Based on the variable structure model reference adaptive control theory, a new output feedback control system, for the formation flying of satellites, is designed. A leader satellite is moving in an elliptic orbit. The objective is to control a follower satellite so that it follows a prescribed path, with respect to the leader satellite. The nonlinear model of the satellite includes unknown parameters, unknown time-varying functions, and disturbance forces; and it is assumed that only the relative position error of the spacecraft is measured for feedback. A variable structure model reference adaptive control system is derived which includes relays and linear first-order filters. In the closed-loop system, including the adaptive control system, the follower satellite tracks given reference trajectories and all the state variables remain bounded. The modulation functions of the relays are functions of certain auxiliary signals and the bounds on the uncertain parameters and unknown signals. A simplified adaptive control law is obtained by the choice of constant modulation functions. Digital simulation results show that the closed-loop system, including the simple control law, has good transient behavior and insensitivity to parametric uncertainties and unknown signals.
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