Existence theorems for optimal control in some problems of trajectories bundles control

In the paper, some control problems by bundles of trajectories for controlled system are considered. For example, such problems arise if initial point of system is not exactly known. Such inaccuracy essentially complicates control of system. Analogous problems arise in modeling of dynamics for bundles of charged particles. In the paper, some sufficient conditions for existence of optimal control in some problems of control by bundles of trajectories were obtained.