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On the set of points of smoothness for the value function for affine optimal control problems

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 Added by Davide Barilari
 Publication date 2016
  fields
and research's language is English




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We study the regularity properties of the value function associated with an affine optimal control problem with quadratic cost plus a potential, for a fixed final time and initial point. Without assuming any condition on singular minimizers, we prove that the value function is continuous on an open and dense subset of the interior of the attainable set. As a byproduct we obtain that it is actually smooth on a possibly smaller set, still open and dense.



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