Second-order sliding-mode on SO(3) and fault-tolerant spacecraft attitude control (Q2681357)

A control system for a rigid body on the group SO(3) of \(3\times 3\) orthogonal matrices with determinant 1 is considered. A second-order sliding-mode surface is introduced, which is a Lie subgroup of \(\mathrm{SO}(3)\times\mathbb{R}^3\). The reduced-order dynamics is shown to be almost globally asymptotically convergent to a stable equilibrium. A quasi-continuous reaching law is designed, and robustness of the closed-loop system is proved. Suppression of the chattering is analyzed. Simulation results are presented.