LP Formulations of Discrete Time Long-Run Average Optimal Control Problems: The Non-Ergodic Case

We formulate and study the infinite dimensional linear programming (LP) problem associated with the deterministic discrete time long-run average criterion optimal control problem. Along with its dual, this LP problem allows one to characterize the optimal value of the optimal control problem. The novelty of our approach is that we focus on the general case wherein the optimal value may depend on the initial condition of the system.