Model Reduction For Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering

We propose reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in en- vironmental marine sciences and engineering. Environmental parametrized optimal control problems are usually studied for differen...

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Bibliographic Details
Published in:arXiv.org 2018-04
Main Authors: Strazzullo, Maria, Ballarin, Francesco, Mosetti, Renzo, Rozza, Gianluigi
Format: Article
Language:English
Subjects:
Control theory
Galerkin method
Marine engineering
Model reduction
Optimal control
Optimization
Parameterization
Partial differential equations
Saddle points
Test procedures
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Summary:We propose reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in en- vironmental marine sciences and engineering. Environmental parametrized optimal control problems are usually studied for different configurations 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 com- putational time, we rely on reduced basis techniques as a reliable 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. Finally, 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, in its linear and nonlinear version, describing North Atlantic Ocean dynamic. 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.
ISSN:2331-8422
DOI:10.48550/arxiv.1710.01640