On some systems controlled by the structure of their memory

TL;DR

This paper studies an optimal control problem where the control is based on the system's memory, proving the existence of solutions and deriving conditions for optimality, with illustrative examples.

Contribution

It introduces a novel control framework where memory influences system control, providing existence proofs and optimality conditions for such systems.

Findings

Existence of optimal solutions established.

Necessary optimality conditions derived.

Illustrative examples discussed.

Abstract

We consider an optimal control problem governed by an ODE with memory playing the role of a control. We show the existence of an optimal solution and derive some necessary optimality conditions. Some examples are then discussed.