Signum-Function-Based Multi-Input Multi-Output Adaptive Homogeneous Finite-Time Control for a Rigid-Body Attitude Tracking

This study is devoted to investigating the robust adaptive finite-time attitude tracking control problem for a rigid body subject to unknown uncertainties. Considering about the nonlinear attitude dynamics for a rigid body, a homogeneous sliding variable is designed by employing the signum-function technique. For the presented homogeneous sliding variable, a real sliding manifold, on which the singularity problem is avoided, could be achieved. Subsequently, a novel signum-function-based MIMO adaptive homogeneous finite-time control (SMAHFTC) algorithm is proposed. Finite-time convergence of the tracking errors to a region around the origin is rigorously proved through the Lyapunov approach. The control gains will not be overestimated, which implies that minimal control gains will be obtained by the adaptation law. Moreover, the controls' signals are continuous for the SMAHFTC law. Then, by means of the proposed design method, an attitude tracking controller is designed for a rigid body described by the modified Rodrigues parameters' (MRPs) representation. A comparison simulation is carried out to show the effectiveness and superiority of the proposed method.