Asymptotic generalised dynamic inversion attitude control

This study introduces a generalised dynamic inversion control methodology for asymptotic spacecraft attitude trajectory tracking. An asymptotically stable second-order servo-constraint attitude deviation dynamics is evaluated along spacecraft equations of motion, resulting in a linear relation in the control vector. A control law that enforces the servo-constraint is derived by generalised inversion of the relation using the Greville formula. The generalised inverse in the particular part of the control law is scaled by a decaying dynamic factor that depends on desired attitude trajectories and body angular velocity components. The scaled generalised inverse uniformly converges to the standard Moore–Penrose generalised inverse, causing the particular part to converge uniformly to its projection on the range space of the controls coefficient generalised inverse, and driving spacecraft attitude variables to nullify attitude deviation. The auxiliary part of the control law acts on the controls coefficient nullspace, and it provides the spacecraft internal stability with the aid of the null-control vector. The null-control vector construction is made by means of novel semidefinite nullprojection control Lyapunov function and state-dependent null-projected Lyapunov equation. The generalised dynamic inversion control signal is multiplied by an exponential factor during transient closed-loop response to enhance the control signal in terms of magnitude and rate of change. Illustrating examples show efficacy of the methodology.