Lunar capture guidance scheme using Lyapunov feedback control

A lunar orbital capture guidance law is presented for a spacecraft with electrical propulsion system using Lyapunov feedback control approach. Construction of the Lyapunov function candidate is based on orbital elements which consist of angular momentum and eccentricity vectors. Unlike the orbit transfer problem between closed orbits, the lunar capture problem has two constraints. One thing is that the spacecraft coming to the planet with hyperbola orbit conditions must be accomplished the closed orbit conditions before passing the first perilune. And the other one is that the perilune altitude of the spacecraft does not smaller than zero to prevent the crashing problem. For this reason, the variable gain approach is used to accomplish the closed orbit conditions rapidly.