Low-thrust reconfiguration for formation flying using Jordan normal form theory

This Paper proposes a control strategy and optimization of low-thrust reconfiguration for formation flying by Jordan norm form to overcome the drawback of eigenvalue decomposition in describing the unstable term of the relative motion. In this Paper, the initial values of general solution from simplified dynamics are regarded as the invariants of formation configuration. The derivation on control acceleration builds a functional from the initial configuration to the final one, which can be approximated by polynomial series. Thus, the selection of time sequence of low thrust can be converted into a parametrical optimization problem that can be achieved by elementary optimization functions. The numerical results show that this proposed strategy realizes the formation reconfiguration with low control acceleration in an orbit period successfully.