabilization for high-order nonlinear systems

In this article, the global adaptive prescribed-time stabilization problem of high-order (p$$ p $$-normal form) nonlinear systems with parametric uncertainties is studied. Compared with the existing results on time-optimal control, our control algorithm eliminates the residual term caused by unknown parameters for the first time. By introducing the new Lyapunov-like function and time-varying function, a prescribed-time controller with adaptive law is constructed, which ensures that the system state variables converge to the origin rather than a residual term, and the setting time can be arbitrarily specified. Moreover, with the help of the state transformations and the power integrator technique, the difficulties of system structure caused by the high power are overcome. Then, based on the differential equations, it is proved that the boundedness of all system signals. Finally, an example of underdrive system simulation is presented to verify the availabilities of the developed control algorithm.