Robust control schemes based on higher order sliding mode with energy reduction

It is well known that higher order sliding mode controllers (HOSMCs) are robust against perturbations but consume large amounts of energy which is mainly due to the chaterring of the control input. This paper proposes a controller allowing to keep the robustness while reducing the energy consumption. This is made by introducing a time-varying parameter α on the exponent term of the controller. The finite time convergence of the closed-loop system to a vicinity of the origin is established. Finally, simulations that validate the effectiveness of the proposed controller are presented. An additional result concerning the use of a different law for varying α is introduced.