Adaptive external torque estimation by means of tracking a Lyapunov function

A real-time method is presented to adoptively estimate three-dimensional unmodeled external torques acting on a spacecraft. This is accomplished by forcing the tracking error dynamics to follow the Lyapunov function underlying the feedback control law. For the case where the external torque is constant, the tracking error dynamics are shown to converge asypmtotically. The methodology applies not only to the control law used in this paper, but can also be applied to most Lyapunov derived feedback control laws. The adaptive external torque estimation is very robust in the presence of measurement noise, since a numerical integration is used instead of a numerical differentiation. Spacecraft modeling errors, such as in the inertia matrix, are also compensated for by this method. Several examples illustrate the practical significance of these ideas.