Linear programming based optimality conditions and approximate solution of a deterministic infinite horizon discounted optimal control problem in discrete time

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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, the latter taking the form of a certain max-min problem. In the present paper, we use these results to establish necessary and sufficient optimality conditions for this optimal control problem and to investigate a way how the latter can be used for the construction of a near optimal control.

LanguageEnglish
Pages1743-1767
Number of pages25
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume24
Issue number4
DOIs
Publication statusPublished - 1 Apr 2019

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Infinite Horizon
Optimality Conditions
Linear programming
Optimal Control Problem
Discrete-time
Approximate Solution
Min-max Problem
Necessary and Sufficient Optimality Conditions
Optimal Control
Form

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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, the latter taking the form of a certain max-min problem. In the present paper, we use these results to establish necessary and sufficient optimality conditions for this optimal control problem and to investigate a way how the latter can be used for the construction of a near optimal control.",
keywords = "Discrete systems, Duality, Infinite horizon, Linear programming, Numerical methods, Occupational measures, Optimal control",
author = "Vladimir Gaitsgory and Alex Parkinson and Ilya Shvartsman",
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