Duality in linear programming problems related to deterministic long run average problems of optimal control with applications to periodic optimization

Deterministic long run average optimal control problems and, in particular, periodic optimization problems are related to certain infinite-dimensional linear programming (LP) problems, which can be approximated by finite-dimensional LP problems. In this paper we study problems dual to these infinite- and finite- dimensional LP problems, and we investigate a possibility of using solutions of the latter for numerical construction of the optimal controls in periodic optimization problems. The construction is illustrated with a numerical example.