Authors :
Paul Anaetodike Oraekie; Chukwuma Uzoma Okele
Volume/Issue :
Volume 8 - 2023, Issue 10 - October
Google Scholar :
https://tinyurl.com/2buwzxy7
Scribd :
https://tinyurl.com/3nwtj74y
DOI :
https://doi.org/10.5281/zenodo.10090693
Abstract :
In this work, Nonlinear Implicit Fractional
Integrodifferential Systems in Banach Spaces with
Distributed Delays in the Control were presented for
Relative Controllability analysis. General argument was
found which was used to establish the relationship
between the relative controllability and the intersection
of the two compact and convex set functions derived
from the mild solution of the system. The establishment
of the relationship gives impetus to the existence of
optimal control for the system as it becomes self-
evidence that the intersection of the two compact and
convex set functions be non-void to establish relative
controllability. Thus we have established relative
controllability of our system. Uses were made of the
notion of the measure of non-compactness of a set and
Dabos’ fixed point theorem, as well as the unsymmetric
Fubinis’ theorem to establish the mild solution of the
system .Necessary and sufficient conditions for the
existence of computable criterion for the relative
controllability of our system were established. The
establishment was built on the usage of definition of
properness of the system and the effects of the existence
of zero in the interior of a reachable set of any dynamical
control system.
Keywords :
Maximization, Dabos’ Fixed Point Theorem, Mild Solution, Optimal Control Relative Controllability, Set Function, Measure of Non-Compactness, Calculus of Variation.
In this work, Nonlinear Implicit Fractional
Integrodifferential Systems in Banach Spaces with
Distributed Delays in the Control were presented for
Relative Controllability analysis. General argument was
found which was used to establish the relationship
between the relative controllability and the intersection
of the two compact and convex set functions derived
from the mild solution of the system. The establishment
of the relationship gives impetus to the existence of
optimal control for the system as it becomes self-
evidence that the intersection of the two compact and
convex set functions be non-void to establish relative
controllability. Thus we have established relative
controllability of our system. Uses were made of the
notion of the measure of non-compactness of a set and
Dabos’ fixed point theorem, as well as the unsymmetric
Fubinis’ theorem to establish the mild solution of the
system .Necessary and sufficient conditions for the
existence of computable criterion for the relative
controllability of our system were established. The
establishment was built on the usage of definition of
properness of the system and the effects of the existence
of zero in the interior of a reachable set of any dynamical
control system.
Keywords :
Maximization, Dabos’ Fixed Point Theorem, Mild Solution, Optimal Control Relative Controllability, Set Function, Measure of Non-Compactness, Calculus of Variation.
