Adaptive Fuzzy Appointed-Time Control for Uncertain Systems Bounded by Positive Functions

This brief presents an appointed-time prescribed performance control design for uncertain nonlinear systems via adaptive fuzzy technique. Compared with existing results, the controller achieves appointed-time tracking control for higher-order nonlinear systems with uncertainties bounded by positive functions. Firstly, barrier Lyapunov functions integrated with appointed-time prescribed performance functions are designed to cope with the requirements of output constraints and quantitative performance constraints. Then, adaptive fuzzy systems are constructed to approximate the unknown continuous upper-bound functions of the uncertainties. Subsequently, through the backstepping framework, a novel adaptive fuzzy appointed-time control scheme is proposed for the uncertain nonlinear system bounded by positive functions. Thus, the appointed settling time, predetermined steady-state error, and quantitative transient-state performance of the closed-loop system are ensured. Finally, the fixed-time convergence of the closed-loop system is proved via Lyapunov analysis, while comparative simulations are conducted to illustrate the superiority of the proposed scheme.