Adaptive dual-layer super-twisting control and observation

In this paper a super-twisting-like structure with adaptive gains is proposed. The structure is parameterized by two scalar gains, both of which adapt, and by an additional time-varying term. The magnitudes of the adaptive terms are allowed to both increase and decrease as appropriate so that they are as small as possible, in the sense that they do not unnecessarily over-bound the uncertainty, and yet are large enough to sustain a sliding motion. In the paper, a new time varying gain is incorporated into the traditional super-twisting architecture. The proposed adaption law has a dual-layer structure which is formally analyzed using Lyapunov techniques. The additional term has the effect of simplifying the stability analysis whilst guaranteeing the second order sliding mode properties of the traditional super-twisting scheme.