Causal state feedback representation for linear quadratic optimal control problems of singular Volterra integral equations

<p style='text-indent:20px;'>This paper is concerned with a linear quadratic optimal control for class of singular Volterra integral equations. Our framework covers the problems fractional differential Under some necessary convexity conditions, an exists, and can be characterized via Fréchet derivative functional in Hilbert space or maximum principle type conditions. However, these (equivalent) characterizations are not causal, meaning that current value depends on future values state. Practically, this feasible. We obtain causal state feedback representation Fredholm equation. Finally, concrete form our results equations presented.</p>