Quaternion Feedback Attitude Control Design: a Nonlinear H∞ Approach

The paper presents a quaternion feedback attitude control law for spacecraft attitude maneuver. A nonlinear feedback controller is designed to achieve L2 gain performance, i.e., the resulting closed-loop system is designed such that the L2 gain from the exogenous disturbance to the performance measure is less than a scalar. The solution of the nonlinear H∞ control problem is known to be related to the existence of a solution to the Hamilton-Jacobi inequality. In the paper, a solution for spacecraft attitude control is conjectured and shown to satisfy the H∞ criterion. The result generalizes existing methods in two regards: the proposed Hamilton-Jacobi function is more general than existing ones and the resulting controller contains a nonlinear term that can be used to address the nonlinear couplings between quaternion terms. The method is applied to the ROCSAT-3 orbit raising control problem to verify its effectiveness.