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

TL;DR

This paper develops an $H_{ {infty}}$ inverse optimal control method for attitude tracking on the $SO(3)$ group, ensuring disturbance attenuation and optimality, with demonstrated competitive simulation results.

Contribution

It introduces a novel inverse optimal $H_{ {infty}}$ control approach for attitude tracking on $SO(3)$, combining disturbance attenuation with optimality conditions.

Findings

Guarantees bounded energy gain from disturbances to errors.

Provides conditions for solving inverse optimal nonlinear $H_{ {infty}}$ control.

Simulation results show competitive performance.

Abstract

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 $H_{\infty}$ 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.