Mathematical Model of Informational Interaction of the Spacecraft with a Surface of the Earth

In the article the mathematical model of informational interaction of the spacecraft with a surface of the Earth is considered. In a basis of construction of model lies proposed of the author the concept of active movable object as the complicated movable system intended for informational, energy or material interaction with an ambient physical environment or with other similar systems. It is shown that the corresponding model can be presented in the form of Fredholm integral operator mapping set of elements of a Hilbert space of controls (a class of admissible control actions) in a Hilbert space of information states. Investigated the properties of this operator and the corresponding reachability sets in space of information states. Considered a simplified variant of the proposed mathematical model - for interaction with the discrete environment (the isolated sources of information).