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Well-posedness and Porosity in Nonconvex Optimal control

In: Nonconvex Optimal Control and Variational Problems

Author

Listed:
  • Alexander J. Zaslavski

    (Technion - Israel Institute of Technology)

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.

Suggested Citation

  • Alexander J. Zaslavski, 2013. "Well-posedness and Porosity in Nonconvex Optimal control," Springer Optimization and Its Applications, in: Nonconvex Optimal Control and Variational Problems, edition 127, chapter 0, pages 63-85, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-7378-7_3
    DOI: 10.1007/978-1-4614-7378-7_3
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