  This paper is concerned with a linear quadratic optimal control for a class
of singular Volterra integral equations. Under proper convexity conditions,
optimal control uniquely exists, and it could be characterized via Frechet
derivative of the quadratic functional in a Hilbert space or via maximum
principle type necessary conditions. However, these (equivalent)
characterizations have a shortcoming that the current value of the optimal
control depends on the future values of the optimal state. Practically, this is
not feasible. The main purpose of this paper is to obtain a causal state
feedback representation of the optimal control.
