Second-order analysis and numerical approximation for bang-bang bilinear control problems

We consider bilinear optimal control problems whose objective functionals do not depend on the controls. Hence, bang-bang solutions will appear. We investigate sufficient secondorder conditions for bang-bang controls, which guarantee local quadratic growth of the objective functional in L1 . In addi...

Full description

Bibliographic Details
Authors: Casas Rentería, Eduardo|||0000-0002-8364-9416, Wachsmuth, Daniel, Wachsmuth, Gerd
Format: article
Publication Date:2018
Country:España
Institution:Universidad de Cantabria (UC)
Repository:UCrea Repositorio Abierto de la Universidad de Cantabria
Language:English
OAI Identifier:oai:repositorio.unican.es:10902/15023
Online Access:http://hdl.handle.net/10902/15023
Access Level:Open access
Keyword:Bang-bang control
Bilinear controls
Second-order conditions
Sufficient optimality conditions
Error analysis
id ES_d0327318d99bd06492d7fa7bdf54792c
oai_identifier_str oai:repositorio.unican.es:10902/15023
network_acronym_str ES
network_name_str España
spelling Second-order analysis and numerical approximation for bang-bang bilinear control problems Casas Rentería, Eduardo|||0000-0002-8364-9416 Wachsmuth, Daniel Wachsmuth, Gerd Bang-bang control Bilinear controls Second-order conditions Sufficient optimality conditions Error analysis We consider bilinear optimal control problems whose objective functionals do not depend on the controls. Hence, bang-bang solutions will appear. We investigate sufficient secondorder conditions for bang-bang controls, which guarantee local quadratic growth of the objective functional in L1 . In addition, we prove that for controls that are not bang-bang, no such growth can be expected. Finally, we study the finite-element discretization and prove error estimates of bang-bang controls in L1 -norms. The first author was partially supported by the Spanish Ministerio de Economía Industria y Competitividad under research projects MTM2014-57531-P and MTM2017-83185-P. The second author was partially supported by DFG under grant Wa 3626/1-1. Society for Industrial and Applied Mathematics http://hdl.handle.net/10902/15023
title Second-order analysis and numerical approximation for bang-bang bilinear control problems
spellingShingle Second-order analysis and numerical approximation for bang-bang bilinear control problems
Casas Rentería, Eduardo|||0000-0002-8364-9416
Bang-bang control
Bilinear controls
Second-order conditions
Sufficient optimality conditions
Error analysis
title_short Second-order analysis and numerical approximation for bang-bang bilinear control problems
title_full Second-order analysis and numerical approximation for bang-bang bilinear control problems
title_fullStr Second-order analysis and numerical approximation for bang-bang bilinear control problems
title_full_unstemmed Second-order analysis and numerical approximation for bang-bang bilinear control problems
title_sort Second-order analysis and numerical approximation for bang-bang bilinear control problems
author Casas Rentería, Eduardo|||0000-0002-8364-9416
author_facet Casas Rentería, Eduardo|||0000-0002-8364-9416
Wachsmuth, Daniel
Wachsmuth, Gerd
author_role author
author2 Wachsmuth, Daniel
Wachsmuth, Gerd
author2_role author
author
topic Bang-bang control
Bilinear controls
Second-order conditions
Sufficient optimality conditions
Error analysis
topic_facet Bang-bang control
Bilinear controls
Second-order conditions
Sufficient optimality conditions
Error analysis
description We consider bilinear optimal control problems whose objective functionals do not depend on the controls. Hence, bang-bang solutions will appear. We investigate sufficient secondorder conditions for bang-bang controls, which guarantee local quadratic growth of the objective functional in L1 . In addition, we prove that for controls that are not bang-bang, no such growth can be expected. Finally, we study the finite-element discretization and prove error estimates of bang-bang controls in L1 -norms.
publishDate 2018
format article
url http://hdl.handle.net/10902/15023
language eng
eu_rights_str_mv openAccess
publisher Society for Industrial and Applied Mathematics
institution Universidad de Cantabria (UC)
collection UCrea Repositorio Abierto de la Universidad de Cantabria
reponame_str UCrea Repositorio Abierto de la Universidad de Cantabria
instname_str Universidad de Cantabria (UC)
_version_ 1878441046579347456
publishDateSort 2018
author_browse Casas Rentería, Eduardo|||0000-0002-8364-9416
Wachsmuth, Daniel
Wachsmuth, Gerd
publisherStr Society for Industrial and Applied Mathematics
score 6,924472

Similar Items