Modal control of an unstable periodic orbit.

Floquet theory is applied to the problem of designing a control system for a satellite in an unstable periodic orbit. Expansion about a periodic orbit produces a time-periodic linear system, which is augmented by a time-periodic control term. It is shown that this can be done such that (1) the application of control produces only inertial accelerations, (2) positive real Poincareexponents are shifted into the left half-plane, and (3) the shift of the exponent is linear with control gain. These developments are applied to an unstable orbit near the earth-moon L(3) point pertubed by the sun. Finally, it is shown that the control theory can be extended to include first order perturbations about the periodic orbit without increase in control cost.