  The design of multitarget rendezvous missions requires a method to quickly
and accurately approximate the optimal transfer between any two rendezvous
targets. In this paper, a deep neural network (DNN)-based method is proposed
for quickly approximating optimal perturbed long-duration impulsive transfers.
This kind of transfer is divided into three types according to the variation
trend of the right ascension of the ascending node (RAAN) difference between
the departure body and the rendezvous target. An efficient database generation
method combined with a reliable optimization approach is developed. Three
regression DNNs are trained individually and applied to approximate the
corresponding types of transfers. The simulation results show that the
well-trained DNNs are capable of quickly estimating the optimal velocity
increments with a relative error of less than 3% for all the three types of
transfers. The tests on the debris chains with the total velocity increments of
several thousand m/s show that the estimated results can be very close to the
optimized ones with a final estimation error of less than 10 m/s.
