Singular stochastic control model for algae growth management in dam downstream
A stochastic control model for finding an ecologically sound, fit-for-purpose dam operation policy to suppress bloom of attached algae in its downstream is presented. A singular exactly solvable and a more realistic regular-singular cases are analysed in terms of a Hamilton–Jacobi–Bellman equation....
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2018-01-01
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| Series: | Journal of Biological Dynamics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/17513758.2018.1436197 |
| _version_ | 1818487442679791616 |
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| author | Hidekazu Yoshioka Yuta Yaegashi |
| author_facet | Hidekazu Yoshioka Yuta Yaegashi |
| author_sort | Hidekazu Yoshioka |
| collection | DOAJ |
| description | A stochastic control model for finding an ecologically sound, fit-for-purpose dam operation policy to suppress bloom of attached algae in its downstream is presented. A singular exactly solvable and a more realistic regular-singular cases are analysed in terms of a Hamilton–Jacobi–Bellman equation. Regularity and consistency of the value function are analysed and its classical verification theorem is established. Practical implications of the mathematical analysis results are discussed focusing on parameter dependence of the optimal controls. An asymptotic analysis with a numerical computation reveals solution behaviour of the Hamilton–Jacobi–Bellman equation near the origin, namely at the early stage of algae growth. |
| first_indexed | 2024-12-10T16:37:42Z |
| format | Article |
| id | doaj.art-26573cf623c54441a4fc714f717848c9 |
| institution | Directory Open Access Journal |
| issn | 1751-3758 1751-3766 |
| language | English |
| last_indexed | 2024-12-10T16:37:42Z |
| publishDate | 2018-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Biological Dynamics |
| spelling | doaj.art-26573cf623c54441a4fc714f717848c92022-12-22T01:41:21ZengTaylor & Francis GroupJournal of Biological Dynamics1751-37581751-37662018-01-0112124227010.1080/17513758.2018.14361971436197Singular stochastic control model for algae growth management in dam downstreamHidekazu Yoshioka0Yuta Yaegashi1Shimane UniversityKyoto UniversityA stochastic control model for finding an ecologically sound, fit-for-purpose dam operation policy to suppress bloom of attached algae in its downstream is presented. A singular exactly solvable and a more realistic regular-singular cases are analysed in terms of a Hamilton–Jacobi–Bellman equation. Regularity and consistency of the value function are analysed and its classical verification theorem is established. Practical implications of the mathematical analysis results are discussed focusing on parameter dependence of the optimal controls. An asymptotic analysis with a numerical computation reveals solution behaviour of the Hamilton–Jacobi–Bellman equation near the origin, namely at the early stage of algae growth.http://dx.doi.org/10.1080/17513758.2018.1436197stochastic differential equationsingular controlregular-singular controlattached algaehamilton–jacobi–bellman equation |
| spellingShingle | Hidekazu Yoshioka Yuta Yaegashi Singular stochastic control model for algae growth management in dam downstream Journal of Biological Dynamics stochastic differential equation singular control regular-singular control attached algae hamilton–jacobi–bellman equation |
| title | Singular stochastic control model for algae growth management in dam downstream |
| title_full | Singular stochastic control model for algae growth management in dam downstream |
| title_fullStr | Singular stochastic control model for algae growth management in dam downstream |
| title_full_unstemmed | Singular stochastic control model for algae growth management in dam downstream |
| title_short | Singular stochastic control model for algae growth management in dam downstream |
| title_sort | singular stochastic control model for algae growth management in dam downstream |
| topic | stochastic differential equation singular control regular-singular control attached algae hamilton–jacobi–bellman equation |
| url | http://dx.doi.org/10.1080/17513758.2018.1436197 |
| work_keys_str_mv | AT hidekazuyoshioka singularstochasticcontrolmodelforalgaegrowthmanagementindamdownstream AT yutayaegashi singularstochasticcontrolmodelforalgaegrowthmanagementindamdownstream |