  In this paper we study the quadratic regulator problem for a process governed
by a Volterra integral equation in ${\mathbb R}^n$. Our main goal is the proof
that it is possible to associate a Riccati differential equation to this
quadratic control problem, which leads to the feedback form of the optimal
control. This is in contrast with previous papers on the subject, which confine
themselves to study the Fredholm integral equation which is solved by the
optimal control.
