Exact and approximate distributed controllability of processes described by KdV and Boussinesq equations: The Green’s function approach

In this paper, we study the constrained exact and approximate controllability of travelingwave solutions of Korteweg-de Vries (third order) and Boussinesq (fourth order) semi-linearequations using the Green’s function approach. Control is carried out by a moving externalsource. Representing the gene...

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Main Authors:	Klamka Jerzy, Avetisyan Ara S., Khurshudyan Asatur Zh.
Format:	Article
Language:	English
Published:	Polish Academy of Sciences 2020-03-01
Series:	Archives of Control Sciences
Subjects:	kdv equation boussinesq equation frasca’s method short time expansion traveling wave heuristic method distributed control constrained controllability
Online Access:	http://journals.pan.pl/dlibra/publication/132591/edition/115854/content

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spelling	doaj-1e9dd0b3694e4fe49177be6de7b7ce9b2020-11-25T02:55:47ZengPolish Academy of SciencesArchives of Control Sciences1230-23842020-03-0130117719310.24425/acs.2020.132591Exact and approximate distributed controllability of processes described by KdV and Boussinesq equations: The Green’s function approach Klamka Jerzy0Avetisyan Ara S.1Khurshudyan Asatur Zh.2Institute of Control Engineering, Silesian University of Technology, Gliwice, PolandDepartment on Dynamics of Deformable Systems and Coupled Fields, Institute of Mechanics, National Academy of Sciences of ArmeniaDepartmenton Dynamics of Deformable Systems and Coupled Fields, Institute of Mechanics, National Academy of Sciences of Armenia; Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, ChinaIn this paper, we study the constrained exact and approximate controllability of travelingwave solutions of Korteweg-de Vries (third order) and Boussinesq (fourth order) semi-linearequations using the Green’s function approach. Control is carried out by a moving externalsource. Representing the general solution of those equations in terms of the Frasca’s shorttime expansion, system of constraints on the distributed control is derived for both types ofcontrollability. Due to the possibility of explicit solution provided by the heuristic method,the controllability analysis becomes straightforward. Numerical analysis confirms theoreticalderivations.http://journals.pan.pl/dlibra/publication/132591/edition/115854/contentkdv equationboussinesq equationfrasca’s methodshort time expansiontraveling waveheuristic methoddistributed controlconstrained controllability
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Klamka Jerzy Avetisyan Ara S. Khurshudyan Asatur Zh.
spellingShingle	Klamka Jerzy Avetisyan Ara S. Khurshudyan Asatur Zh. Exact and approximate distributed controllability of processes described by KdV and Boussinesq equations: The Green’s function approach Archives of Control Sciences kdv equation boussinesq equation frasca’s method short time expansion traveling wave heuristic method distributed control constrained controllability
author_facet	Klamka Jerzy Avetisyan Ara S. Khurshudyan Asatur Zh.
author_sort	Klamka Jerzy
title	Exact and approximate distributed controllability of processes described by KdV and Boussinesq equations: The Green’s function approach
title_short	Exact and approximate distributed controllability of processes described by KdV and Boussinesq equations: The Green’s function approach
title_full	Exact and approximate distributed controllability of processes described by KdV and Boussinesq equations: The Green’s function approach
title_fullStr	Exact and approximate distributed controllability of processes described by KdV and Boussinesq equations: The Green’s function approach
title_full_unstemmed	Exact and approximate distributed controllability of processes described by KdV and Boussinesq equations: The Green’s function approach
title_sort	exact and approximate distributed controllability of processes described by kdv and boussinesq equations: the green’s function approach
publisher	Polish Academy of Sciences
series	Archives of Control Sciences
issn	1230-2384
publishDate	2020-03-01
description	In this paper, we study the constrained exact and approximate controllability of travelingwave solutions of Korteweg-de Vries (third order) and Boussinesq (fourth order) semi-linearequations using the Green’s function approach. Control is carried out by a moving externalsource. Representing the general solution of those equations in terms of the Frasca’s shorttime expansion, system of constraints on the distributed control is derived for both types ofcontrollability. Due to the possibility of explicit solution provided by the heuristic method,the controllability analysis becomes straightforward. Numerical analysis confirms theoreticalderivations.
topic	kdv equation boussinesq equation frasca’s method short time expansion traveling wave heuristic method distributed control constrained controllability
url	http://journals.pan.pl/dlibra/publication/132591/edition/115854/content
work_keys_str_mv	AT klamkajerzy exactandapproximatedistributedcontrollabilityofprocessesdescribedbykdvandboussinesqequationsthegreensfunctionapproach AT avetisyanaras exactandapproximatedistributedcontrollabilityofprocessesdescribedbykdvandboussinesqequationsthegreensfunctionapproach AT khurshudyanasaturzh exactandapproximatedistributedcontrollabilityofprocessesdescribedbykdvandboussinesqequationsthegreensfunctionapproach
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Exact and approximate distributed controllability of processes described by KdV and Boussinesq equations: The Green’s function approach

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