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

Abstract 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.