Optimal control in environmental systems and stability analysis
This paper aims at optimizing control in an environmental system with pollution dynamics, economic activity and climatic parameters. The optimal control is calculated using the Pontryagin’s Maximum Principle. The stability of the system is investigated by two methods: Lyapunov’s second method and ei...
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| Format: | Article |
| Language: | English |
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EDP Sciences
2025-01-01
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| Series: | E3S Web of Conferences |
| Online Access: | https://www.e3s-conferences.org/articles/e3sconf/pdf/2025/23/e3sconf_aees2025_01030.pdf |
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| author | Muhamediyeva D. T. Mamatov N. S. Raupova M. H. Kholiyorov Umirzok Yakhyaev Maksud |
| author_facet | Muhamediyeva D. T. Mamatov N. S. Raupova M. H. Kholiyorov Umirzok Yakhyaev Maksud |
| author_sort | Muhamediyeva D. T. |
| collection | DOAJ |
| description | This paper aims at optimizing control in an environmental system with pollution dynamics, economic activity and climatic parameters. The optimal control is calculated using the Pontryagin’s Maximum Principle. The stability of the system is investigated by two methods: Lyapunov’s second method and eigenvalue analysis of the Jacobian matrix. The Lyapunov method can give a conclusion about the system’s asymptotic stability, while the eigenvalue analysis can give information about the stability in the neighbourhood of the equilibrium points. We present a numerical solution of the model and discuss the conditions for stability and the possibility of adjusting the system’s parameters to reach environmental equilibrium. |
| format | Article |
| id | doaj-art-b462a7d46a9a4a3a9cdc25c0d9537284 |
| institution | DOAJ |
| issn | 2267-1242 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | E3S Web of Conferences |
| spelling | doaj-art-b462a7d46a9a4a3a9cdc25c0d95372842025-08-20T03:08:47ZengEDP SciencesE3S Web of Conferences2267-12422025-01-016230103010.1051/e3sconf/202562301030e3sconf_aees2025_01030Optimal control in environmental systems and stability analysisMuhamediyeva D. T.0Mamatov N. S.1Raupova M. H.2Kholiyorov Umirzok3Yakhyaev Maksud4Tashkent Institute of Irrigation and Agricultural Mechanization Engineers National Research UniversityTashkent Institute of Irrigation and Agricultural Mechanization Engineers National Research UniversityChirchik State Pedagogical UniversityTashkent Institute of Irrigation and Agricultural Mechanization Engineers National Research UniversityTashkent Institute of Irrigation and Agricultural Mechanization Engineers National Research UniversityThis paper aims at optimizing control in an environmental system with pollution dynamics, economic activity and climatic parameters. The optimal control is calculated using the Pontryagin’s Maximum Principle. The stability of the system is investigated by two methods: Lyapunov’s second method and eigenvalue analysis of the Jacobian matrix. The Lyapunov method can give a conclusion about the system’s asymptotic stability, while the eigenvalue analysis can give information about the stability in the neighbourhood of the equilibrium points. We present a numerical solution of the model and discuss the conditions for stability and the possibility of adjusting the system’s parameters to reach environmental equilibrium.https://www.e3s-conferences.org/articles/e3sconf/pdf/2025/23/e3sconf_aees2025_01030.pdf |
| spellingShingle | Muhamediyeva D. T. Mamatov N. S. Raupova M. H. Kholiyorov Umirzok Yakhyaev Maksud Optimal control in environmental systems and stability analysis E3S Web of Conferences |
| title | Optimal control in environmental systems and stability analysis |
| title_full | Optimal control in environmental systems and stability analysis |
| title_fullStr | Optimal control in environmental systems and stability analysis |
| title_full_unstemmed | Optimal control in environmental systems and stability analysis |
| title_short | Optimal control in environmental systems and stability analysis |
| title_sort | optimal control in environmental systems and stability analysis |
| url | https://www.e3s-conferences.org/articles/e3sconf/pdf/2025/23/e3sconf_aees2025_01030.pdf |
| work_keys_str_mv | AT muhamediyevadt optimalcontrolinenvironmentalsystemsandstabilityanalysis AT mamatovns optimalcontrolinenvironmentalsystemsandstabilityanalysis AT raupovamh optimalcontrolinenvironmentalsystemsandstabilityanalysis AT kholiyorovumirzok optimalcontrolinenvironmentalsystemsandstabilityanalysis AT yakhyaevmaksud optimalcontrolinenvironmentalsystemsandstabilityanalysis |