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

Abstract

The problem of attitude tracking using rotation matrices is addressed using an approach which combines inverse optimality and L 2 disturbance attenuation. Conditions are provided which solve the inverse optimal nonlinear H ∞ 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.