Currently, there is a rapid development of modern unmanned aerial vehicles (UAVs), which are widely used in various areas of the economy. For the effective and reliable operation of UAVs, it is necessary to create modern distributed UAV control systems. The paper proposes a method for formalizing and solving the problem of designing the structure of a UAV control system, which includes finding the best distribution of UAV control functions over a spatial system of control units and technical means. We reduced this problem to a special case of the generalized quadratic assignment problem (GQAP), which is formulated in terms of quadratic integer programming. The proposed approach to solving the problem allows us to consider it in a multicriterial setting. A polynomial algorithm for solving it based on the branch and bound method is developed, data on the time of finding a solution for various strategies for moving along the tree of options and the dimension of the problem are given.