One of the fundamental problems in spacecraft trajectory design is finding the optimal transfer trajec-tory that minimizes the propellant consumption and transfer time simultaneously. We formulate this as a multi-objective optimal control (MOC) problem that involves optimizing over the initial or final state, subject to state constraints. Drawing on recent developments in reachability analysis subject to state con-straints, we show that the proposed MOC problem can be stated as an optimization problem subject to a constraint that involves the sub-level set of the viscosity solution of a quasi-variational inequality. We then generalize this approach to account for more general optimal control problems in Bolza form. We relate these problems to the Pareto front of the developed multi-objective programs. The proposed ap-proach is demonstrated on two low-thrust orbital transfer problems around a rotating asteroid.(c) 2022 The Author(s). Published by Elsevier Ltd on behalf of European Control Association. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )
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