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Well-posedness and Porosity in Nonconvex Optimal control

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

Abstract

In[86, 88] we considered a class of optimal control problems which is identified with the corresponding complete metric space of integrands, say \(\mathcal{F}\). We did not impose any convexity assumptions. The main result in[86, 88] establishes that for a generic integrand \(f \in \mathcal{F}\) the corresponding optimal control problem is well posed. In this chapter based on[89] we study the set of all integrands \(f \in \mathcal{F}\) for which the corresponding optimal control problem is well posed. We show that the complement of this set is not only of the first category but also of a σ-porous set.

Keywords

Optimal Control Problem Closed Subset Weak Topology Domain Space Lower Semicontinuous Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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