Well-posedness and Porosity in Nonconvex Optimal control

Alexander J. Zaslavski
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Alexander J. Zaslavski: Technion - Israel Institute of Technology

Chapter Chapter 3 in Nonconvex Optimal Control and Variational Problems, 2013, pp 63-85 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-7378-7_3

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DOI: 10.1007/978-1-4614-7378-7_3

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