%0 Journal Article
%T Use of approximations of Hamilton-Jacobi-Bellman inequality for solving periodic optimization problems
%A Vladimir Gaitsgory
%A Ludmila Manic
%J Mathematics
%D 2013
%I arXiv
%X We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max-min type variational problem considered on the space of continuously differentiable functions. We approximate the latter with a maximin problem on a finite dimensional subspace of the space of continuously differentiable functions and show that a solution of this problem (existing under natural controllability conditions) can be used for construction of near optimal controls. We illustrate the construction with a numerical example.
%U http://arxiv.org/abs/1309.1824v1