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Mathematical Programming

, Volume 104, Issue 2–3, pp 347–373 | Cite as

Relaxation of an optimal control problem involving a perturbed sweeping process

  • J.F. Edmond
  • L. ThibaultEmail author
Article

Abstract

We establish first, in the setting of infinite dimensional Hilbert space, a result concerning the existence of solutions for perturbed sweeping processes whose perturbations are Lipschitz single-valued maps. Then we use this result to extend to the infinite dimensional setting a relaxation result concerning optimal control problems involving such processes.

Keywords

Sweeping process Perturbation Prox-regular set Normal cone Optimal control Relaxation Young measure Set-valued map 

Mathematics Subject Classification (2000)

34A60 49J52 49J24 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Département Scientifique Interfacultaire, Campus de SchoelcherUniversité des Antilles et de la GuyaneSchoelcher cedexFrance
  2. 2.Département de MathématiquesUniversité Montpellier IIMontpellier Cedex 5France

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