Controllability of dynamic systems with respect to part of the variables

The formulation of the problem on control with respect to part of the variables is considered for the case, that both the initial and final states of the system fall into the same subspace. The necessary and sufficient conditions of controllability with respect to part of the variables for linear self-regulating systems are proved. On the basis of the method of oriented manifolds, a number of theorems on the partial controllability of nonlinear self-regulating systems are derived. A problem on controlling the angular motion of a solid body by means of one rotor is studied.