New Optimal Control Problems for Wastewater Treatment with Different Types of Bacteria
The aim of this paper is to propose mathematical models to predict and optimize the cost of wastewater treatment using bacteria and oxygen under fluctuating resource and cultivation conditions. We have thus developed deterministic mathematical models based on dynamic systems and applied optimal cont...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-06-01
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| Series: | AppliedMath |
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| Online Access: | https://www.mdpi.com/2673-9909/5/2/73 |
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| _version_ | 1839654995167805440 |
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| author | Séverine Bernard Estive Germain Alain Piétrus |
| author_facet | Séverine Bernard Estive Germain Alain Piétrus |
| author_sort | Séverine Bernard |
| collection | DOAJ |
| description | The aim of this paper is to propose mathematical models to predict and optimize the cost of wastewater treatment using bacteria and oxygen under fluctuating resource and cultivation conditions. We have thus developed deterministic mathematical models based on dynamic systems and applied optimal control theory to reduce treatment costs. Two wastewater treatment models are proposed: one using only one type of aerobic bacteria, thermophilic bacteria; and the second using two types of aerobic bacteria, thermophilic and mesophilic bacteria. For each model, an optimal control problem is solved and numerical simulations illustrate the theoretical results. |
| format | Article |
| id | doaj-art-d154bb192a0c4f32b10b62d3ad5ee351 |
| institution | Matheson Library |
| issn | 2673-9909 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | AppliedMath |
| spelling | doaj-art-d154bb192a0c4f32b10b62d3ad5ee3512025-06-25T13:24:10ZengMDPI AGAppliedMath2673-99092025-06-01527310.3390/appliedmath5020073New Optimal Control Problems for Wastewater Treatment with Different Types of BacteriaSéverine Bernard0Estive Germain1Alain Piétrus2Laboratoire de Mathématiques Informatique et Applications (LAMIA), Université des Antilles, EA4540, Campus de Fouillole, BP 250, 97159 Pointe-à-Pitre CEDEX, FranceDFR Sciences et Technologies, Université de Guyane, Campus de Troubiran, BP 20792, 97337 Cayenne CEDEX, FranceLaboratoire de Mathématiques Informatique et Applications (LAMIA), Université des Antilles, EA4540, Campus de Fouillole, BP 250, 97159 Pointe-à-Pitre CEDEX, FranceThe aim of this paper is to propose mathematical models to predict and optimize the cost of wastewater treatment using bacteria and oxygen under fluctuating resource and cultivation conditions. We have thus developed deterministic mathematical models based on dynamic systems and applied optimal control theory to reduce treatment costs. Two wastewater treatment models are proposed: one using only one type of aerobic bacteria, thermophilic bacteria; and the second using two types of aerobic bacteria, thermophilic and mesophilic bacteria. For each model, an optimal control problem is solved and numerical simulations illustrate the theoretical results.https://www.mdpi.com/2673-9909/5/2/73wastewateraerobic bacteriaoxygendynamical systemordinary differential equationoptimal control |
| spellingShingle | Séverine Bernard Estive Germain Alain Piétrus New Optimal Control Problems for Wastewater Treatment with Different Types of Bacteria AppliedMath wastewater aerobic bacteria oxygen dynamical system ordinary differential equation optimal control |
| title | New Optimal Control Problems for Wastewater Treatment with Different Types of Bacteria |
| title_full | New Optimal Control Problems for Wastewater Treatment with Different Types of Bacteria |
| title_fullStr | New Optimal Control Problems for Wastewater Treatment with Different Types of Bacteria |
| title_full_unstemmed | New Optimal Control Problems for Wastewater Treatment with Different Types of Bacteria |
| title_short | New Optimal Control Problems for Wastewater Treatment with Different Types of Bacteria |
| title_sort | new optimal control problems for wastewater treatment with different types of bacteria |
| topic | wastewater aerobic bacteria oxygen dynamical system ordinary differential equation optimal control |
| url | https://www.mdpi.com/2673-9909/5/2/73 |
| work_keys_str_mv | AT severinebernard newoptimalcontrolproblemsforwastewatertreatmentwithdifferenttypesofbacteria AT estivegermain newoptimalcontrolproblemsforwastewatertreatmentwithdifferenttypesofbacteria AT alainpietrus newoptimalcontrolproblemsforwastewatertreatmentwithdifferenttypesofbacteria |