Adaptive Backstepping Control Based on Global HOSM Differentiators With Dynamic Gains

The present paper proposes the application of global and exact differentiators with dynamic gains based on higher-order sliding modes (HOSM) to the design of adaptive backstepping control for nonlinear uncertain systems of strict-feedback type. The use of this kind of differentiator in the closed-loop system allow us to guarantee global uniform stability (for any initial conditions) due to the variable nature of the dynamic gain. The dynamic gain can grow or decrease with the unmeasured state. In addition, asymptotic output tracking is also assured. In order to illustrate the results of the new theorem, the proposed controller is applied to a high-performance aircraft system, suppressing the wing-rock phenomenon usually observed for fast-speed flight conditions. Comparison results with a linear-inexact differentiator, a local HOSM differentiator with fixed gains and the proposed global and exact HOSM differentiator with dynamic gain shows the superiority of the latter over the former approaches. To demonstrate the practical efficacy of the proposed approach, we conclude with an experimental test featuring a DC motor and the novel differentiator-based backstepping control scheme.