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Decentralized Stochastic Control with Finite-Dimensional Memories: A Memory Limitation Approach
Decentralized stochastic control (DSC) is a stochastic optimal control problem consisting of multiple controllers. DSC assumes that each controller is unable to accurately observe the target system and the other controllers. This setup results in two difficulties in DSC; one is that each controller...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2023
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10217446/ https://www.ncbi.nlm.nih.gov/pubmed/37238546 http://dx.doi.org/10.3390/e25050791 |
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author | Tottori, Takehiro Kobayashi, Tetsuya J. |
author_facet | Tottori, Takehiro Kobayashi, Tetsuya J. |
author_sort | Tottori, Takehiro |
collection | PubMed |
description | Decentralized stochastic control (DSC) is a stochastic optimal control problem consisting of multiple controllers. DSC assumes that each controller is unable to accurately observe the target system and the other controllers. This setup results in two difficulties in DSC; one is that each controller has to memorize the infinite-dimensional observation history, which is not practical, because the memory of the actual controllers is limited. The other is that the reduction of infinite-dimensional sequential Bayesian estimation to finite-dimensional Kalman filter is impossible in general DSC, even for linear-quadratic-Gaussian (LQG) problems. In order to address these issues, we propose an alternative theoretical framework to DSC—memory-limited DSC (ML-DSC). ML-DSC explicitly formulates the finite-dimensional memories of the controllers. Each controller is jointly optimized to compress the infinite-dimensional observation history into the prescribed finite-dimensional memory and to determine the control based on it. Therefore, ML-DSC can be a practical formulation for actual memory-limited controllers. We demonstrate how ML-DSC works in the LQG problem. The conventional DSC cannot be solved except in the special LQG problems where the information the controllers have is independent or partially nested. We show that ML-DSC can be solved in more general LQG problems where the interaction among the controllers is not restricted. |
format | Online Article Text |
id | pubmed-10217446 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-102174462023-05-27 Decentralized Stochastic Control with Finite-Dimensional Memories: A Memory Limitation Approach Tottori, Takehiro Kobayashi, Tetsuya J. Entropy (Basel) Article Decentralized stochastic control (DSC) is a stochastic optimal control problem consisting of multiple controllers. DSC assumes that each controller is unable to accurately observe the target system and the other controllers. This setup results in two difficulties in DSC; one is that each controller has to memorize the infinite-dimensional observation history, which is not practical, because the memory of the actual controllers is limited. The other is that the reduction of infinite-dimensional sequential Bayesian estimation to finite-dimensional Kalman filter is impossible in general DSC, even for linear-quadratic-Gaussian (LQG) problems. In order to address these issues, we propose an alternative theoretical framework to DSC—memory-limited DSC (ML-DSC). ML-DSC explicitly formulates the finite-dimensional memories of the controllers. Each controller is jointly optimized to compress the infinite-dimensional observation history into the prescribed finite-dimensional memory and to determine the control based on it. Therefore, ML-DSC can be a practical formulation for actual memory-limited controllers. We demonstrate how ML-DSC works in the LQG problem. The conventional DSC cannot be solved except in the special LQG problems where the information the controllers have is independent or partially nested. We show that ML-DSC can be solved in more general LQG problems where the interaction among the controllers is not restricted. MDPI 2023-05-12 /pmc/articles/PMC10217446/ /pubmed/37238546 http://dx.doi.org/10.3390/e25050791 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Tottori, Takehiro Kobayashi, Tetsuya J. Decentralized Stochastic Control with Finite-Dimensional Memories: A Memory Limitation Approach |
title | Decentralized Stochastic Control with Finite-Dimensional Memories: A Memory Limitation Approach |
title_full | Decentralized Stochastic Control with Finite-Dimensional Memories: A Memory Limitation Approach |
title_fullStr | Decentralized Stochastic Control with Finite-Dimensional Memories: A Memory Limitation Approach |
title_full_unstemmed | Decentralized Stochastic Control with Finite-Dimensional Memories: A Memory Limitation Approach |
title_short | Decentralized Stochastic Control with Finite-Dimensional Memories: A Memory Limitation Approach |
title_sort | decentralized stochastic control with finite-dimensional memories: a memory limitation approach |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10217446/ https://www.ncbi.nlm.nih.gov/pubmed/37238546 http://dx.doi.org/10.3390/e25050791 |
work_keys_str_mv | AT tottoritakehiro decentralizedstochasticcontrolwithfinitedimensionalmemoriesamemorylimitationapproach AT kobayashitetsuyaj decentralizedstochasticcontrolwithfinitedimensionalmemoriesamemorylimitationapproach |