Generalized Model Reference Adaptive Control by Means of Global HOSM Differentiators

Abstract

In this paper, we combine a global differentiator based on higher-order sliding modes (HOSM) and dynamic gains with classical model reference adaptive control (MRAC) schemes to solve the relevant and yet open problem of trajectory tracking via output feedback of uncertain plants with arbitrary relative degree in a simple-closed form for the control design. The gains of the differentiator are adapted through state-norm observers for the unmeasured state, whereas the control parametrization explores the input–output filters commonly used in the MRAC design. Global asymptotic stability and robust exact tracking are rigorously demonstrated. Simulations highlight the claimed properties as well as the remarkable simplicity of the proposed adaptive control system using robust exact differentiators when compared to more involved alternatives found in standard approaches. The theoretical results are also illustrated with an application to bilateral teleoperation.