A Novel Adaptive Prescribed-Time Controller for Uncertain Systems With Unknown Non-Smooth Nonlinearities

This paper studies the adaptive prescribed-time control problem for the strict-feedback systems with unknown non-smooth nonlinearities. Different from the existing adaptive prescribed-time designs where the nonlinearities are required to be known and smooth, a novel design is developed, for the first time, in the presence of the unknown non-smooth nonlinearities eliminating the need for smoothness or knowledge. Moreover, in the design we suggest a new scaled quadratic Lyapunov function depending on a tuning parameter, which together with the characteristics of the introduced scaling function constructs a state-feedback controller allowing to balance the tradeoff between the transient performance and control effort. As a byproduct of this development, we also provide solutions to prescribed-time control of the strict-feedback nonlinear systems. It should be noted that the designed controller has smaller gains thus with reduced control effort while ensuring the prescribed-time stabilization. Finally, three examples are provided to illustrate the efficiency of the proposed method.