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This paper proposes a nonsingular terminal sliding mode control scheme with fast fixed-time convergence for a class of second-order nonlinear systems in the presence of matched uncertainties and perturbations. First, based on fixed-time stability theory, a novel stable system is proposed. Then, using the fixed-time stable system, a fast fixed-time nonsingular terminal sliding surface is derived. The settling time is independent of the initial system state and can be set in advance with the design parameters; the upper-bound of convergence time is derived from the Lyapunov theory. Moreover, the proposed control scheme has an advantage in convergence rate over existing results and achieves better control performance with low control energy cost. The simulation results for a tracking system with a single inverted pendulum are presented to validate the effectiveness and superiority of the proposed control method.
Tian et al. (Wed,) studied this question.