Robust H∞ Control for a Class of Nonlinear Distributed Parameter Systems via Proportional-Spatial Derivative Control Approach
This paper addresses the problem of robust H∞ control design via the proportional-spatial derivative (P-sD) control approach for a class of nonlinear distributed parameter systems modeled by semilinear parabolic partial differential equations (PDEs). By using the Lyapunov direct method and the techn...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/631071 |
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| author | Cheng-Dong Yang Jianlong Qiu Jun-Wei Wang |
| author_facet | Cheng-Dong Yang Jianlong Qiu Jun-Wei Wang |
| author_sort | Cheng-Dong Yang |
| collection | DOAJ |
| description | This paper addresses the problem of robust H∞ control design via the proportional-spatial derivative (P-sD) control approach for a class of nonlinear distributed parameter systems modeled by semilinear parabolic partial differential equations (PDEs). By using the Lyapunov direct method and the technique of integration by parts, a simple linear matrix inequality (LMI) based design method of the robust H∞ P-sD controller is developed such that the closed-loop PDE system is exponentially stable with a given decay rate and a prescribed H∞ performance of disturbance attenuation. Moreover, a suboptimal H∞ controller is proposed to minimize the attenuation level for a given decay rate. The proposed method is successfully employed to address the control problem of the FitzHugh-Nagumo (FHN) equation, and the achieved simulation results show its effectiveness. |
| format | Article |
| id | doaj-art-277c14607dbf4b9f863d87f41f1c7398 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-277c14607dbf4b9f863d87f41f1c73982025-02-03T01:13:11ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/631071631071Robust H∞ Control for a Class of Nonlinear Distributed Parameter Systems via Proportional-Spatial Derivative Control ApproachCheng-Dong Yang0Jianlong Qiu1Jun-Wei Wang2School of Informatics, Linyi University, Linyi 276005, ChinaSchool of Science, Linyi University, Linyi 276005, ChinaSchool of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, ChinaThis paper addresses the problem of robust H∞ control design via the proportional-spatial derivative (P-sD) control approach for a class of nonlinear distributed parameter systems modeled by semilinear parabolic partial differential equations (PDEs). By using the Lyapunov direct method and the technique of integration by parts, a simple linear matrix inequality (LMI) based design method of the robust H∞ P-sD controller is developed such that the closed-loop PDE system is exponentially stable with a given decay rate and a prescribed H∞ performance of disturbance attenuation. Moreover, a suboptimal H∞ controller is proposed to minimize the attenuation level for a given decay rate. The proposed method is successfully employed to address the control problem of the FitzHugh-Nagumo (FHN) equation, and the achieved simulation results show its effectiveness.http://dx.doi.org/10.1155/2014/631071 |
| spellingShingle | Cheng-Dong Yang Jianlong Qiu Jun-Wei Wang Robust H∞ Control for a Class of Nonlinear Distributed Parameter Systems via Proportional-Spatial Derivative Control Approach Abstract and Applied Analysis |
| title | Robust H∞ Control for a Class of Nonlinear Distributed Parameter Systems via Proportional-Spatial Derivative Control Approach |
| title_full | Robust H∞ Control for a Class of Nonlinear Distributed Parameter Systems via Proportional-Spatial Derivative Control Approach |
| title_fullStr | Robust H∞ Control for a Class of Nonlinear Distributed Parameter Systems via Proportional-Spatial Derivative Control Approach |
| title_full_unstemmed | Robust H∞ Control for a Class of Nonlinear Distributed Parameter Systems via Proportional-Spatial Derivative Control Approach |
| title_short | Robust H∞ Control for a Class of Nonlinear Distributed Parameter Systems via Proportional-Spatial Derivative Control Approach |
| title_sort | robust h∞ control for a class of nonlinear distributed parameter systems via proportional spatial derivative control approach |
| url | http://dx.doi.org/10.1155/2014/631071 |
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