Adaptive finite/fixed-time stabilizing control for nonlinear systems with parametric uncertainty

This article investigates the adaptive finite/fixed-time stabilizing control problem for a class of uncertain nonlinear systems. Remarkably, the studied system allows the nonlinear parametric uncertainties. Compared with the existing results on adaptive finite/fixed-time stabilizing control, the proposed state feedback stabilizing process consists of the first phase of steering the system states into a region of the fixed-time stability in finite-time and the second phase of further driving the states to the origin in fixed-time, while the other signals in closed-loop system are kept bounded. The adaptive finite/fixed-time stabilizing control scheme is developed using a recursive design method, which is inspired by the adding-a-power-integrator technique. The proof is based on the nonsmooth finite/fixed-time Lyapunov stability theorem developed recently for nonlinear control systems. The angular set-point stabilizing control of a pendulum system is used to demonstrate the effectiveness of the presented algorithm.