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Title
On the use of state constraints in optimal control of singular PDEs
AuthorClason, Christian ; Kaltenbacher, Barbara
Published in
Systems & control letters / Ed. R.W. Brockett [u.a.], Amsterdam [u.a.] : Elsevier, 1.1981/82 - 62.2013; Vol. 63.2014 -, Vol. 62, Issue 1, page 48-54
PublishedElsevier
LanguageEnglish
Document typeJournal Article
Keywords (EN)Optimal control of PDEs / Control constraints / State constraints / Singular PDEs / Microelectromechanical systems (MEMS)
ISSN1872-7956
URNurn:nbn:at:at-ubg:3-467 Persistent Identifier (URN)
DOIdoi:10.1016/j.sysconle.2012.10.006 
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 The work is publicly available
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Abstract (English)

We consider optimal control of nonlinear partial differential equations involving potentially singular solution-dependent terms. Singularity can be prevented by either restricting controls to a closed admissible set for which well-posedness of the equation can be guaranteed, or by explicitly enforcing pointwise bounds on the state. By means of an elliptic model problem, we contrast the requirements for deriving the existence of solutions and first order optimality conditions for both the control-constrained and the state-constrained formulation. Our analysis as well as numerical tests illustrate that control constraints lead to severe restrictions on the attainable states, which is not the case for state constraints.

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