Linear Programming Based Optimality Conditions and Approximate Solution of a Deterministic Infinite Horizon Discounted Optimal Control Problem in Discrete Time

TL;DR

This paper links infinite horizon discounted optimal control problems to linear programming, establishing optimality conditions and constructing near-optimal controls using these connections.

Contribution

It introduces necessary and sufficient optimality conditions for discrete-time infinite horizon control problems via linear programming methods.

Findings

Established optimality conditions based on linear programming duality.

Constructed near-optimal controls using the derived conditions.

Linked control problems to infinite-dimensional linear programming frameworks.

Abstract

It has been recently established that a deterministic infinite horizon discounted optimal control problem in discrete time is closely related to a certain infinite dimensional linear programming problem and its dual. In the present paper, we use these results to establish necessary and sufficient optimality conditions for this optimal control problem and apply them to construct a near optimal control.