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Well-posedness of Optimal Control Problems Without Convexity Assumptions

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

Abstract

In this chapter we prove generic existence results for classes of optimal control problems in which constraint maps are also subject to variations as well as the cost functions. These results were obtained in [87, 90]. More precisely, we establish generic existence results for classes of optimal control problems (with the same system of differential equations, the same boundary conditions and without convexity assumptions) which are identified with the corresponding complete metric spaces of pairs (f, U) (where f is an integrand satisfying a certain growth condition and U is a constraint map) endowed with some natural topology. We will show that for a generic pair (f, U) the corresponding optimal control problem has a unique solution.

Keywords

Optimal Control Problem Variational Principle Closed Subset Lower Semicontinuous Weak Topology 
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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