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Title
Optimal control with Lp(), p [0, 1), Control Cost
AuthorIto, Kazufumi In der Gemeinsamen Normdatei der DNB nachschlagen ; Kunisch, Karl In der Gemeinsamen Normdatei der DNB nachschlagen
Published in
SIAM Journal on Control and Optimization, Philadelphia, Pa., 2014, Vol. 52, Issue 2, page 1251-1275
PublishedSIAM
Edition
Publisher version
LanguageEnglish
Document typeJournal Article
Keywords (EN)L0 minimization / optimal control / bang-bang control / sparsity optimization / maximum principle / nonsmooth optimization / primal-dual active set method
ISSN1095-7138
URNurn:nbn:at:at-ubg:3-1239 Persistent Identifier (URN)
DOI10.1137/120896529 
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 The work is publicly available
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Abstract (English)

Lp optimal control with p [0, 1) is investigated. The difficulty of natural lack of convexity and thus of weak lower semicontinuity is addressed by introducing appropriately chosen regularization terms. Existence results and necessary optimality conditions are obtained, and convergence of a monotone scheme is proved. Special attention is given to the particular case of optimal control problems with quadratic tracking and regularized L0 control costs are given. A maximum principle is derived and existence of controls, in some cases relaxed controls, is proved, and an estimate on the consequences of relaxation are estimated.

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