  Within the framework of the Accardi-Fagnola-Quaegebeur (AFQ) representation
free calculus of \cite{b}, we consider the problem of controlling the size of a
quantum stochastic flow generated by a unitary stochastic evolution affected by
quantum noise. In the case when the evolution is driven by first order white
noise (which includes quantum Brownian motion) the control is shown to be given
in terms of the solution of an algebraic Riccati equation.
  This is done by first solving the problem of controlling (by minimizing an
associated quadratic performance criterion) a stochastic process whose
evolution is described by a stochastic differential equation of the type
considerd in \cite{b}. The solution is given as a feedback control law in terms
of the solution of a stochastic Riccati equation.
