Analytical Solution for Low-Thrust Minimum Time Control of a Satellite Formation

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Satellite formations or distributed satellite systems provide advantages not feasible with single satellites. Efficient operation of this platform requires the use of optimal control of the entire satellite formation. While the optimal control theory is well established, only a very simple dynamical system affords an analytical solution. Any practical optimal control problem solve the resulting two-point boundary value (TPBV) problem numerically. In this research, the optimization of satellite formation control is solved analytically. The relative satellite dynamics using Hill’s coordinate system and approximations made by Clohessy and Wiltshire, combined with body-fixed thruster control, result in a linearized dynamic system.