Stabilization for the Stochastic Heat Equation with Boundary Control
This paper investigates the stabilization of an unstable stochastic heat equation. By the backstepping technique, a boundary feedback control is designed to stabilize the unstable stochastic system, including the 2nd-moment and almost-sure exponential stabilization. We also prove that the system wit...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/5623756 |
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| _version_ | 1832553598121148416 |
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| author | Baolin Ma Yiyue Sun Guojie Zheng |
| author_facet | Baolin Ma Yiyue Sun Guojie Zheng |
| author_sort | Baolin Ma |
| collection | DOAJ |
| description | This paper investigates the stabilization of an unstable stochastic heat equation. By the backstepping technique, a boundary feedback control is designed to stabilize the unstable stochastic system, including the 2nd-moment and almost-sure exponential stabilization. We also prove that the system with a disturbance in the control channel possesses good robust stability under our control strategy and suitable conditions. Finally, we also provide numerical simulations which illustrate the effectiveness of the theoretical results. |
| format | Article |
| id | doaj-art-2d2855d719ce4f2ca285a17cf50375b1 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-2d2855d719ce4f2ca285a17cf50375b12025-02-03T05:53:38ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/5623756Stabilization for the Stochastic Heat Equation with Boundary ControlBaolin Ma0Yiyue Sun1Guojie Zheng2School of Mathematical ScienceCollege of Mathematics and Information ScienceCollege of Mathematics and Information ScienceThis paper investigates the stabilization of an unstable stochastic heat equation. By the backstepping technique, a boundary feedback control is designed to stabilize the unstable stochastic system, including the 2nd-moment and almost-sure exponential stabilization. We also prove that the system with a disturbance in the control channel possesses good robust stability under our control strategy and suitable conditions. Finally, we also provide numerical simulations which illustrate the effectiveness of the theoretical results.http://dx.doi.org/10.1155/2022/5623756 |
| spellingShingle | Baolin Ma Yiyue Sun Guojie Zheng Stabilization for the Stochastic Heat Equation with Boundary Control Journal of Mathematics |
| title | Stabilization for the Stochastic Heat Equation with Boundary Control |
| title_full | Stabilization for the Stochastic Heat Equation with Boundary Control |
| title_fullStr | Stabilization for the Stochastic Heat Equation with Boundary Control |
| title_full_unstemmed | Stabilization for the Stochastic Heat Equation with Boundary Control |
| title_short | Stabilization for the Stochastic Heat Equation with Boundary Control |
| title_sort | stabilization for the stochastic heat equation with boundary control |
| url | http://dx.doi.org/10.1155/2022/5623756 |
| work_keys_str_mv | AT baolinma stabilizationforthestochasticheatequationwithboundarycontrol AT yiyuesun stabilizationforthestochasticheatequationwithboundarycontrol AT guojiezheng stabilizationforthestochasticheatequationwithboundarycontrol |