Linear Programming Formulation of Long Run Average Optimal Control Problem

TL;DR

This paper presents a linear programming approach to solve the long-run average optimal control problem, providing a way to characterize the optimal value even when initial conditions influence the system.

Contribution

It introduces an infinite dimensional linear programming formulation and its dual for the long-run average optimal control problem, accommodating initial condition dependencies.

Findings

Linear programming characterizes the optimal control value.

Dual problem provides additional insights into optimality.

Method applies to general systems with initial condition dependence.

Abstract

We introduce and study the infinite dimensional linear programming problem which along with its dual allows one to characterize the optimal value of the deterministic long-run average optimal control problem in the general case when the latter may depend on the initial conditions of the system.