Fuel efficient periodic gain control strategies for spacecraft relative motion in elliptic chief orbits

Periodic gain continuous control strategies are applied to the nonlinear time periodic equations of spacecraft relative motion when the chief orbit is elliptic. Specifically, control strategies based on time-varying linear quadratic regulator (LQR), Lyapunov–Floquet transformation (LFT) with time-invariant LQR, LFT with backstepping, and feedback linearization are implemented and shown to be much more fuel efficient than constant gain feedback control. Both natural and constrained leader-follower two-spacecraft formations are studied. Furthermore, a dead-band control is added for the constrained formation to reduce the amount of the fuel used. The closed-loop response and control effort required are investigated and compared for the same settling time envelopes for all control strategies.