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. Note to Practitioners—Many practical engineering systems, such as robotic arms and ship rudders, exhibit unknown non-smooth nonlinearities. The characteristic may cause the conventional prescribed-time controllers to be not applicable. This paper proposes a novel adaptive prescribed-time control strategy, which achieves the prescribed-time stability of the uncertain non-smooth nonlinear system. Since a new scaled quadratic Lyapunov function depending on a tuning parameter is proposed, the merit of the proposed strategy involves smaller gains thus with less control effort compared with existing methods, which offers efficient solutions that hold immense promise in practical applications.