Predefined‐time tracking control of a class of nonlinear systems via a novel C∞ performance function

Abstract

AbstractIt is well‐known that the finite‐time and the fixed‐time control can ensure the finite‐time and the fixed‐time stabilities of systems, respectively. Therein the finite convergence time depends on both the initial conditions of systems and the controller design parameters, and the fixed convergence time only depends on the controller design parameters. The recently reported predefined‐time control removes the above limitations. Nevertheless, the existing predefined‐time control methods either require sliding modes, or suffer from the high‐gain control problem at the predefined time, or cannot be applied to high‐order systems. This article develops an alternative predefined‐time tracking control scheme of a class of nonlinear systems by introducing a novel performance function which reaches its terminal value at a predefined time. The developed predefined‐time tracking control scheme has higher compatibility, does not cause the high‐gain control problem at the predefined time and is applicable to arbitrary order systems. Theoretical analyses and simulations verify the effectiveness of our developed predefined‐time tracking control scheme.