Active formation along a circular orbit by pulse control

The relative motion of a follower satellite with respect to the leader in a given circular orbit is described by autonomous nonlinear differential equations. The linearized equations around the null solution are known as Hill-Clohessy-Wiltshire (HCW) equations. In this paper, active formation flying for the HCW system with pulse (impulse) control input is considered, where the desired relative orbit of the follower is generated by an exosystem. This allows for flexibility of the shape and period of the reference orbit. The output regulation theory for discrete linear system is employed. To show the effectiveness of this approach, numerical examples are given.