A Novel Nonsingular Fast Fixed-Time Sliding Mode Control and Its Application to Satellite Attitude Control

Abstract

In this paper, a Lyapunov-like sufficient condition for the fast fixed-time stability of autonomous systems is proposed. The proposed fast fixed-time stability theorem ensures a smaller upper bound on the convergence time than the existing fixed-time stability theorems. The fixed-time sliding mode controls require switching from the fixed-time sliding surface to the general sliding surface in the vicinity of the origin to avoid non-differentiability at that point. It is demonstrated that the switching method converges the system states either to a residual set around the equilibrium point or directly to the equilibrium point, depending on the tuning parameter settings. To address this issue, a new nonsingular sliding surface is proposed based on the fast fixed-time stability theorem. This approach ensures singularity-free convergence of the system states to the equilibrium point without additional switching logic for the sliding surfaces or any constraints on tuning parameters. Furthermore, a novel continuous adaptive fast fixed-time sliding mode control (AFFTSMC) law is proposed for attitude control of a satellite in the presence of the satellite inertia uncertainty and unknown upper-bounded external disturbance torques. The proposed AFFTSMC law ensures chattering-free and singularity-free satellite attitude control. Simulation results are presented for both rest-to-rest and tracking attitude maneuvers of a satellite, demonstrating the superiority of the proposed controller.