Solvable cases of optimal control problems for integral equations

TL;DR

This paper identifies specific solvable cases of optimal control problems involving Volterra and Fredholm integral equations, simplifying their solution process by reducing them to solvable integral equations, similar to Riccati systems in differential control.

Contribution

It introduces new solvable cases for optimal control of integral equations, extending the analogy with Riccati systems in differential equations.

Findings

Certain classes of Volterra and Fredholm integral control problems are reducible to solvable integral equations.

The approach parallels the Riccati differential system in ordinary differential equation control.

Provides a framework for solving integral control problems more efficiently.

Abstract

We present a number of cases of optimal control of Volterra and Fredholm integral equations that are solvable in the sense that the problem can be reduced to a solvable integral equation. This is conceptually analogous to the role of the Riccati differential system in the optimal control of ordinary differential equations.