Hölder-Continuous Finite-Time-Stable Tracking Control of Attitude Dynamics

This article presents an attitude tracking control scheme with Hölder continuity and finite-time stability. The first part of this article discusses and compares the features of first-order multivariable Hölder-continuous systems with coupled-scalar sliding-mode systems. The advantages of Hölder-continuous systems over sliding-mode systems are presented from the perspectives of control continuity and noise robustness. Thereafter, a Hölder-continuous second-order differentiator is presented with its stability and robustness properties. This is followed by its use in an attitude tracking control scheme, which is covered in the second part of the article. The proposed tracking control scheme is designed directly on the state-space of rigid-body rotational motion, which is the tangent bundle of the Lie group of 3D rotations. The control scheme design, its stability, and its robustness properties are obtained through Lyapunov stability analyses. The proposed Hölder-continuous design is compared with three comparable sliding-mode designs. Numerical simulations on a simulated CubeSat demonstrate the performance of the proposed control scheme and compare it with the sliding-mode control schemes. The numerical simulations also compare the proposed control scheme with other state-of-the-art sliding-mode control approaches in existing research publications. The comparison results demonstrate that the proposed Hölder-continuous attitude control scheme exhibits lower control efforts and tracking control errors over these sliding-mode control schemes in simulations that incorporate actuator dynamics and measurement uncertainties.