Immersion and invariance based command-filtered adaptive backstepping control of VTOL vehicles

The main contributions of this article are twofold. Firstly, a guidance law based on a nested saturation function combined with the I&I methodology is proposed for controlling VTOL vehicles subject to mass uncertainty and thrust saturation simultaneously. To simplify the calculations, the virtual attitude extracted from the guidance law is propagated through a command filter, the output of which is tracked by the attitude subsystem. The other contribution is that the influence of the command filter’s frequency on the closed-loop system is rigorously analyzed. The main difficulty in proving the stability is that the command filter’s tracking performance could not be guaranteed when the thrust force encounters the singularity problem. The study avoids this problem by utilizing the properties of nested saturation functions and establishes the semi-global ultimate boundness of the overall closed-loop system. Finally, simulations are presented to show the effectiveness of the proposed control scheme.