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Preprint . 2023
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Discrete & Continuous Dynamical Systems - B
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https://dx.doi.org/10.48550/ar...
Article . 2023
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Compactification method in linear programming approach to infinite-horizon optimal control problems with a noncompact state constraint

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2024Embargo end date: 01 Jan 2023Publisher:American Institute of Mathematical Sciences (AIMS)Journal:Discrete and Continuous Dynamical Systems - B, volume 29, pages 110-123 (issn: 1531-3492, eissn: 1553-524X, Copyright policy )
Authors: Shvartsman, Ilya;

doi: 10.3934/dcdsb.2023087 , 10.48550/arxiv.2304.12446

arXiv: http://arxiv.org/abs/2304.12446

Compactification method in linear programming approach to infinite-horizon optimal control problems with a noncompact state constraint

Abstract

This paper is devoted to a study of infinite horizon optimal control problems with time discounting and time averaging criteria in discrete time. It is known that these problems are related to certain infinite-dimensional linear programming problems, but compactness of the state constraint is a common assumption imposed in analysis of these LP problems. In this paper, we consider an unbounded state constraint and use Alexandroff compactification to carry out the analysis. We also establish asymptotic relationships between the optimal values of problems with time discounting and long-run average criteria.

Related Organizations
Keywords

93C55, 49N99, linear programming, optimal control, long-run average, Optimization and Control (math.OC), Linear programming, discrete-time systems, FOS: Mathematics, Existence theories for free problems in two or more independent variables, Mathematics - Optimization and Control, Multi-objective and goal programming, infinite horizon, time discounting

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Green