(abstract) Optimal Low Thrust Trajectories Using Differential Inclusion Concepts

Abstract

Low thrust propulsion systems typically have their greatest benefit for high energy missions or missions with large post-launch maneuver requirements. Missions which have been examined include main belt asteroid rendezvous, comet rendezvous, outer planet and Mercury orbiters, Pluto flyby, and solar probe missions. Low thrust mission design software used to determine these trajectories is based on two distinct formulations of the optimal control problem: the indirect and direct methods. The traditional approach (indirect) is to use the calculus of variations to obtain first order necessary conditions on the states and costates. In contrast, direct methods are conceptually different in that no explicit integration takes place. A direct method based on differential inclusion concepts has been developed and successfully used to compute low thrust trajectories. This new approach removes explicit control dependence from the problem thereby reducing the dimension of the parameter space for the nonlinear programming problem. Also when compared to other direct methods, fewer nonlinear constraints are required to represent the dynamics of the problem.