Satellite formation and reconfiguration with restricted control interval

A new formulation of formation flying in an elliptic orbit with restricted control interval is discussed. The main performance index is the L₁ norm of the control input generated by an employed feedback control, which is proportional to the fuel consumption. The null controllability with vanishing energy (NCVE) property enables to design feedback controllers through the linear quadratic regulator (LQR) theory, which generate control inputs with arbitrarily small L₂ norms by imposing a large penalty on control. The L₁ norm of the control input decreases monotonically as the penalty on control increases, and suboptimal controllers are designed. The velocity of the satellite near the apogee is smaller, a relatively small velocity change is required for orbit control and it is assumed that t = 0 is the perigee passage time of the leader, and restrict the control input to the interval.