Determination of optimal controls in a hierarchical system in the presence of external factors

The class of problems that determine the optimal controls in a hierarchical system in the presence of external factors is investigated. These are specific variational problems with coupled constraints on the set of all possible mappings of the control spaces of the system elements. These complicated variational problems are reduced to a number of maximin and extremal problems on the original control sets for two versions of the model, which assume different availability of initial information to the system elements and different optimality criteria.