MODEL REDUCTION FOR PARAMETRIZED OPTIMAL CONTROL PROBLEMS IN ENVIRONMENTAL MARINE SCIENCES AND ENGINEERING
In this work we propose reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in environmental marine sciences and engineering. Environmental parametrized optimal control problems are usually studied f...
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ftpoltorinoiris:oai:iris.polito.it:11583/2971223 2024-04-14T08:15:55+00:00 MODEL REDUCTION FOR PARAMETRIZED OPTIMAL CONTROL PROBLEMS IN ENVIRONMENTAL MARINE SCIENCES AND ENGINEERING Strazzullo, M Ballarin, F Mosetti, R Rozza, G Strazzullo, M Ballarin, F Mosetti, R Rozza, G 2018 http://hdl.handle.net/11583/2971223 https://doi.org/10.1137/17M1150591 eng eng SIAM PUBLICATIONS info:eu-repo/semantics/altIdentifier/wos/WOS:000443152600035 volume:40 issue:4 firstpage:B1055 lastpage:B1079 numberofpages:24 journal:SIAM JOURNAL ON SCIENTIFIC COMPUTING http://hdl.handle.net/11583/2971223 doi:10.1137/17M1150591 info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-85053770604 info:eu-repo/semantics/closedAccess reduced order method proper orthogonal decomposition parametrized optimal control problem PDE state equation environmental marine application quasi-geostrophic equation info:eu-repo/semantics/article 2018 ftpoltorinoiris https://doi.org/10.1137/17M1150591 2024-03-21T16:08:55Z In this work we propose reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in environmental marine sciences and engineering. Environmental parametrized optimal control problems are usually studied for different con figurations described by several physical and/or geometrical parameters representing different phenomena and structures. The solution of parametrized problems requires a demanding computational effort. In order to save computational time, we rely on reduced basis techniques as a suitable and rapid tool to solve parametrized problems. We introduce general parametrized linear quadratic optimal control problems and the saddle-point structure of their optimality system. Then, we propose a POD-Galerkin reduction of the optimality system. We test the resulting method on two environmental applications: a pollutant control in the Gulf of Trieste, Italy, and a solution tracking governed by quasi-geostrophic equations describing the North Atlantic Ocean dynamics. The two experiments underline how reduced order methods are a reliable and convenient tool to manage several environmental optimal control problems, for different mathematical models, geographical scale, as well as physical meaning. The quasi-geostrophic optimal control problem is also presented in its nonlinear version. Article in Journal/Newspaper North Atlantic PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino) Saddle Point ENVELOPE(73.483,73.483,-53.017,-53.017) SIAM Journal on Scientific Computing 40 4 B1055 B1079 |
institution |
Open Polar |
collection |
PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino) |
op_collection_id |
ftpoltorinoiris |
language |
English |
topic |
reduced order method proper orthogonal decomposition parametrized optimal control problem PDE state equation environmental marine application quasi-geostrophic equation |
spellingShingle |
reduced order method proper orthogonal decomposition parametrized optimal control problem PDE state equation environmental marine application quasi-geostrophic equation Strazzullo, M Ballarin, F Mosetti, R Rozza, G MODEL REDUCTION FOR PARAMETRIZED OPTIMAL CONTROL PROBLEMS IN ENVIRONMENTAL MARINE SCIENCES AND ENGINEERING |
topic_facet |
reduced order method proper orthogonal decomposition parametrized optimal control problem PDE state equation environmental marine application quasi-geostrophic equation |
description |
In this work we propose reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in environmental marine sciences and engineering. Environmental parametrized optimal control problems are usually studied for different con figurations described by several physical and/or geometrical parameters representing different phenomena and structures. The solution of parametrized problems requires a demanding computational effort. In order to save computational time, we rely on reduced basis techniques as a suitable and rapid tool to solve parametrized problems. We introduce general parametrized linear quadratic optimal control problems and the saddle-point structure of their optimality system. Then, we propose a POD-Galerkin reduction of the optimality system. We test the resulting method on two environmental applications: a pollutant control in the Gulf of Trieste, Italy, and a solution tracking governed by quasi-geostrophic equations describing the North Atlantic Ocean dynamics. The two experiments underline how reduced order methods are a reliable and convenient tool to manage several environmental optimal control problems, for different mathematical models, geographical scale, as well as physical meaning. The quasi-geostrophic optimal control problem is also presented in its nonlinear version. |
author2 |
Strazzullo, M Ballarin, F Mosetti, R Rozza, G |
format |
Article in Journal/Newspaper |
author |
Strazzullo, M Ballarin, F Mosetti, R Rozza, G |
author_facet |
Strazzullo, M Ballarin, F Mosetti, R Rozza, G |
author_sort |
Strazzullo, M |
title |
MODEL REDUCTION FOR PARAMETRIZED OPTIMAL CONTROL PROBLEMS IN ENVIRONMENTAL MARINE SCIENCES AND ENGINEERING |
title_short |
MODEL REDUCTION FOR PARAMETRIZED OPTIMAL CONTROL PROBLEMS IN ENVIRONMENTAL MARINE SCIENCES AND ENGINEERING |
title_full |
MODEL REDUCTION FOR PARAMETRIZED OPTIMAL CONTROL PROBLEMS IN ENVIRONMENTAL MARINE SCIENCES AND ENGINEERING |
title_fullStr |
MODEL REDUCTION FOR PARAMETRIZED OPTIMAL CONTROL PROBLEMS IN ENVIRONMENTAL MARINE SCIENCES AND ENGINEERING |
title_full_unstemmed |
MODEL REDUCTION FOR PARAMETRIZED OPTIMAL CONTROL PROBLEMS IN ENVIRONMENTAL MARINE SCIENCES AND ENGINEERING |
title_sort |
model reduction for parametrized optimal control problems in environmental marine sciences and engineering |
publisher |
SIAM PUBLICATIONS |
publishDate |
2018 |
url |
http://hdl.handle.net/11583/2971223 https://doi.org/10.1137/17M1150591 |
long_lat |
ENVELOPE(73.483,73.483,-53.017,-53.017) |
geographic |
Saddle Point |
geographic_facet |
Saddle Point |
genre |
North Atlantic |
genre_facet |
North Atlantic |
op_relation |
info:eu-repo/semantics/altIdentifier/wos/WOS:000443152600035 volume:40 issue:4 firstpage:B1055 lastpage:B1079 numberofpages:24 journal:SIAM JOURNAL ON SCIENTIFIC COMPUTING http://hdl.handle.net/11583/2971223 doi:10.1137/17M1150591 info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-85053770604 |
op_rights |
info:eu-repo/semantics/closedAccess |
op_doi |
https://doi.org/10.1137/17M1150591 |
container_title |
SIAM Journal on Scientific Computing |
container_volume |
40 |
container_issue |
4 |
container_start_page |
B1055 |
op_container_end_page |
B1079 |
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