$H_{\mathrm{\infty }}$ Inverse Optimal Attitude Tracking on the Special Orthogonal Group $SO(3)$

The problem of attitude tracking using rotation matrices is addressed using an approach which combines inverse optimality and ${\mathcal{L}}_2$ disturbance attenuation. Conditions are provided which solve the inverse optimal nonlinear $H_{\mathrm{\infty }}$ control problem by minimizing a meaningful cost function. The approach guarantees that the energy gain from an exogenous disturbance to a specified error signal respects a given upper bound. For numerical simulations, a simple problem setup from literature is considered and results demonstrate competitive performance.