Optimal control of systems represented by differential-integral equations: An iterative method

In a previous note the author obtained necessary conditions for the optimal control of a system represented by a non-linear differential-integral equation with a general cost function. This note considers the special case of a linear system with a quadratic cost and proposes an iterative method for the solution of the necessary conditions. The method proposed is based on a similar approach suggested by Mueller in his report on systems with constant time lag.