Adaptive reliable guaranteed performance control of uncertain nonlinear systems by using exponent-dependent barrier Lyapunov function

This paper investigates the issue of adaptive reliable tracking control for a class of uncertain nonlinear parametric strict-feedback systems under actuator faults. To guarantee better transient performance of adaptive systems especially when actuator faults occur, a novel prescribed performance bounds (PPBs) method based on exponent-dependent barrier Lyapunov function is developed. Differing from the existing results where the control schemes have introduced the strictly monotone smooth function to achieve constrained error transformation, the proposed PPBs scheme is designed by using the time-varying barriers to constrain the error trajectories, which accurately characterizes the convergence rates and convergence bounds of errors. Finally, under the framework of backstepping technique and Lyapunov stability theorem, an adaptive reliable controller is designed to ensure that all the closed-loop signals are semiglobally uniformly ultimately bounded with the tracking errors converging to the specified PPBs. Simulation results demonstrate the effectiveness of the proposed approach.