Satellite formation with restricted control interval

In this paper, a formation problem of a satellite with a leader in an eccentric orbit is considered, where the transition to a periodic relative orbit is required, and the control input is restricted to a subinterval of the period of the leader´s orbit. As preliminaries, the same problem in the special case of the circular orbit is considered, and feedback controls based on a differential Riccati equation with a periodic control matrix are designed. The performance index is the L1-norm of the feedback control, and suboptimal controls are obtained by virtue of the null controllability with vanishing energy of the controlled system. Then the original problem is transformed into a special form by the change of variables, and using the structure of the resulting system, feedback controls are designed based on those of the circular problem.