Uniqueness of Optimal Control of Nonlinear Infinite Neutral Functional Differential Systems with Distributed Delays in the Control

Abstract

In this paper, Nonlinear Infinitely Neutral Functional Differential Systems with Distributed Delays in the Control was presented for controllability analysis. The system was linearized using Chukwu (1992)-like arguments. After linearization, we obtained the mild solution of the system using variation of constant formula and the Unsymmetric Fubuni Theorem to establish the results. The set functions (reachable set, target set, attainable set and controllability grammian) upon which our study hinged were extracted. Necessary and sufficient conditions for the establishment of the uniqueness of the system were derived. Use was made of some controllability standards to establish results. The establishment of the uniqueness of the optimal control provided a new approach for the proof of the existence of an optimal control of any dynamical control system.