Linear-quadratic control of Volterra integral systems and extensions

Abstract

We study linear-quadratic optimal control problems for Voterra systems, and problems that are linear-quadratic in the control but generally nonlinear in the state. In the case of linear-quadratic Volterra control, we obtain sharp necessary and sufficient conditions for optimality. For problems that are linear-quadratic in the control only, we obtain a novel form of necessary conditions in the form of double Volterra equation; we prove the solvability of such equations.

This work contains further developments of the Volterra portion of arXiv: 1606.05803 (that work contains also Fredholm integral equations). There is minimal partial overlap of this work with arXiv: 1606.05803, in order to keep the present work coherent and readily understandable