Trigonometric-Type Sliding Mode Control with Exact Convergence Time

In most of the fixed-time or predefined-time control in the literature, the settling time of the system is unknown or its estimation is very conservative. A state-of-the-art design to ensure the exact-time convergence is drawing many attentions. A positive solution to this quest is given in this letter where a new scheme of predefined-time controller design is proposed. The proposed control method is capable of adjusting the settling time arbitrarily and exactly in the presence of disturbances by proposing a novel trigonometric-type sliding mode. In addition, the control does not contain an exponential function such that the initial control signal is effectively reduced. An illustrative example is discussed to highlight the main motivation of the strategy, after which a systematic design method of the proposed control for nonlinear systems is presented. Simulations validate the exact-time convergence feature of the proposed method in the presence of bounded disturbance.