Prescribed-Time Control of Nonlinear Systems With Global Prescribed Performance for State Errors

This paper studies the prescribed-time tracking control problem for nonlinear systems with unknown time-varying parameters, mismatched nonvanishing uncertainties, unknown control coefficients, and potential actuator faults. The proposed control strategy employs a prescribed-time adjustment function to guarantee that state errors converge to zero within a specified time, despite the presence of nonvanishing mismatched uncertainties. The proposed controller avoids the need to use adaptive mechanisms and is therefore simple to implement. Moreover, the proposed control strategy does not require the control coefficient bounds to be known. Based on a prescribed-time scaling function and a barrier function, prescribed performance for state errors is guaranteed, which is uniform with respect to initial conditions, eliminating the need for an offline optimization algorithm to determine the controller gains. The simulation results demonstrate the effectiveness of the proposed control framework.