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

Abstract

Listen

Translate article

ABSTRACTIn 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.