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Generic Nonoccurrence of the Lavrentiev Phenomenon

  • Alexander J. Zaslavski
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 82)

Abstract

In this chapter we study nonoccurrence of the Lavrentiev phenomenon for a large class of nonconvex optimal control problems. We show that for most problems (in the sense of Baire category) the infimum on the full admissible class of trajectory-control pairs is equal to the infimum on a subclass of trajectory-control pairs with bounded controls.

References

  1. 73.
    Reich S, Zaslavski AJ (2002) Generic existence of fixed points for set-valued mappings. Set-Valued Anal 10:287–296MathSciNetzbMATHCrossRefGoogle Scholar
  2. 103.
    Zaslavski AJ (2008) Generic nonoccurrence of the Lavrentiev phenomenon for a class of optimal control problems. J Dynam Contr Syst 14:95–119MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Alexander J. Zaslavski
    • 1
  1. 1.Department of MathematicsTechnion - Israel Institute of TechnologyHaifaIsrael

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