The use of solutions to problems of spacecraft trajectory optimization in impulse formulation when solving the problems of optimal control of trajectories of a spacecraft with limited thrust engine: I

Inserting a Maximum-Mass Spacecraft into a Target Orbit Using a Limited-Thrust Engine with Releasing the Separable Part of Its Launch Vehicle into the Earth’s Atmosphere

“…The initial approximation to the values of the phase and conjugate variables in the shooting parameter vector is chosen using the solution obtained previously in the modified pulse statement [1] in accordance with [12]: at the thrust activation time instants they correspond to the values of the phase and conjugate variables before the impulse action; at the thrust deactivation time instants, to the values of the phase and conjugate variables after the impulse action. The duration of active segments is estimated based on fuel consumption for a given engine activation; the duration of passive segments is equal to the corresponding duration of passive segments between the impulse actions.…”

“…As it has turned out, the solution of the spacecraft transfer problem with a high limited-thrust engine is, to some extent, close to that obtained in the pulse statement. In the case under consideration, the method for passing from the latter solution to the former one [12] is effective: the Pontryagin extremal has been constructed.…”

“…The problem under consideration is an optimal control problem with intermediate conditions. It can be solved using Pontryagin's maximum principle [12].…”

“…The problems under consideration are formalized as optimal control problems for a set of dynamic systems. Based on the corresponding Pontryagin's maximum principle [12], they are reduced to multipoint boundary-value problems. The boundary-value problems of the maximum principle are solved numerically by the shooting method [13,14].…”