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Erschienen in:
2013 | OriginalPaper | Buchkapitel
3. Well-posedness and Porosity in Nonconvex Optimal control
verfasst von : Alexander J. Zaslavski
Erschienen in: Nonconvex Optimal Control and Variational Problems
Verlag: Springer New York
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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.