On some problems of trajectory beam program control. Part I

This paper deals with problems of program control of a trajectory beam. We investigate formulations that arise when considering problems of charged particle beams control, as well as, for example, in image processing. In applied problems, it is often necessary to investigate the problem of the gravity center control of some set or changing the density distribution of particles according to some given one. The functionals proposed in the paper can be effectively used for the velocity field constructing in various image processing, in particular, medical diagnostic images. In this paper, the problem of constructing a velocity field is considered as a control and optimization problem, and, unlike the previous works of the authors, macroparameters characterizing the objects under study are used in optimization. In the article, variations of the studied functionals are obtained and the necessary optimality conditions are given.