A convex penalty for switching control of partial differential equations

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• 作者：Christian Clason^a ; ^{christian.clason@uni-due.de" class="auth_mail" title="E-mail the corresponding author} ; Armin Rund^b ; ^{armin.rund@uni-graz.at" class="auth_mail" title="E-mail the corresponding author} ; Karl Kunisch^b ; ^{karl.kunisch@uni-graz.at" class="auth_mail" title="E-mail the corresponding author} ; Richard C. Barnard^c ; ^{barnardrc@ornl.gov" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Optimal control ; Switching control ; Partial differential equations ; Nonsmooth optimization ; Convex analysis ; Semi-smooth Newton method
• 刊名：Systems & Control Letters
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：89
• 期：Complete
• 页码：66-73
• 全文大小：432 K

文摘

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. The efficiency of this approach and the structure of the obtained controls are demonstrated by numerical examples.