We consider a terminal control problem for processes governed by a nonlinear system of fractional ODEs. In order to show existence of the control, we first consider the linear counterpart of the system and reprove a number of classical theorems in the fractional setting (representation of the solution through the Gramian type matrix, Kalman's principle, equivalence of the controllability and observability). We are then in the position to use a fixed point theorem approach and various techniques from the fractional calculus theory to get the desired result.