The article focuses on the development of an on-board system design method for optimal control of an autonomous mobile group of objects. It is assumed that the group consists of a leader and some agents. A new method for the synthesis of an optimal multivariable control system, which is needed for preserving desired position of the agent relatively to the leader was substantiated in the article. The leader passes along a random trajectory and measurement of the agent position with respect to the leader is accompanied with random noise. All group members experience the action of random disturbances.