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

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 solves the resulting two-point boundary value (TPBV) problem numerically. 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. This dissertation provides the analysis for the minimum time satellite formation control by decoupling the in-plane motion from the out-of-plane motion. While the out-of-plane motion is fully analytic, the in-plane motion is only semi-analytic. The TPBV problem is transformed to solving simultaneous nonlinear equations for the critical control switching times, resulting in an open-loop, bang-bang controller.
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