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Infinite-Dimensional Linear Control Problems

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

Abstract

In this chapter we show nonoccurrence of gap for two large classes of infinite-dimensional linear control systems in a Hilbert space with nonconvex integrands. These classes are identified with the corresponding complete metric spaces of integrands which satisfy a growth condition common in the literature. For most elements of the first space of integrands (in the sense of Baire category) we establish the existence of a minimizing sequence of trajectory-control pairs with bounded controls. We also establish that for most elements of the second space (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.

References

  1. 98.
    Zaslavski AJ (2006) Nonoccurrence of gap for infinite dimensional control problems with nonconvex integrands. Optimization 55:171–186MathSciNetzbMATHCrossRefGoogle Scholar
  2. 104.
    Zaslavski AJ (2008) Nonoccurrence of the Lavrentiev phenomenon for many infinite dimensional linear control problems with nonconvex integrands. Dynam Syst Appl 17:407–434MathSciNetzbMATHGoogle 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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