On the properness of an impulsive control extension of dynamic optimization problems

This article investigates the properness, or well-posedness, of impulsive extension of a conventional optimal control problem. This includes both well-posedness of the solution to impulsive control systems arising as result of an impulsive extension of ordinary differential systems, and existence th...

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Bibliographic Details
Published inESAIM. Control, optimisation and calculus of variations Vol. 21; no. 3; pp. 857 - 875
Main Authors Karamzin, D.Y., de Oliveira, V.A., Pereira, F.L., Silva, G.N.
Format Journal Article
LanguageEnglish
Published Les Ulis EDP Sciences 01.07.2015
Subjects
49J15
49N25
existence of solutions
Existence theorems
impulsive control
Optimal control
Optimal control extensions
Optimization
Well posed problems
well-posedness of solutions
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Summary:This article investigates the properness, or well-posedness, of impulsive extension of a conventional optimal control problem. This includes both well-posedness of the solution to impulsive control systems arising as result of an impulsive extension of ordinary differential systems, and existence theorems. Well-posedness in the classic Cauchy sense is proved. Approximation lemmas that guarantee sensitivity to small perturbations in control variables are obtained. Filippov type existence theorems are established. A model example is provided to show the relevance of the impulsive controls problems which are under study.
Bibliography:dmitrykaramzin@mail.ru, antunes@ibilce.unesp.br & gsilva@ibilce.unesp.br
publisher-ID:cocv140053
PII:S1292811914000530
istex:CE8B70AD3C2A5F729C2CCD27BD82C19FD141C365
ark:/67375/80W-Q2BZ6PRX-W
ISSN:1292-8119
1262-3377
DOI:10.1051/cocv/2014053