Monitoring function for switching adaptation in control and estimation schemes with sliding modes

A novel strategy for gain adaptation of higherorder sliding mode (HOSM) based differentiators is developed, considering that the upper bound for the higher timederivatives of the output tracking error exist but they are unknown. Differently of earlier approaches, the proposed adaptive method is based on switching monitoring functions, which assures global stability and exact tracking when applied to output feedback. The challenging class of uncertain nonlinear plants of arbitrary relative degree handled in the paper includes time-varying and state-dependent disturbances with unknown bounds as well as unknown control directions. The unmeasured state is norm bounded through an adaptive state-norm estimator with hybrid dynamics. Simulations illustrate the potential applicability for control design and estimation in sliding mode schemes.