Singularity-free fixed-time sliding mode control for a class of nonlinear systems

In this paper, the fixed-time control for a class of second-order nonlinear system is investigated. Considering that the presented fixed-time controllers in most existing results are singular, we aim to develop a fixed-time sliding mode controller without singularity. The contribution of this work is not only developing a novel cosine function-based sliding function to ensure the fixed-time convergence of system states on the sliding surface but also designing a novel sliding mode controller to guarantee the fixed-time stability of the obtained closed-loop system without singularity. First, it is proven that the system trajectories converge to the origin in a fixed time on the novel proposed cosine function-based sliding surface. It is further proven by Lyapunov theory that the obtained closed-loop system under the presented controller is fixed-time stable. Moreover, the chattering problem is settled by slightly modifying the presented controller. It is also proven that the system trajectories converge into a small neighborhood of the origin in a fixed time. The results are illustrated in the simulation.