Nonoccurrence of the Lavrentiev Phenomenon in Optimal Control

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


In this chapter we study nonoccurrence of the Lavrentiev phenomenon for a large class of nonconvex optimal control problems which is identified with the corresponding complete metric space of integrands \(\mathcal{M}\) which satisfy a growth condition common in the literature and are Lipschitzian on bounded sets. We establish that for most elements of \(\mathcal{M}\) (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 whose controls are bounded by a certain constant.


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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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