Uniqueness of Optimal Control for the Relative Controllability of Neutral Integro-differential Systems in Banach Spaces with Distributed Delays in the Control

Abstract

A new method of approach is derived for the proof of the existence of an optimal control for Neutral Integrodifferential Systems in Banach Spaces with Distributed Delays in the Control, using the properties of optimal control energy function. The set functions upon which our studies hinged were extracted from the mild solution of the system. Use was also made of the unsymmetric Fubini theorem to establish the mild solution. Necessary and sufficient conditions for an admissible control to be an optimal control are established.