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 traveling wave solutions of Korteweg-de Vries (third order) and Boussinesq (fourth order) semi-linear equations using the Green’s function approach. Control is carried out by a moving external source. Representing the g...
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| Format: | Article |
| Language: | English |
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Polish Academy of Sciences
2020-03-01
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| Series: | Archives of Control Sciences |
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| Online Access: | https://journals.pan.pl/Content/115854/PDF/ACS-2020-1-9.pdf |
| _version_ | 1811330379834982400 |
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| author | Jerzy, Klamka Ara, S., Avetisyan Asatur, Zh., Khurshudyan |
| author_facet | Jerzy, Klamka Ara, S., Avetisyan Asatur, Zh., Khurshudyan |
| author_sort | Jerzy, Klamka |
| collection | DOAJ |
| description | In this paper, we study the constrained exact and approximate controllability of traveling wave solutions of Korteweg-de Vries (third order) and Boussinesq (fourth order) semi-linear equations using the Green’s function approach. Control is carried out by a moving external source. Representing the general solution of those equations in terms of the Frasca’s short time expansion, system of constraints on the distributed control is derived for both types of controllability. Due to the possibility of explicit solution provided by the heuristic method, the controllability analysis becomes straightforward. Numerical analysis confirms theoretical derivations. |
| first_indexed | 2024-04-13T16:01:31Z |
| format | Article |
| id | doaj.art-1e9dd0b3694e4fe49177be6de7b7ce9b |
| institution | Directory Open Access Journal |
| issn | 1230-2384 |
| language | English |
| last_indexed | 2024-04-13T16:01:31Z |
| publishDate | 2020-03-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | Archives of Control Sciences |
| spelling | doaj.art-1e9dd0b3694e4fe49177be6de7b7ce9b2022-12-22T02:40:31ZengPolish Academy of SciencesArchives of Control Sciences1230-23842020-03-01vol. 30No 1177193https://doi.org/10.24425/acs.2020.132591Exact and approximate distributed controllability of processes described by KdV and Boussinesq equations: The Green’s function approachJerzy, KlamkaAra, S., AvetisyanAsatur, Zh., KhurshudyanIn this paper, we study the constrained exact and approximate controllability of traveling wave solutions of Korteweg-de Vries (third order) and Boussinesq (fourth order) semi-linear equations using the Green’s function approach. Control is carried out by a moving external source. Representing the general solution of those equations in terms of the Frasca’s short time expansion, system of constraints on the distributed control is derived for both types of controllability. Due to the possibility of explicit solution provided by the heuristic method, the controllability analysis becomes straightforward. Numerical analysis confirms theoretical derivations.https://journals.pan.pl/Content/115854/PDF/ACS-2020-1-9.pdfkdv equationboussinesq equationfrasca’s methodshort time expansiontraveling waveheuristic methoddistributed controlconstrained controllability |
| spellingShingle | Jerzy, Klamka Ara, S., Avetisyan Asatur, Zh., Khurshudyan 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 |
| title | 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_short | 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 |
| topic | kdv equation boussinesq equation frasca’s method short time expansion traveling wave heuristic method distributed control constrained controllability |
| url | https://journals.pan.pl/Content/115854/PDF/ACS-2020-1-9.pdf |
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