Existence and multiple solutions of the minimum-fuel orbit transfer problem. (English) Zbl 0896.49021

Oberle, H. J.; Taubert, K.

J. Optimization Theory Appl. 95, No. 2, 243-262 (1997).

Summary: The well-known problem of piloting a rocket with a low thrust propulsion system in an inverse square law field (say from Earth orbit to Mars orbit or from Earth orbit to Mars) is considered. By direct methods, it is shown that the existence of a fuel-optimal solution of this problem can be guaranteed, if one restricts the admissible transfer times by an arbitrarily prescribed upper bound. Numerical solutions of the problem with different numbers of thrust subarcs are presented which are obtained by multiple shooting techniques. Further, a general principle for the construction of such solutions with increasing numbers of thrust subarcs is given. The numerical results indicate that there might not exist an overall optimal solution of the Earth-orbit problem with unbounded free transfer time.

MSC:

49N70	Differential games and control
49N75	Pursuit and evasion games
49J15	Existence theories for optimal control problems involving ordinary differential equations
70P05	Variable mass, rockets

Keywords:

orbit transfer; existence of optimal control; control constraints; minimum principle; numerical method; multiple solutions; multiple shooting techniques

Software:

BNDSCO

References:

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