  We consider exact and averaged control problem for a system of quasi-linear
ODEs and SDEs with a non-negative definite symmetric matrix of the system. The
strategy of the proof is the standard linearization of the system by fixing the
function appearing in the nonlinear part of the system, and then applying the
Leray-Schauder fixed point theorem. We shall also need the continuous induction
arguments to prolong the control to the final state which is a novel approach
in the field. This enables us to obtain controllability for arbitrarily large
initial data (so called global controllability).
