On the convergence of the gradient projection method for convex optimal control problems with bang–bang solutions

We revisit the gradient projection method in the framework of nonlinear optimal control problems with bang–bang solutions. We obtain the strong convergence of the iterative sequence of controls and the corresponding trajectories. Moreover, we establish a convergence rate, depending on a constant app...

Descripción completa

Detalles Bibliográficos
Autores principales: Preininger, J., Vuong, P. T.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2018
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6560933/
https://www.ncbi.nlm.nih.gov/pubmed/31258250
http://dx.doi.org/10.1007/s10589-018-9981-6
_version_ 1783426052591190016
author Preininger, J.
Vuong, P. T.
author_facet Preininger, J.
Vuong, P. T.
author_sort Preininger, J.
collection PubMed
description We revisit the gradient projection method in the framework of nonlinear optimal control problems with bang–bang solutions. We obtain the strong convergence of the iterative sequence of controls and the corresponding trajectories. Moreover, we establish a convergence rate, depending on a constant appearing in the corresponding switching function and prove that this convergence rate estimate is sharp. Some numerical illustrations are reported confirming the theoretical results.
format Online
Article
Text
id pubmed-6560933
institution National Center for Biotechnology Information
language English
publishDate 2018
publisher Springer US
record_format MEDLINE/PubMed
spelling pubmed-65609332019-06-26 On the convergence of the gradient projection method for convex optimal control problems with bang–bang solutions Preininger, J. Vuong, P. T. Comput Optim Appl Article We revisit the gradient projection method in the framework of nonlinear optimal control problems with bang–bang solutions. We obtain the strong convergence of the iterative sequence of controls and the corresponding trajectories. Moreover, we establish a convergence rate, depending on a constant appearing in the corresponding switching function and prove that this convergence rate estimate is sharp. Some numerical illustrations are reported confirming the theoretical results. Springer US 2018-01-29 2018 /pmc/articles/PMC6560933/ /pubmed/31258250 http://dx.doi.org/10.1007/s10589-018-9981-6 Text en © The Author(s) 2018 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Preininger, J.
Vuong, P. T.
On the convergence of the gradient projection method for convex optimal control problems with bang–bang solutions
title On the convergence of the gradient projection method for convex optimal control problems with bang–bang solutions
title_full On the convergence of the gradient projection method for convex optimal control problems with bang–bang solutions
title_fullStr On the convergence of the gradient projection method for convex optimal control problems with bang–bang solutions
title_full_unstemmed On the convergence of the gradient projection method for convex optimal control problems with bang–bang solutions
title_short On the convergence of the gradient projection method for convex optimal control problems with bang–bang solutions
title_sort on the convergence of the gradient projection method for convex optimal control problems with bang–bang solutions
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6560933/
https://www.ncbi.nlm.nih.gov/pubmed/31258250
http://dx.doi.org/10.1007/s10589-018-9981-6
work_keys_str_mv AT preiningerj ontheconvergenceofthegradientprojectionmethodforconvexoptimalcontrolproblemswithbangbangsolutions
AT vuongpt ontheconvergenceofthegradientprojectionmethodforconvexoptimalcontrolproblemswithbangbangsolutions

Ejemplares similares