On LP Formulations of Optimal Control Problems with Time Averaging and Time Discounting Criteria in Non-Ergodic Case

This paper is devoted to the study of infinite horizon optimal control problems with time discounting and time averaging criteria. These problems are related to certain infinite-dimensional linear programming (IDLP) problems, and this relation is used to obtain properties of the optimal value functions. We focus on the general non-ergodic case, where the optimal value functions may depend on the initial condition of the system. We also obtain IDLP-based sufficient and necessary optimality conditions for optimal control problems.