Time-Delayed Feedback Control of a Hydraulic Model Governed by a Diffusive Wave System
This paper is concerned with the feedback flow control of an open-channel hydraulic system modeled by a diffusive wave equation with delay. Firstly, we put forward a feedback flow control subject to the action of a constant time delay. Thereafter, we invoke semigroup theory to substantiate that the...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/4986026 |
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| _version_ | 1832547163942420480 |
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| author | Boumediène Chentouf Nejib Smaoui |
| author_facet | Boumediène Chentouf Nejib Smaoui |
| author_sort | Boumediène Chentouf |
| collection | DOAJ |
| description | This paper is concerned with the feedback flow control of an open-channel hydraulic system modeled by a diffusive wave equation with delay. Firstly, we put forward a feedback flow control subject to the action of a constant time delay. Thereafter, we invoke semigroup theory to substantiate that the closed-loop system has a unique solution in an energy space. Subsequently, we deal with the eigenvalue problem of the system. More importantly, exponential decay of solutions of the closed-loop system is derived provided that the feedback gain of the control is bounded. Finally, the theoretical findings are validated via a set of numerical results. |
| format | Article |
| id | doaj-art-953daa8cc989458b834c872cc6d65551 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-953daa8cc989458b834c872cc6d655512025-02-03T06:45:59ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/49860264986026Time-Delayed Feedback Control of a Hydraulic Model Governed by a Diffusive Wave SystemBoumediène Chentouf0Nejib Smaoui1Kuwait University, Faculty of Science, Department of Mathematics, Safat 13060, KuwaitKuwait University, Faculty of Science, Department of Mathematics, Safat 13060, KuwaitThis paper is concerned with the feedback flow control of an open-channel hydraulic system modeled by a diffusive wave equation with delay. Firstly, we put forward a feedback flow control subject to the action of a constant time delay. Thereafter, we invoke semigroup theory to substantiate that the closed-loop system has a unique solution in an energy space. Subsequently, we deal with the eigenvalue problem of the system. More importantly, exponential decay of solutions of the closed-loop system is derived provided that the feedback gain of the control is bounded. Finally, the theoretical findings are validated via a set of numerical results.http://dx.doi.org/10.1155/2020/4986026 |
| spellingShingle | Boumediène Chentouf Nejib Smaoui Time-Delayed Feedback Control of a Hydraulic Model Governed by a Diffusive Wave System Complexity |
| title | Time-Delayed Feedback Control of a Hydraulic Model Governed by a Diffusive Wave System |
| title_full | Time-Delayed Feedback Control of a Hydraulic Model Governed by a Diffusive Wave System |
| title_fullStr | Time-Delayed Feedback Control of a Hydraulic Model Governed by a Diffusive Wave System |
| title_full_unstemmed | Time-Delayed Feedback Control of a Hydraulic Model Governed by a Diffusive Wave System |
| title_short | Time-Delayed Feedback Control of a Hydraulic Model Governed by a Diffusive Wave System |
| title_sort | time delayed feedback control of a hydraulic model governed by a diffusive wave system |
| url | http://dx.doi.org/10.1155/2020/4986026 |
| work_keys_str_mv | AT boumedienechentouf timedelayedfeedbackcontrolofahydraulicmodelgovernedbyadiffusivewavesystem AT nejibsmaoui timedelayedfeedbackcontrolofahydraulicmodelgovernedbyadiffusivewavesystem |