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Decentralized social‐optimal solution of finite number of average field linear quadratic control

Decentralized social‐optimal solution of finite number of average field linear quadratic control This paper studies the decentralized solution to the linear quadratic social‐optimal mean field control problem, when a finite number subsystems is considered. We use the term average field, to distinguish this case from the one with infinite subsystems. The goal of each subsystem is to design its input to optimize a common cost of social type. To this end, each subsystem use only real‐time information which can be either its local state, or a linear measurement noisy measurement of it. Our result generalizes previous ones in three senses. First, it permits designing controls when there are a finite number of subsystems. Second, it permits considering heterogeneous subsystems, that is, having different structural parameters. Third, it permits designing not only state feedback controls but also output feedback ones. In particular, we show that the separation principle holds in the latter case. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Asian Journal of Control Wiley

Decentralized social‐optimal solution of finite number of average field linear quadratic control

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References (23)

Publisher
Wiley
Copyright
© 2022 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd
ISSN
1561-8625
eISSN
1934-6093
DOI
10.1002/asjc.2588
Publisher site
See Article on Publisher Site

Abstract

This paper studies the decentralized solution to the linear quadratic social‐optimal mean field control problem, when a finite number subsystems is considered. We use the term average field, to distinguish this case from the one with infinite subsystems. The goal of each subsystem is to design its input to optimize a common cost of social type. To this end, each subsystem use only real‐time information which can be either its local state, or a linear measurement noisy measurement of it. Our result generalizes previous ones in three senses. First, it permits designing controls when there are a finite number of subsystems. Second, it permits considering heterogeneous subsystems, that is, having different structural parameters. Third, it permits designing not only state feedback controls but also output feedback ones. In particular, we show that the separation principle holds in the latter case.

Journal

Asian Journal of ControlWiley

Published: Jul 1, 2022

Keywords: decentralized control; mean field; social‐optimal

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