Spacecraft Generalized Dynamic Inversion Attitude Control

a This paper introduces a generalized 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 generalized inversion of the relation using the Greville formula. The generalized 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 generalized inverse uniformly converges to the standard Moore-Penrose generalized inverse, causing the particular part to converge uniformly to its projection on the range space of the controls coefficient generalized 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 generalized 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. An illustrating example shows efficacy of the methodology.