On a linear-quadratic problem with Caputo derivative

In this paper, we study a linear-quadratic optimal control problem with a fractional control system containing a Caputo derivative of unknown function. First, we derive the formulas for the differential and gradient of the cost functional under given constraints. Next, we prove an existence result a...

Full description

Bibliographic Details
Main Authors:	Dariusz Idczak, Stanislaw Walczak
Format:	Article
Language:	English
Published:	AGH Univeristy of Science and Technology Press 2016-01-01
Series:	Opuscula Mathematica
Subjects:	fractional Caputo derivative linear-quadratic problem existence and uniqueness of a solution maximum principle gradient method projection of the gradient method
Online Access:	http://www.opuscula.agh.edu.pl/vol36/1/art/opuscula_math_3603.pdf

id	doaj-0f2934d96f944c43a9240c66c7af812d
record_format	Article
spelling	doaj-0f2934d96f944c43a9240c66c7af812d2020-11-24T23:59:45ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742016-01-013614968http://dx.doi.org/10.7494/OpMath.2016.36.1.493603On a linear-quadratic problem with Caputo derivativeDariusz Idczak0Stanislaw Walczak1University of Lodz, Faculty of Mathematics and Computer Science, Banacha 22, 90-238 Lodz, PolandUniversity of Lodz, Faculty of Mathematics and Computer Science, Banacha 22, 90-238 Lodz, PolandIn this paper, we study a linear-quadratic optimal control problem with a fractional control system containing a Caputo derivative of unknown function. First, we derive the formulas for the differential and gradient of the cost functional under given constraints. Next, we prove an existence result and derive a maximum principle. Finally, we describe the gradient and projection of the gradient methods for the problem under consideration.http://www.opuscula.agh.edu.pl/vol36/1/art/opuscula_math_3603.pdffractional Caputo derivativelinear-quadratic problemexistence and uniqueness of a solutionmaximum principlegradient methodprojection of the gradient method
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Dariusz Idczak Stanislaw Walczak
spellingShingle	Dariusz Idczak Stanislaw Walczak On a linear-quadratic problem with Caputo derivative Opuscula Mathematica fractional Caputo derivative linear-quadratic problem existence and uniqueness of a solution maximum principle gradient method projection of the gradient method
author_facet	Dariusz Idczak Stanislaw Walczak
author_sort	Dariusz Idczak
title	On a linear-quadratic problem with Caputo derivative
title_short	On a linear-quadratic problem with Caputo derivative
title_full	On a linear-quadratic problem with Caputo derivative
title_fullStr	On a linear-quadratic problem with Caputo derivative
title_full_unstemmed	On a linear-quadratic problem with Caputo derivative
title_sort	on a linear-quadratic problem with caputo derivative
publisher	AGH Univeristy of Science and Technology Press
series	Opuscula Mathematica
issn	1232-9274
publishDate	2016-01-01
description	In this paper, we study a linear-quadratic optimal control problem with a fractional control system containing a Caputo derivative of unknown function. First, we derive the formulas for the differential and gradient of the cost functional under given constraints. Next, we prove an existence result and derive a maximum principle. Finally, we describe the gradient and projection of the gradient methods for the problem under consideration.
topic	fractional Caputo derivative linear-quadratic problem existence and uniqueness of a solution maximum principle gradient method projection of the gradient method
url	http://www.opuscula.agh.edu.pl/vol36/1/art/opuscula_math_3603.pdf
work_keys_str_mv	AT dariuszidczak onalinearquadraticproblemwithcaputoderivative AT stanislawwalczak onalinearquadraticproblemwithcaputoderivative
_version_	1725446360187011072

On a linear-quadratic problem with Caputo derivative

Similar Items