Low-Thrust Transfers using Primer Vector Theory and a Second-Order Penalty Method

The low-thrust trajectory problem is formulated using techniques from calculus of variations, parameter optimization, and differential dynamic programming. Primer vector theory provides the thrust profile as a feedback law, parameterized by the initial co-states. The first and second derivatives of various penalty functions are derived from principles of static-dynamic control and dynamic programming. Both bang-bang/constant ejection velocity and variable specific impulse cases are considered, the former being complicated by the mapping of derivatives across switching times. A trust-region optimizer is then developed, where these derivatives are used to solve transfers between periodic orbits in the circular, restricted, three-body problem.