Linear programming approach to optimal impulse control problems with functional constraints

Alexey Piunovskiy; Yi Zhang

doi:10.1016/j.jmaa.2020.124817

Linear programming approach to optimal impulse control problems with functional constraints

Alexey Piunovskiy, Yi Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

36 Downloads (Pure)

Abstract

This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple constraints on performance functionals of a similar type. Under a natural set of compactness-continuity conditions on the system primitives, we establish a linear programming approach, and prove the existence of a stationary optimal control strategy out of a more general class of randomized strategies. This is done by making use of the tools from Markov decision processes.

Original language	English
Article number	124817
Number of pages	16
Journal	Journal of Mathematical Analysis and Applications
Volume	496
Issue number	2
Early online date	26 Nov 2020
DOIs	https://doi.org/10.1016/j.jmaa.2020.124817
Publication status	Published - 15 Apr 2021

Bibliographical note

Funding Information:
This work was partially supported by the Royal Society International Exchanges award IE160503. The authors are grateful to Professor Alexander Plakhov from University of Aveiro (Portugal) and Institute for Information Transmission Problems (Russia) for fruitful discussions.

Publisher Copyright:
© 2020 Elsevier Inc.

Keywords

Constraints
Dynamical system
Impulse control
Linear programming
Markov decision process
Randomized strategy

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2020.124817Licence: None: All rights reserved

PiunovskiyA2021LinearAccepted author manuscript, 311 KBLicence: Creative Commons: Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)

Cite this

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N2 - This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple constraints on performance functionals of a similar type. Under a natural set of compactness-continuity conditions on the system primitives, we establish a linear programming approach, and prove the existence of a stationary optimal control strategy out of a more general class of randomized strategies. This is done by making use of the tools from Markov decision processes.

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KW - Impulse control

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Linear programming approach to optimal impulse control problems with functional constraints

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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