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

The quadratic regulator problem and the Riccati equation for a process governed by a linear Volterra integrodifferential equations