On the strong convergence of derivatives in a time optimal problem

We consider a time optimal problem for a system described by a differential inclusion, whose right hand side is not necessarily convex valued. Under the assumption of strict convexity of the map obtained by convexifying the original, non-convex valued map, we obtain the strong convergence of the der...

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Bibliographic Details
Published inNonlinear analysis Vol. 69; no. 7; pp. 1966 - 1970
Main Authors Cellina, A., Monti, F., Spadoni, M.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Ltd 01.10.2008
Elsevier
Subjects
Convergence
Convexity
Derivatives
Differential inclusions
Exact sciences and technology
Fermat principle
Inclusions
Mathematical analysis
Mathematics
Nonlinearity
Ordinary differential equations
Sciences and techniques of general use
Strong convergence
Time optimal
49J12
Strong convergence
Differential inclusions
Time optimal
Time optimal; Differential inclusions; Strong convergence
Differential inclusion
Mathematical model
Nonlinear analysis
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Summary:We consider a time optimal problem for a system described by a differential inclusion, whose right hand side is not necessarily convex valued. Under the assumption of strict convexity of the map obtained by convexifying the original, non-convex valued map, we obtain the strong convergence of the derivatives of any uniformly converging minimizing sequence. The assumptions required by this result are satisfied, for instance, by the classical brachystochrone problem and by Fermat’s principle.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2007.07.037