OPTIMAL CONTROL FOR ENGINES WITH ELECTRO-IONIC PROPULSION UNDER CONSTRAINT OF ECLIPSE

We are interested in the calculation of the optimal low-thrust transfer of a satellite subjected to solar eclipses. The modeling of this constraint leads to a set of admissible controls U( t, x) discontinuously dependent on the time t and on the state of the system x (the satellite's position). This set of controls does not allow to use the classical Pontryagin's principle (see Epenoy, Technical Report DGA/T/TI/MS/MN/98-014, CNES, 1998 and Ferrier, Technical Report T/TS/TI/MS/MN/98-031, CNES, 1998). We show then how to envelope this problem by means of two neighboring problems. These problems, which are built by means of change of variable and smoothing, fulfill the assumptions of Pontryagin's principle and their optimal cost function encloses the original problem. Finally, we apply these results to the geostationary transfer.