HOSM controller design with an output constraint and its application

This work has developed an approach to a high-order sliding mode (HOSM) controller design for nonlinear systems subject to output constraints. To handle the output constraints, a barrier Lyapunov function (BLF) has been adopted. By inserting the BLF into the revamped adding a power integrator (API) technique, a HOSM controller, which can handle the closed-loop sliding mode dynamics synchronously with and without output constraints, is constructively framed. The strictly mathematical proof shows that the presented strategy can assure the finite-time stability of the closed-loop system and the achievement of a pre-set output constraint. The differences between the proposed HOSM controller and the traditional HOSM controller are discussed via a numerical example. Finally, the theoretical results obtained are successfully applied to a series elastic actuator system. The simulation results clearly confirm the merit of the presented HOSM algorithm.