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

Vladimir Gaitsgory; Alex Parkinson; Ilya Shvartsman

doi:10.3934/dcdsb.2018235

Article Contents

2019, Volume 24, Issue 4: 1743-1767. Doi: 10.3934/dcdsb.2018235

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

1.
Department of Mathematics, Macquarie University, Macquarie Park, NSW 2113, Australia
2.
Department of Mathematics and Computer Science, Penn State Harrisburg, Middletown, PA 17057, USA

* Corresponding author
* Corresponding author

Received: August 31, 2017

Revised: December 31, 2017

Early access: August 2018

Published: January 2019

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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.

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Mathematics Subject Classification: Primary: 49N15, 49M29, 93C55.

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Figure 1. The state trajectory - 50 time steps

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Figure 2. The state trajectory - time step 1

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Figure 3. The state trajectory - time steps 1 and 2

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Figure 4. The state trajectory - 50 time steps

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