Quasi optimal interorbit transfers of an electrically propelled spacevehicle in strong central gravity field
- Paper number
IAC-08.C1.2.12
- Author
Mr. Igor Vasil'ev, National Taras Shevchenko University of Kyiv, Ukraine
- Coauthor
Prof. Boris Kiforenko, S.P. Timoshenko Institute of Mechanics NASU, Ukraine
- Year
2008
- Abstract
The optimal control problem on the minimum time transfer between arbitrary elliptic orbits in the central gravity field of a spacevehicle equipped with low thrust electric rocket engine is under consideration. Both cases of variable and constant in magnitude rocket thrust are assumed. Increase in interest in such a problem is caused by the beginning of the practical use of electric propulsion nowadays. It is known, that trajectories of low thrust orbit-to-orbit transfers between distant elliptic orbits include a big number of revolutions around attracting center and the two-point boundary problem to which the problem under consideration is reduced by means of the Pontryagin’s maximum principle may be solved only numerically even in the case of the simplest model of the central gravity field. Moreover, the process of such numerical solution is as a rule connected with essential slowdown of the convergence of traditional optimization methods. At the same time, the presence of a small parameter (magnitude of jet acceleration) in motion equations stimulates application of the averaging method for construction of approximate solution of the problem on optimal interorbital transfer. The averaged solution gives in the first approximation estimate of the minimized functional and averaged dependencies on time for slow variables of the problem, but doesn’t solve the problem of finding the control functions of the exact optimal motion equations, that would ensure results close to predicted. That is why it seems to be very useful to develop the methods of solving the exact equations of motion on the trajectories close to optimal ones. An approach is proposed to compute quasi optimal numerical solution of equations of motion of an electrically propelled spacevehicle, which based on using the averaged solution of the corresponding optimal control problem. The examples of solutions of exact optimal motion equations are given, which proof the validity of the proposed approach in combination with using of the averaged solutions.
- Abstract document
- Manuscript document
(absent)