A Novel Prescribed-Time Control Approach Under Unknown Control Gain and Mismatched Disturbance

In this article, a prescribed-time output feedback controller is proposed for a class of uncertain nonlinear systems with unknown control coefficients and mismatched nonvanishing disturbances. Both unknown control coefficients and mismatched disturbances are tricky to address by the existing prescribed-time output feedback control frameworks. Differently, a novel prescribed-time control criterion in conjunction with Nussbaum functions is proposed, and prescribed-time stability is achieved. Furthermore, design methods for a state observer and a prescribed-time output feedback controller are developed. With the proposed control design, both the system output and observer errors are rigorously proved to converge to zero within a prescribed time. Moreover, the unified prescribed performance (UPP) of the system output and the satisfaction of output constraints are simultaneously achieved. Numerical simulations and experiments are provided to illustrate the effectiveness of the proposed control design.