Fixed-time SOSM controller design with output constraint

In this paper, a novel fixed-time second-order sliding mode (SOSM) controller has been developed for a class of nonlinear systems with output constraints. Based on the output constraint condition, a new barrier Lyapunov function, which can be used to deal with the output constraint, is first constructed. Then, with the help of adding a power integrator technique, the SOSM algorithm can be constructed step by step. The feature of the proposed SOSM algorithm lies in that it will not only fixed-time stabilize the sliding variable to the origin, but also keep the output variable staying inside the constraint set. This also implies that the setting time of sliding variables will be independent of their initial conditions. Finally, the feasibility and effectiveness of proposed SOSM control method are verified by a numerical example and a practical pendulum system.