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Title: A convex penalty for switching control of partial differential equations

A convex penalty for promoting switching controls for partial differential equations is introduced; such controls consist of an arbitrary number of components of which at most one should be simultaneously active. Using a Moreau–Yosida approximation, a family of approximating problems is obtained that is amenable to solution by a semismooth Newton method. In conclusion, the efficiency of this approach and the structure of the obtained controls are demonstrated by numerical examples.
Authors:
 [1] ;  [2] ;  [2] ;  [3]
  1. Univ. of Duisburg-Essen, Essen (Germany)
  2. Karl-Franzens-Univ. Graz, Graz (Austria)
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Grant/Contract Number:
AC05-00OR22725
Type:
Accepted Manuscript
Journal Name:
Systems & Control Letters
Additional Journal Information:
Journal Volume: 89; Journal ID: ISSN 0167-6911
Publisher:
Elsevier
Research Org:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; optimal control; switching control; partial differential equations; nonsmooth optimization; convex analysis; semi-smooth Newton method
OSTI Identifier:
1266013

Clason, Christian, Rund, Armin, Kunisch, Karl, and Barnard, Richard C. A convex penalty for switching control of partial differential equations. United States: N. p., Web. doi:10.1016/j.sysconle.2015.12.013.
Clason, Christian, Rund, Armin, Kunisch, Karl, & Barnard, Richard C. A convex penalty for switching control of partial differential equations. United States. doi:10.1016/j.sysconle.2015.12.013.
Clason, Christian, Rund, Armin, Kunisch, Karl, and Barnard, Richard C. 2016. "A convex penalty for switching control of partial differential equations". United States. doi:10.1016/j.sysconle.2015.12.013. https://www.osti.gov/servlets/purl/1266013.
@article{osti_1266013,
title = {A convex penalty for switching control of partial differential equations},
author = {Clason, Christian and Rund, Armin and Kunisch, Karl and Barnard, Richard C.},
abstractNote = {A convex penalty for promoting switching controls for partial differential equations is introduced; such controls consist of an arbitrary number of components of which at most one should be simultaneously active. Using a Moreau–Yosida approximation, a family of approximating problems is obtained that is amenable to solution by a semismooth Newton method. In conclusion, the efficiency of this approach and the structure of the obtained controls are demonstrated by numerical examples.},
doi = {10.1016/j.sysconle.2015.12.013},
journal = {Systems & Control Letters},
number = ,
volume = 89,
place = {United States},
year = {2016},
month = {1}
}