OPTIMAL-CONTROL ON LIE-GROUPS WITH APPLICATIONS TO ATTITUDE-CONTROL

In this paper we solve a class of optimal control problems on Lie grou ps in the sense that we derive differential equations which the optima l controls must satisfy. These results are applied to the attitude con trol of a spacecraft modeled as a rigid body. Specifically, we derive control laws (both in open-loop and closed-loop form) to maneuver the spacecraft between two given rotational states in finite time. The law s are such that a cost functional measuring the overall angular veloci ty during the spacecraft's motion is minimized. They do not require re course to numerical methods and hence can be easily implemented in an on-board attitude control system. After dealing with a three-axis cont rolled spacecraft we also discuss the case that only torques about two principal axes of an axisymmetric spacecraft can be exerted.