Fast methods of synthesis and effective algorithms of airborne antenna beam control for modern high-effciency satellite communication space-based systems have been worked out for the following:

• reflector antennas fed by the antennas array with the amplitude-phase, only phase and double phase control (hybrid reflector antennas, HRA);

• specially shaped reflector with a single feed.

     The developed synthesis methods make it possible to obtain a structure of the antenna, which is steady to manufacturing errors and possesses optimal characteristics of radiation pattern. The proposed algorithms for antenna control allow a wide range of tasks to be solved:

1. To shape fxed beams of complicated form (contour beams) covering the specifed areas on the Earth;

2. To shape reconfgurable contour beams that provide coverage of a specifed territory when a satellite is changing its stationary point in the geostationary orbit or is moving in the elliptic orbit;

3. To shape several simple beams simultaneously;

4. To realize a scanning regime with a shaped contour beam;

5. To realize a scanning regime by undistorted beams within the service area;

6. To optimize reflector's surface and the antenna feeding array according to a given class of rays, etc.

    Our methods of contour beams synthesis are very fast and can be used with onboard equipment of the communication satellites, including LEO-satellite communication systems (Low Earth Orbit), for real-time control of contour beams.

It is feasible to perform the optimum synthesis of hybrid reflector antennas with an umbrella reflector of large electric sizes and with real-time controlled feeding array.