Adaptive continuous higher order sliding mode control

This paper proposes an adaptive continuous higher order sliding mode control scheme. The control law comprises a structure which provides smooth finite time stabilization of the origin for a nominal disturbance-free system formed from a chain of integrators, together with a super-twisting term to guarantee robustness to a class of twice differentiable uncertainty. The super-twisting scheme is adaptive in nature and seeks to minimize the size of the gains whilst still ensuring sliding. The adaptive scheme has a novel dual-layer structure based on equivalent injection concepts, which necessitates that the first and second derivatives of the uncertainty exist and are bounded, but knowledge of these bounds is not required. Simulation examples are provided to show the effectiveness of the proposed scheme.