Continuous higher order sliding mode control based on adaptive disturbance compensation

In this paper a new continuous adaptive r-th order sliding mode controller is proposed. It is built from two components: one which guarantees smooth finite time stabilization of the origin for the known nominal system, and one which represents a disturbance observer, based on a super-twisting structure, to guarantee robustness to a class of twice differentiable uncertainty. The observer has adaptive features which minimize the size of the gains, whilst still guaranteeing the existence of a sliding motion. The adaptive scheme has a dual-layer structure based on equivalent injection concepts. The paper provides computer simulations to validate the theory.