Towards Tensor Representation of Controlled Coupled Markov Chains
For a controlled system of coupled Markov chains, which share common control parameters, a tensor description is proposed. A control optimality condition in the form of a dynamic programming equation is derived in tensor form. This condition can be reduced to a system of coupled ordinary differentia...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/10/1712 |
| _version_ | 1797551804280471552 |
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| author | Daniel McInnes Boris Miller Gregory Miller Sergei Schreider |
| author_facet | Daniel McInnes Boris Miller Gregory Miller Sergei Schreider |
| author_sort | Daniel McInnes |
| collection | DOAJ |
| description | For a controlled system of coupled Markov chains, which share common control parameters, a tensor description is proposed. A control optimality condition in the form of a dynamic programming equation is derived in tensor form. This condition can be reduced to a system of coupled ordinary differential equations and admits an effective numerical solution. As an application example, the problem of the optimal control for a system of water reservoirs with phase and balance constraints is considered. |
| first_indexed | 2024-03-10T15:51:16Z |
| format | Article |
| id | doaj.art-e9237e7e77694272b137fc6981c2a999 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:51:16Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e9237e7e77694272b137fc6981c2a9992023-11-20T16:05:24ZengMDPI AGMathematics2227-73902020-10-01810171210.3390/math8101712Towards Tensor Representation of Controlled Coupled Markov ChainsDaniel McInnes0Boris Miller1Gregory Miller2Sergei Schreider3School of Mathematics, Monash University, Wellington Road, Clayton VIC 3800, AustraliaSchool of Mathematics, Monash University, Wellington Road, Clayton VIC 3800, AustraliaInstitute of Informatics Problems of Federal Research Center “Computer Science and Control” RAS, 44/2 Vavilova Str., 119333 Moscow, RussiaDepartment of Management and Information Systems, Rutgers Business School, Rutgers—The State University of New Jersey, New Brunswick, NJ 07102, USAFor a controlled system of coupled Markov chains, which share common control parameters, a tensor description is proposed. A control optimality condition in the form of a dynamic programming equation is derived in tensor form. This condition can be reduced to a system of coupled ordinary differential equations and admits an effective numerical solution. As an application example, the problem of the optimal control for a system of water reservoirs with phase and balance constraints is considered.https://www.mdpi.com/2227-7390/8/10/1712coupled markov chainsstochastic controloptimal controltensor representationdynamic programming |
| spellingShingle | Daniel McInnes Boris Miller Gregory Miller Sergei Schreider Towards Tensor Representation of Controlled Coupled Markov Chains Mathematics coupled markov chains stochastic control optimal control tensor representation dynamic programming |
| title | Towards Tensor Representation of Controlled Coupled Markov Chains |
| title_full | Towards Tensor Representation of Controlled Coupled Markov Chains |
| title_fullStr | Towards Tensor Representation of Controlled Coupled Markov Chains |
| title_full_unstemmed | Towards Tensor Representation of Controlled Coupled Markov Chains |
| title_short | Towards Tensor Representation of Controlled Coupled Markov Chains |
| title_sort | towards tensor representation of controlled coupled markov chains |
| topic | coupled markov chains stochastic control optimal control tensor representation dynamic programming |
| url | https://www.mdpi.com/2227-7390/8/10/1712 |
| work_keys_str_mv | AT danielmcinnes towardstensorrepresentationofcontrolledcoupledmarkovchains AT borismiller towardstensorrepresentationofcontrolledcoupledmarkovchains AT gregorymiller towardstensorrepresentationofcontrolledcoupledmarkovchains AT sergeischreider towardstensorrepresentationofcontrolledcoupledmarkovchains |