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Е.В. Кирилюк, М.Н. Степанов
22
Инженерный журнал: наука и инновации
# 3
⋅
2016
Some aspects of solving the optimal control problem
on the basis of the maximum principle for non-coplanar
interorbital transfer
© E.V. Kiriluk
1
, M.N. Stepanov
1, 2
1
Bauman Moscow State Technical University, Moscow, 105005, Russia
2
4th Central Research Institute of the Ministry of Defence of the Russian Federation,
Yubileynyy town, 141091, Russia
The article considers the approach to solve the problem of determining the optimal thrust
vector control of propulsion system according to the criterion of maximization of the
payload mass in the orbital unit launch into an arbitrary target orbit, which is non-
coplanar to the original one.
The problem is solved using Pontryagin’s maximum
principle, which reduces the problem of optimal control search to solve a boundary value
problem.
The successful solution of the problem depends on the quality of the initial
approximation of its unknown parameters. In solving the problem the parameter
continuation method was applied. The technique of operational conversion of the
conjugate variable initial values using the symmetry properties of the target orbit
inclination with respect to the plane of the initial reference orbit was also applied.
As a
part of the work numerical modeling of the orbital block motion in the central
gravitational field of the Earth with the optimal control, obtained on the basis of the
maximum principle, was carried out. The dependence of the optimal launch scenario on
the form (eccentricity) of the target orbit was analyzed. The behavior of conjugate
variables, determining the vector of optimal control, which delivers a maximum output
payload mass with set limits on the duration of transfer, was analyzed for a wide range of
target orbit’s inclination. The analysis revealed the symmetry properties of the behavior
of conjugate variables, the use of which improves the efficiency of finding the optimal
solution. The obtained results can be applied in the field of ballistic design calculations
related to the development of launch vehicles (boosters, space tugs) and spacecraft for
various purposes. They can also be applied for assessing the capacity of existing launch
vehicles and determining the first approximation in the development of transfer schemes.
Keywords:
Pontryagin's maximum principle, non-coplanar interorbital transfer, optimal
control, launch.
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