Parametrization of the attainable set for a nonlinear control model of a biochemical process
In this paper, we study a three-dimensional nonlinear model of a controllable reaction$ [X] + [Y] + [Z] \rightarrow [Z] $, where the reaction rate is given by a unspecifiednonlinear function. A model of this type describes a variety of real-life processes in chemicalkinetics and biology; in this pap...
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AIMS Press
2013-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1067 |
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| author | Ellina Grigorieva Evgenii Khailov Andrei Korobeinikov |
| author_facet | Ellina Grigorieva Evgenii Khailov Andrei Korobeinikov |
| author_sort | Ellina Grigorieva |
| collection | DOAJ |
| description | In this paper, we study a three-dimensional nonlinear model of a controllable reaction$ [X] + [Y] + [Z] \rightarrow [Z] $, where the reaction rate is given by a unspecifiednonlinear function. A model of this type describes a variety of real-life processes in chemicalkinetics and biology; in this paper our particular interests is in its application to wastewater biotreatment. For this control model, we analytically study the corresponding attainableset and parameterize it by the moments of switching of piecewise constant control functions.This allows us to visualize the attainable sets using a numerical procedure. These analytical results generalize the earlier findings, which were obtained for a trilinearreaction rate (which corresponds to the law of mass action) and reportedin [18,19], to the case of a general rate of reaction. These results allow toreduce the problem of constructing the optimal control to a straightforward constrained finitedimensional optimization problem. |
| format | Article |
| id | doaj-art-b36515bfc5f840d58db1353b2f68a485 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-b36515bfc5f840d58db1353b2f68a4852025-01-24T02:26:20ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-05-011041067109410.3934/mbe.2013.10.1067Parametrization of the attainable set for a nonlinear control model of a biochemical processEllina Grigorieva0Evgenii Khailov1Andrei Korobeinikov2Department of Mathematics and Computer Sciences, Texas Woman's University, Denton, TX 76204Department of Mathematics and Computer Sciences, Texas Woman's University, Denton, TX 76204Department of Mathematics and Computer Sciences, Texas Woman's University, Denton, TX 76204In this paper, we study a three-dimensional nonlinear model of a controllable reaction$ [X] + [Y] + [Z] \rightarrow [Z] $, where the reaction rate is given by a unspecifiednonlinear function. A model of this type describes a variety of real-life processes in chemicalkinetics and biology; in this paper our particular interests is in its application to wastewater biotreatment. For this control model, we analytically study the corresponding attainableset and parameterize it by the moments of switching of piecewise constant control functions.This allows us to visualize the attainable sets using a numerical procedure. These analytical results generalize the earlier findings, which were obtained for a trilinearreaction rate (which corresponds to the law of mass action) and reportedin [18,19], to the case of a general rate of reaction. These results allow toreduce the problem of constructing the optimal control to a straightforward constrained finitedimensional optimization problem.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1067waste water biotreatmentenvironmental problemnonlinear reaction rateattainable set. |
| spellingShingle | Ellina Grigorieva Evgenii Khailov Andrei Korobeinikov Parametrization of the attainable set for a nonlinear control model of a biochemical process Mathematical Biosciences and Engineering waste water biotreatment environmental problem nonlinear reaction rate attainable set. |
| title | Parametrization of the attainable set for a nonlinear control model of a biochemical process |
| title_full | Parametrization of the attainable set for a nonlinear control model of a biochemical process |
| title_fullStr | Parametrization of the attainable set for a nonlinear control model of a biochemical process |
| title_full_unstemmed | Parametrization of the attainable set for a nonlinear control model of a biochemical process |
| title_short | Parametrization of the attainable set for a nonlinear control model of a biochemical process |
| title_sort | parametrization of the attainable set for a nonlinear control model of a biochemical process |
| topic | waste water biotreatment environmental problem nonlinear reaction rate attainable set. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1067 |
| work_keys_str_mv | AT ellinagrigorieva parametrizationoftheattainablesetforanonlinearcontrolmodelofabiochemicalprocess AT evgeniikhailov parametrizationoftheattainablesetforanonlinearcontrolmodelofabiochemicalprocess AT andreikorobeinikov parametrizationoftheattainablesetforanonlinearcontrolmodelofabiochemicalprocess |