Formation flying along an elliptic orbit by pulse control

The linearized equations of relative motion of a follower satellite with respect to the leader in a given elliptic orbit are described by Tschauner-Hempel (TH) equations. In this paper, formation flying for the TH system with pulse control input is considered. First, the reconfiguration problem where the desired relative orbit of the follower is natural periodic orbit. Next, the active formation problem where the desired relative orbit is generated by an exosystem is considered. This allows for flexibility of the shape and period of the reference orbit. To realize such a formation flying, the output regulation theory for linear periodic systems is employed. To achieve asymptotic tracking, stabilizing feedback controls are designed by the periodic solution of discrete-time Riccati equation of the linear quadratic regulator (LQR) theory.